Class implementing the generic maths of the axisym poroelasticity equations: axisym linear elasticity coupled with axisym Darcy equations (using Raviart-Thomas elements with both edge and internal degrees of freedom) including inertia in both. More...

#include <axisym_poroelasticity_elements.h>

Inheritance diagram for oomph::AxisymmetricPoroelasticityEquations:

Public Types
typedef void(*	SourceFctPt) (const double &time, const Vector< double > &x, Vector< double > &f)
	Source function pointer typedef. More...

typedef void(*	MassSourceFctPt) (const double &time, const Vector< double > &x, double &f)
	Mass source function pointer typedef. More...

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
	Function pointer for function that computes vector-valued steady "exact solution" ${\bf f}({\bf x})$ as $\mbox{\tt fct}({\bf x}, {\bf f})$ . More...

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
	Function pointer for function that computes Vector-valued time-dependent function ${\bf f}(t,{\bf x})$ as $\mbox{\tt fct}(t, {\bf x}, {\bf f})$ . More...

Public Member Functions
	AxisymmetricPoroelasticityEquations ()
	Constructor. More...

const double &	youngs_modulus () const
	Access function to non-dim Young's modulus (ratio of actual Young's modulus to reference stress used to non-dim the equations. (const version) More...

double *&	youngs_modulus_pt ()
	Pointer to non-dim Young's modulus (ratio of actual Young's modulus to reference stress used to non-dim the equations. More...

const double &	nu () const
	Access function for Poisson's ratio. More...

double *&	nu_pt ()
	Access function for pointer to Poisson's ratio. More...

const double &	lambda_sq () const
	Access function for timescale ratio (nondim density) More...

double *&	lambda_sq_pt ()
	Access function for pointer to timescale ratio (nondim density) More...

const double &	density_ratio () const
	Access function for the density ratio (fluid to solid) More...

double *&	density_ratio_pt ()
	Access function for pointer to the density ratio (fluid to solid) More...

const double &	permeability () const
	Access function for the nondim permeability. More...

double *&	permeability_pt ()
	Access function for pointer to the nondim permeability. More...

const double &	permeability_ratio () const
	Access function for the ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations. More...

double *&	permeability_ratio_pt ()
	Access function for pointer to ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations. More...

const double &	alpha () const
	Access function for alpha, the Biot parameter. More...

double *&	alpha_pt ()
	Access function for pointer to alpha, the Biot parameter. More...

const double &	porosity () const
	Access function for the porosity. More...

double *&	porosity_pt ()
	Access function for pointer to the porosity. More...

SourceFctPt &	solid_body_force_fct_pt ()
	Access function: Pointer to solid body force function. More...

SourceFctPt	solid_body_force_fct_pt () const
	Access function: Pointer to solid body force function (const version) More...

SourceFctPt &	fluid_body_force_fct_pt ()
	Access function: Pointer to fluid force function. More...

SourceFctPt	fluid_body_force_fct_pt () const
	Access function: Pointer to fluid force function (const version) More...

MassSourceFctPt &	mass_source_fct_pt ()
	Access function: Pointer to mass source function. More...

MassSourceFctPt	mass_source_fct_pt () const
	Access function: Pointer to mass source function (const version) More...

void	solid_body_force (const double &time, const Vector< double > &x, Vector< double > &b) const
	Indirect access to the solid body force function - returns 0 if no forcing function has been set. More...

void	fluid_body_force (const double &time, const Vector< double > &x, Vector< double > &b) const
	Indirect access to the fluid body force function - returns 0 if no forcing function has been set. More...

void	mass_source (const double &time, const Vector< double > &x, double &b) const
	Indirect access to the mass source function - returns 0 if no mass source function has been set. More...

virtual unsigned	required_nvalue (const unsigned &n) const =0
	Number of values required at node n. More...

virtual unsigned	u_index_axisym_poroelasticity (const unsigned &j) const =0
	Return the nodal index of the j-th solid displacement unknown. More...

virtual int	q_edge_local_eqn (const unsigned &j) const =0
	Return the equation number of the j-th edge (flux) degree of freedom. More...

virtual int	q_internal_local_eqn (const unsigned &j) const =0
	Return the equation number of the j-th internal degree of freedom. More...

virtual Vector< Data * >	q_edge_data_pt () const =0
	Return vector of pointers to the Data objects that store the edge flux values. More...

virtual Data *	q_internal_data_pt () const =0
	Return pointer to the Data object that stores the internal flux values. More...

virtual unsigned	q_edge_index (const unsigned &j) const =0
	Return the nodal index at which the jth edge unknown is stored. More...

virtual unsigned	q_internal_index () const =0
	Return the index of the internal data where the q internal degrees of freedom are stored. More...

virtual unsigned	q_edge_node_number (const unsigned &j) const =0
	Return the number of the node where the jth edge unknown is stored. More...

virtual double	q_edge (const unsigned &j) const =0
	Return the values of the j-th edge (flux) degree of freedom. More...

virtual double	q_edge (const unsigned &t, const unsigned &j) const =0
	Return the values of the j-th edge (flux) degree of freedom at time history level t. More...

virtual unsigned	face_index_of_q_edge_basis_fct (const unsigned &j) const =0
	Return the face index associated with j-th edge flux degree of freedom. More...

virtual unsigned	face_index_of_edge (const unsigned &j) const =0
	Return the face index associated with specified edge. More...

virtual void	face_local_coordinate_of_flux_interpolation_point (const unsigned &edge, const unsigned &n, Vector< double > &s) const =0
	Compute the face element coordinates of the nth flux interpolation point along an edge. More...

virtual double	q_internal (const unsigned &j) const =0
	Return the values of the j-th internal degree of freedom. More...

virtual double	q_internal (const unsigned &t, const unsigned &j) const =0
	Return the values of the j-th internal degree of freedom at time history level t. More...

virtual void	set_q_edge (const unsigned &j, const double &value)=0
	Set the values of the j-th edge (flux) degree of freedom. More...

virtual void	set_q_internal (const unsigned &j, const double &value)=0
	Set the values of the j-th internal degree of freedom. More...

virtual void	set_q_edge (const unsigned &t, const unsigned &j, const double &value)=0
	Set the values of the j-th edge (flux) degree of freedom at time history level t. More...

virtual void	set_q_internal (const unsigned &t, const unsigned &j, const double &value)=0
	Set the values of the j-th internal degree of freedom at time history level t. More...

virtual unsigned	nq_basis () const
	Return the total number of computational basis functions for q. More...

virtual unsigned	nq_basis_edge () const =0
	Return the number of edge basis functions for q. More...

virtual unsigned	nq_basis_internal () const =0
	Return the number of internal basis functions for q. More...

virtual void	get_q_basis_local (const Vector< double > &s, Shape &q_basis) const =0
	Comute the local form of the q basis at local coordinate s. More...

virtual void	get_div_q_basis_local (const Vector< double > &s, Shape &div_q_basis_ds) const =0
	Compute the local form of the q basis and dbasis/ds at local coordinate s. More...

void	get_q_basis (const Vector< double > &s, Shape &q_basis) const
	Compute the transformed basis at local coordinate s. More...

virtual unsigned	nedge_flux_interpolation_point () const =0
	Returns the number of flux_interpolation points along each edge of the element. More...

virtual Vector< double >	edge_flux_interpolation_point (const unsigned &edge, const unsigned &j) const =0
	Returns the local coordinate of the jth flux_interpolation point along the specified edge. More...

virtual void	edge_flux_interpolation_point_global (const unsigned &edge, const unsigned &j, Vector< double > &x) const =0
	Compute the global coordinates of the jth flux_interpolation point along an edge. More...

virtual void	pin_q_internal_value (const unsigned &j, const double &value)=0
	Pin the jth internal q value and set it to specified value. More...

virtual void	pin_q_edge_value (const unsigned &j, const double &value)=0
	Pin the j-th edge (flux) degree of freedom and set it to specified value. More...

virtual int	p_local_eqn (const unsigned &j) const =0
	Return the equation number of the j-th pressure degree of freedom. More...

virtual double	p_value (const unsigned &j) const =0
	Return the jth pressure value. More...

virtual unsigned	np_basis () const =0
	Return the total number of pressure basis functions. More...

virtual void	get_p_basis (const Vector< double > &s, Shape &p_basis) const =0
	Compute the pressure basis. More...

virtual void	pin_p_value (const unsigned &j, const double &p)=0
	Pin the jth pressure value and set it to p. More...

virtual void	set_p_value (const unsigned &j, const double &value)=0
	Set the jth pressure value. More...

virtual Data *	p_data_pt () const =0
	Return pointer to the Data object that stores the pressure values. More...

virtual void	scale_basis (Shape &basis) const =0
	Scale the edge basis to allow arbitrary edge mappings. More...

double	transform_basis (const Vector< double > &s, const Shape &q_basis_local, Shape &psi, DShape &dpsi, Shape &q_basis) const
	Performs a div-conserving transformation of the vector basis functions from the reference element to the actual element. More...

double	transform_basis (const Vector< double > &s, const Shape &q_basis_local, Shape &psi, Shape &q_basis) const
	Performs a div-conserving transformation of the vector basis functions from the reference element to the actual element. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in contribution to residuals for the Darcy equations. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Fill in the Jacobian matrix for the Newton method. More...

double	interpolated_div_du_dt (const Vector< double > &s, Vector< double > &div_dudt_components) const
	Calculate the FE representation of the divergence of the skeleton velocity, div(du/dt), and its components: 1/r diff(r*du_r/dt,r) and diff(du_z/dt,z). More...

double	interpolated_div_u (const Vector< double > &s, Vector< double > &div_u_components) const
	Calculate the FE representation of the divergence of the skeleton displ, div(u), and its components: 1/r diff(r*u_r,r) and diff(u_z,z). More...

void	interpolated_u (const Vector< double > &s, Vector< double > &disp) const
	Calculate the FE representation of u. More...

double	interpolated_u (const Vector< double > &s, const unsigned &i) const
	Calculate the FE representation of the i-th component of u. More...

double	interpolated_u (const unsigned &t, const Vector< double > &s, const unsigned &i) const
	Calculate the FE representation of the i-th component of u at time level t (t=0: current) More...

void	interpolated_du_dt (const Vector< double > &s, Vector< double > &du_dt) const
	Calculate the FE representation of du_dt. More...

void	interpolated_q (const Vector< double > &s, Vector< double > &q) const
	Calculate the FE representation of q. More...

void	interpolated_q (const unsigned &t, const Vector< double > &s, Vector< double > &q) const
	Calculate the FE representation of q at time level t (t=0: current) More...

double	interpolated_q (const Vector< double > &s, const unsigned i) const
	Calculate the FE representation of the i-th component of q. More...

double	interpolated_q (const unsigned &t, const Vector< double > &s, const unsigned i) const
	Calculate the FE representation of the i-th component of q at time level t (t=0: current) More...

void	interpolated_div_q (const Vector< double > &s, double &div_q) const
	Calculate the FE representation of div u. More...

double	interpolated_div_q (const Vector< double > &s) const
	Calculate the FE representation of div q and return it. More...

void	interpolated_p (const Vector< double > &s, double &p) const
	Calculate the FE representation of p. More...

double	interpolated_p (const Vector< double > &s) const
	Calculate the FE representation of p and return it. More...

double	du_dt (const unsigned &n, const unsigned &i) const
	du/dt at local node n More...

double	d2u_dt2 (const unsigned &n, const unsigned &i) const
	d^2u/dt^2 at local node n More...

double	dq_edge_dt (const unsigned &n) const
	dq_edge/dt for the n-th edge degree of freedom More...

double	dq_internal_dt (const unsigned &n) const
	dq_internal/dt for the n-th internal degree of freedom More...

void	set_q_internal_timestepper (TimeStepper *const time_stepper_pt)
	Set the timestepper of the q internal data object. More...

bool	darcy_is_switched_off ()
	Is Darcy flow switched off? More...

void	switch_off_darcy ()
	Switch off Darcy flow. More...

unsigned	self_test ()
	Self test. More...

unsigned	nscalar_paraview () const
	Number of scalars/fields output by this element. Reimplements broken virtual function in base class. More...

void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
	Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type. More...

std::string	scalar_name_paraview (const unsigned &i) const
	Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements. More...

void	point_output_data (const Vector< double > &s, Vector< double > &data)
	Output solution in data vector at local cordinates s: r,z,u_r,u_z,q_r,q_z,div_q,p,durdt,duzdt. More...

void	output (std::ostream &outfile)
	Output with default number of plot points. More...

void	output (std::ostream &outfile, const unsigned &nplot)
	Output FE representation of soln: x,y,u1,u2,div_q,p at Nplot^2 plot points. More...

void	output_with_projected_flux (std::ostream &outfile, const unsigned &nplot, const Vector< double > unit_normal)
	Output incl. projection of fluxes into direction of the specified unit vector. More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output FE representation of exact soln: x,y,u1,u2,div_q,p at Nplot^2 plot points. More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output FE representation of exact soln: x,y,u1,u2,div_q,p at Nplot^2 plot points. Unsteady version. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for p. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for p. Unsteady version. More...

unsigned	num_Z2_flux_terms ()
	Number off flux terms for Z2 error estimator (use Darcy flux) More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Z2 flux (use Darcy flux) More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)
	Set the dimension of the element and initially set the dimension of the nodes to be the same as the dimension of the element. More...

void	set_nodal_dimension (const unsigned &nodal_dim)
	Set the dimension of the nodes in the element. This will typically only be required when constructing FaceElements or in beam and shell type elements where a lower dimensional surface is embedded in a higher dimensional space. More...

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)
	Set the number of nodes in the element to n, by resizing the storage for pointers to the Node objects. More...

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const
	Return the local equation number corresponding to the i-th value at the n-th local node. More...

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const
	Compute the geometric shape functions (psi) at integration point ipt. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of "detJ" w.r.t. the nodal coordinates. More...

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()
	The destructor cleans up the static memory allocated for shape function storage. Internal and external data get wiped by the GeneralisedElement destructor; nodes get killed in mesh destructor. More...

	FiniteElement (const FiniteElement &)=delete
	Broken copy constructor. More...

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

virtual void	move_local_coord_back_into_element (Vector< double > &s) const
	Adjust local coordinates so that they're located inside the element. More...

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const
	Compute centre of gravity of all nodes and radius of node that is furthest from it. Used to assess approximately if a point is likely to be contained with an element in locate_zeta-like operations. More...

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size (broken virtual) More...

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of the node j in the element A dumb, but correct default implementation is provided. More...

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)
	Get the local fraction of any node in the n-th position in a one dimensional expansion along the i-th local coordinate. More...

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)
	Set pointer to macro element – can be overloaded in derived elements to perform additional tasks. More...

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

void	get_x (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0) More...

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). Either via FE representation of QElement or via macro-element (if Macro_elem_pt!=0). More...

virtual void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates using macro element representation. (Broken virtual — this must be overloaded in specific geometric element classes) More...

virtual void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). using macro element representation (Broken virtual – overload in specific geometric element class if you want to use this functionality.) More...

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

virtual void	shape (const Vector< double > &s, Shape &psi) const =0
	Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element. More...

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const
	Return the geometric shape function at the ipt-th integration point. More...

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Function to compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element. (Broken virtual function — specifies the interface) More...

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
	Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point. More...

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Function to compute the geometric shape functions and also first and second derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element (if required). (Broken virtual function — specifies the interface). Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Return the geometric shape function and its first and second derivatives w.r.t. the local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual double	J_eulerian (const Vector< double > &s) const
	Return the Jacobian of mapping from local to global coordinates at local position s. More...

virtual double	J_eulerian_at_knot (const unsigned &ipt) const
	Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point. More...

void	check_J_eulerian_at_knots (bool &passed) const
	Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive. More...

void	check_jacobian (const double &jacobian) const
	Helper function used to check for singular or negative Jacobians in the transform from local to global or Lagrangian coordinates. More...

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
	Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
	Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
	Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at the ipt-th integration point. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of both "detJ" and "dpsidx" w.r.t. the nodal coordinates. More...

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d x^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Return the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d s^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for Data stored at the nodes Virtual so that it can be overloaded by RefineableFiniteElements. If the boolean is true then the pointers to the degrees of freedom associated with each equation number are stored in Dof_pt. More...

virtual void	describe_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
	Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt. More...

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const
	Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements. More...

double	raw_nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. Do not use the hanging node representation. NOTE: Moved to cc file because of a possible compiler bug in gcc (yes, really!). The move to the cc file avoids inlining which appears to cause problems (only) when compiled with gcc and -O3; offensive "illegal read" is in optimised-out section of code and data that is allegedly illegal is readily readable (by other means) just before this function is called so I can't really see how we could possibly be responsible for this... More...

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level). Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is handled by the position function in the Node class. More...

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level) Returns suitably interpolated version for hanging nodes. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. More...

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. More...

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. More...

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
	Compute derivatives of elemental residual vector with respect to nodal coordinates. Default implementation by FD can be overwritten for specific elements. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}. More...

virtual void	disable_ALE ()
	This is an empty function that establishes a uniform interface for all (derived) elements that involve time-derivatives. Such elements are/should be implemented in ALE form to allow mesh motions. The additional expense associated with the computation of the mesh velocities is, of course, superfluous if the elements are used in problems in which the mesh is stationary. This function should therefore be overloaded in all derived elements that are formulated in ALE form to suppress the computation of the mesh velocities. The user disables the ALE functionality at his/her own risk! If the mesh does move after all, then the results will be wrong. Here we simply issue a warning message stating that the empty function has been called. More...

virtual void	enable_ALE ()
	(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. This function is empty and simply establishes a common interface for all derived elements that are formulated in ALE form. More...

unsigned	nnodal_position_type () const
	Return the number of coordinate types that the element requires to interpolate the geometry between the nodes. For Lagrange elements it is 1. More...

bool	has_hanging_nodes () const
	Return boolean to indicate if any of the element's nodes are geometrically hanging. More...

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

virtual Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to the newly created node object. More...

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n)
	Construct the local node n as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

int	get_node_number (Node *const &node_pt) const
	Return the number of the node *node_pt if this node is in the element, else return -1;. More...

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	If there is a node at this local coordinate, return the pointer to the node. More...

double	raw_nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n but do NOT take hanging nodes into account. More...

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps), but do NOT take hanging nodes into account. More...

double	nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes. More...

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps). Produces suitably interpolated values for hanging nodes. More...

unsigned	dim () const
	Return the spatial dimension of the element, i.e. the number of local coordinates required to parametrise its geometry. More...

virtual ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

virtual double	interpolated_x (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s. More...

virtual double	interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s at previous timestep t (t=0: present; t>0: previous timestep) More...

virtual void	interpolated_x (const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s as Vector. More...

virtual void	interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s at previous timestep t as Vector (t=0: present; t>0: previous timestep) More...

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)
	Return t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s. More...

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)
	Compte t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s. More...

unsigned	ngeom_data () const
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

Data *	geom_data_pt (const unsigned &j)
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

void	position (const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its incarnation as a GeomObject, r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s). More...

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its GeomObject incarnation: r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s) This version of the function returns the position as a function of time t=0: current time; t>0: previous timestep. Works for t=0 but needs to be overloaded if genuine time-dependence is required. More...

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
	Return the t-th time derivative of the parametrised position of the FiniteElement in its GeomObject incarnation: $\frac{d^{t} dr(zeta)}{d t^{t}}$ . Call the t-th time derivative of the FE-interpolated Eulerian coordinate. More...

virtual double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements. More...

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
	Calculate the interpolated value of zeta, the intrinsic coordinate of the element when viewed as a compound geometric object within a Mesh as a function of the local coordinate of the element, s. The default assumption is the zeta is interpolated using the shape functions of the element with the values given by zeta_nodal(). A MacroElement representation of the intrinsic coordinate parametrised by the local coordinate s is used if available. Choosing the MacroElement representation of zeta (Eulerian x by default) allows a correspondence to be established between elements on different Meshes covering the same curvilinear domain in cases where one element is much coarser than the other. More...

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
	For a given value of zeta, the "global" intrinsic coordinate of a mesh of FiniteElements represented as a compound geometric object, find the local coordinate in this element that corresponds to the requested value of zeta. If zeta cannot be located in this element, geom_object_pt is set to NULL. If zeta is located in this element, we return its "this" pointer. By default don't use any value passed in to the local coordinate s as the initial guess in the Newton method. More...

virtual void	node_update ()
	Update the positions of all nodes in the element using each node update function. The default implementation may be overloaded so that more efficient versions can be written. More...

virtual void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)
	The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. The information will typically be used in interaction problems in which the FiniteElement provides a forcing term for an ElementWithExternalElement. The Data must be provided as `paired_load` data containing. More...

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)
	The purpose of this function is to identify all `Data` objects that affect the elements' geometry. This function is implemented as an empty virtual function since it can only be implemented in conjunction with a node-update strategy. A specific implementation is provided in the ElementWithMovingNodes class. More...

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const
	Calculate the size of the element (length, area, volume,...) in Eulerian computational coordinates. Use suitably overloaded compute_physical_size() function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual double	compute_physical_size () const
	Broken virtual function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

void	point_output (std::ostream &outfile, const Vector< double > &s)
	Output solution (as defined by point_output_data()) at local cordinates s. More...

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const
	Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const
	Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const
	Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file. More...

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
	Fill in the offset information for paraview plot. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
	Return the paraview element type. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
	Return the offsets for the paraview sub-elements. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
	Output the element data at time step t. This is const because it is newly added and so can be done easily. Really all the output(...) functions should be const! More...

virtual void	output (FILE *file_pt)
	Output the element data — typically the values at the nodes in a format suitable for post-processing. (C style output) More...

virtual void	output (FILE *file_pt, const unsigned &n_plot)
	Output the element data — pass (some measure of) the number of plot points per element (C style output) More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

virtual void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
	Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction"). Generally these plot points will be uniformly spaced across the element. The optional final boolean flag (default: false) allows them to be shifted inwards to avoid duplication of plot point points between elements – useful when they are used in locate_zeta, say. More...

virtual std::string	tecplot_zone_string (const unsigned &nplot) const
	Return string for tecplot zone header (when plotting nplot points in each "coordinate direction") More...

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
	Add tecplot zone "footer" to output stream (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
	Add tecplot zone "footer" to C-style output. (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual unsigned	nplot_points (const unsigned &nplot) const
	Return total number of plot points (when plotting nplot points in each "coordinate direction") More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. More...

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the maximum absolute error. More...

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Evaluate integral of a Vector-valued function ${\bf f}({\bf x})$ over the element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Evaluate integral of a Vector-valued, time-dependent function ${\bf f}(t,{\bf x})$ over the element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)
	Function for building a lower dimensional FaceElement on the specified face of the FiniteElement. The arguments are the index of the face, an integer whose value depends on the particular element type, and a pointer to the FaceElement. More...

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const
	Get the number of the ith node on face face_index (in the bulk node vector). More...

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

virtual unsigned	nnode_on_face () const

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const
	Get a pointer to the function mapping face coordinates to bulk coordinates. More...

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const
	Get a pointer to the derivative of the mapping from face to bulk coordinates. More...

Public Member Functions inherited from oomph::GeneralisedElement
GeneralisedElement()	GeneralisedElement (const GeneralisedElement &)=delete
	Constructor: Initialise all pointers and all values to zero. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const
	Return the global equation number corresponding to the ieqn_local-th local equation number. More...

int	local_eqn_number (const unsigned long &ieqn_global) const
	Return the local equation number corresponding to the ieqn_global-th global equation number. Returns minus one (-1) if there is no local degree of freedom corresponding to the chosen global equation number. More...

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) external data object to the element and return its index (i.e. the index required to obtain it from the access function `external_data_pt(...)`. The optional boolean flag indicates whether the data should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite-differencing. More...

bool	external_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the external data is included in the finite difference loop. More...

void	exclude_external_data_fd (const unsigned &i)
	Set the boolean flag to exclude the external datum from the the finite difference loop when computing the jacobian matrix. More...

void	include_external_data_fd (const unsigned &i)
	Set the boolean flag to include the external datum in the the finite difference loop when computing the jacobian matrix. More...

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)
	Set the timestepper associated with the i-th internal data object. More...

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)
	Assign the global equation numbers to the internal Data. The arguments are the current highest global equation number (which will be incremented) and a Vector of pointers to the global variables (to which any unpinned values in the internal Data are added). More...

void	describe_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
	Add pointers to the internal data values to map indexed by the global equation number. More...

void	add_internal_data_values_to_vector (Vector< double > &vector_of_values)
	Add all internal data and time history values to the vector in the internal storage order. More...

void	read_internal_data_values_from_vector (const Vector< double > &vector_of_values, unsigned &index)
	Read all internal data and time history values from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

void	add_internal_eqn_numbers_to_vector (Vector< long > &vector_of_eqn_numbers)
	Add all equation numbers associated with internal data to the vector in the internal storage order. More...

void	read_internal_eqn_numbers_from_vector (const Vector< long > &vector_of_eqn_numbers, unsigned &index)
	Read all equation numbers associated with internal data from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)
	Setup the arrays of local equation numbers for the element. If the optional boolean argument is true, then pointers to the associated degrees of freedom are stored locally in the array Dof_pt. More...

virtual void	complete_setup_of_dependencies ()
	Complete the setup of any additional dependencies that the element may have. Empty virtual function that may be overloaded for specific derived elements. Used, e.g., for elements with algebraic node update functions to determine the "geometric Data", i.e. the Data that affects the element's shape. This function is called (for all elements) at the very beginning of the equation numbering procedure to ensure that all dependencies are accounted for. More...

virtual void	get_residuals (Vector< double > &residuals)
	Calculate the vector of residuals of the equations in the element. By default initialise the vector to zero and then call the fill_in_contribution_to_residuals() function. Note that this entire function can be overloaded if desired. More...

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the elemental Jacobian matrix "d equation / d variable". More...

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and the elemental "mass" matrix, the matrix that multiplies the time derivative terms in a problem. More...

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and jacobian and elemental "mass" matrix, the matrix that multiplies the time derivative terms. More...

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Calculate the derivatives of the residuals with respect to a parameter. More...

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Calculate the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. More...

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Calculate the derivatives of the elemental Jacobian matrix mass matrix and residuals with respect to a parameter. More...

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Calculate the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Return the vector of inner product of the given pairs of history values. More...

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...

virtual void	compute_norm (Vector< double > &norm)
	Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More...

virtual void	compute_norm (double &norm)
	Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More...

void	set_halo (const unsigned &non_halo_proc_ID)
	Label the element as halo and specify processor that holds non-halo counterpart. More...

void	set_nonhalo ()
	Label the element as not being a halo. More...

bool	is_halo () const
	Is this element a halo? More...

int	non_halo_proc_ID ()
	ID of processor ID that holds non-halo counterpart of halo element; negative if not a halo. More...

void	set_must_be_kept_as_halo ()
	Insist that this element be kept as a halo element during a distribute? More...

void	unset_must_be_kept_as_halo ()
	Do not insist that this element be kept as a halo element during distribution. More...

bool	must_be_kept_as_halo () const
	Test whether the element must be kept as a halo element. More...

virtual unsigned	ndof_types () const
	The number of types of degrees of freedom in this element are sub-divided into. More...

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const
	Create a list of pairs for the unknowns that this element is "in charge of" – ignore any unknowns associated with external `Data`. The first entry in each pair must contain the global equation number of the unknown, while the second one contains the number of the DOF type that this unknown is associated with. (The function can obviously only be called if the equation numbering scheme has been set up.) More...

Public Member Functions inherited from oomph::GeomObject
	GeomObject ()
	Default constructor. More...

	GeomObject (const unsigned &ndim)
	Constructor: Pass dimension of geometric object (# of Eulerian coords = # of Lagrangian coords; no time history available/needed) More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)
	Constructor: pass # of Eulerian and Lagrangian coordinates. No time history available/needed. More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)
	Constructor: pass # of Eulerian and Lagrangian coordinates and pointer to time-stepper which is used to handle the position at previous timesteps and allows the evaluation of veloc/acceleration etc. in cases where the GeomData varies with time. More...

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

void	operator= (const GeomObject &)=delete
	Broken assignment operator. More...

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()
	Access function for pointer to time stepper: Null if object is not time-dependent. More...

TimeStepper *	time_stepper_pt () const
	Access function for pointer to time stepper: Null if object is not time-dependent. Const version. More...

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
	Parametrised position on object: r(zeta). Evaluated at the continuous time value, t. More...

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
	Derivative of position Vector w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
	2nd derivative of position Vector w.r.t. to coordinates: $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
	Posn Vector and its 1st & 2nd derivatives w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()
	A stuitable error estimator for a multi-physics elements may require one Z2 error estimate for each field (e.g. velocity and temperature in a fluid convection problem). It is assumed that these error estimates will each use selected flux terms. The number of compound fluxes returns the number of such combinations of the flux terms. Default value is one and all flux terms are combined with equal weight. More...

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)
	Plot the error when compared against a given exact flux. Also calculates the norm of the error and that of the exact flux. More...

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)
	Return the compound flux index of each flux component The default (do nothing behaviour) will mean that all indices remain at the default value zero. More...

virtual unsigned	nvertex_node () const =0
	Number of vertex nodes in the element. More...

virtual Node *	vertex_node_pt (const unsigned &j) const =0
	Pointer to the j-th vertex node in the element. Needed for efficient patch assmbly. More...

virtual unsigned	nrecovery_order ()=0
	Order of recovery shape functions. More...

virtual double	geometric_jacobian (const Vector< double > &x)
	Return the geometric jacobian (should be overloaded in cylindrical and spherical geometries). Default value one is suitable for Cartesian coordinates. More...

Protected Member Functions
virtual double	shape_basis_test_local (const Vector< double > &s, Shape &psi, DShape &dpsi, Shape &u_basis, Shape &u_test, DShape &du_basis_dx, DShape &du_test_dx, Shape &q_basis, Shape &q_test, Shape &p_basis, Shape &p_test, Shape &div_q_basis_ds, Shape &div_q_test_ds) const =0
	Compute the geometric basis, and the q, p and divergence basis functions and test functions at local coordinate s. More...

virtual double	shape_basis_test_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, Shape &u_basis, Shape &u_test, DShape &du_basis_dx, DShape &du_test_dx, Shape &q_basis, Shape &q_test, Shape &p_basis, Shape &p_test, Shape &div_q_basis_ds, Shape &div_q_test_ds) const =0
	Compute the geometric basis, and the q, p and divergence basis functions and test functions at integration point ipt. More...

virtual void	fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, bool flag)
	Fill in residuals and, if flag==true, jacobian. More...

Protected Member Functions inherited from oomph::FiniteElement
virtual void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
	Assemble the jacobian matrix for the mapping from local to Eulerian coordinates, given the derivatives of the shape function w.r.t the local coordinates. More...

virtual void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
	Assemble the the "jacobian" matrix of second derivatives of the mapping from local to Eulerian coordinates, given the second derivatives of the shape functions w.r.t. local coordinates. More...

virtual void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const
	Assemble the covariant Eulerian base vectors, assuming that the derivatives of the shape functions with respect to the local coordinates have already been constructed. More...

template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Take the matrix passed as jacobian and return its inverse in inverse_jacobian. This function is templated by the dimension of the element because matrix inversion cannot be written efficiently in a generic manner. More...

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	A template-free interface that takes the matrix passed as jacobian and return its inverse in inverse_jacobian. By default the function will use the dimension of the element to call the correct invert_jacobian(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates. Returns the determinant of the jacobian, the jacobian and inverse jacobian. More...

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates, Return only the determinant of the jacobian and the inverse of the mapping (ds/dx). More...

virtual double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates given the derivatives of the shape functions w.r.t the local coordinates. assuming that the coordinates are aligned in the direction of the local coordinates, i.e. there are no cross terms and the jacobian is diagonal. This function returns the determinant of the jacobian, the jacobian and the inverse jacobian. More...

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	A template-free interface that calculates the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. To do this it requires the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. By default the function will use the dimension of the element to call the correct dJ_eulerian_dnodal_coordinates_templated_helper(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij using the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. This function is templated by the dimension of the element. More...

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	A template-free interface that calculates the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions $\psi_j$ w.r.t. the global eulerian coordinates . I.e. this function calculates. More...

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates , using the determinant of the jacobian mapping, its derivative w.r.t. the nodal coordinates $X_{pq}$ , the inverse jacobian and the derivatives of the shape functions w.r.t. the local coordinates. The result is returned as a tensor of rank four. Numbering: d_dpsidx_dX(p,q,j,i) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ This function is templated by the dimension of the element. More...

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t.local coordinates to derivatives w.r.t the coordinates used to assemble the inverse_jacobian passed in the mapping. On entry, dbasis must contain the basis function derivatives w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates on exit. This is virtual so that it may be overloaded if desired for efficiency reasons. More...

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian passed in the mapping, assuming that the coordinates are aligned in the direction of the local coordinates. On entry dbasis must contain the derivatives of the basis functions w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates. are converted into the new using the mapping inverse_jacobian. More...

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordiantes to derivatives and second derivatives w.r.t. the coordinates used to assemble the jacobian, inverse jacobian and jacobian2 passed to the function. By default this function will call transform_second_derivatives_template<>(...) using the dimension of the element as the template parameter. It is virtual so that it can be overloaded by a specific element to save using a switch statement. Optionally, the element writer may wish to use the transform_second_derivatives_diagonal<>(...) function On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This is templated by dimension because the method of calculation varies significantly with the dimension. On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This version of the function assumes that the local coordinates are aligned with the global coordinates, i.e. the jacobians are diagonal On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. More...

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

virtual void	update_before_nodal_fd ()
	Function that is called before the finite differencing of any nodal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_nodal_fd ()
	Function that is call after the finite differencing of the nodal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after a change in the i-th nodal value. More...

virtual void	reset_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after the i-th nodal values is reset. The default behaviour is to call the update function. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Add the elemental contribution to the jacobian matrix. and the residuals vector. Note that this function will NOT initialise the residuals vector or the jacobian matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is to use finite differences to calculate the jacobian. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Three-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Zero-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	One-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Two-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Three-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Zero-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	One-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Two-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
	Three-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly. Specialisation to two spatial dimensions. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert second derivatives w.r.t. local coordinates to second derivatives w.r.t. the coordinates passed in the tensor coordinate. Specialised to two spatial dimension. More...

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) internal data object to the element and return the index required to obtain it from the access function `internal_data_pt()`. The boolean indicates whether the datum should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite differencing. More...

bool	internal_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the internal data is included in the finite difference loop. More...

void	exclude_internal_data_fd (const unsigned &i)
	Set the boolean flag to exclude the internal datum from the finite difference loop when computing the jacobian matrix. More...

void	include_internal_data_fd (const unsigned &i)
	Set the boolean flag to include the internal datum in the finite difference loop when computing the jacobian matrix. More...

void	clear_global_eqn_numbers ()
	Clear the storage for the global equation numbers and pointers to dofs (if stored) More...

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
	Add the contents of the queue global_eqn_numbers to the local storage for the local-to-global translation scheme. It is essential that the entries in the queue are added IN ORDER i.e. from the front. More...

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for the internal and external Data This must be called after the global equation numbers have all been assigned. It is virtual so that it can be overloaded by ElementWithExternalElements so that any external data from the external elements in included in the numbering scheme. If the boolean argument is true then pointers to the dofs will be stored in Dof_pt. More...

virtual void	assign_additional_local_eqn_numbers ()
	Setup any additional look-up schemes for local equation numbers. Examples of use include using local storage to refer to explicit degrees of freedom. The additional memory cost of such storage may or may not be offset by fast local access. More...

int	internal_local_eqn (const unsigned &i, const unsigned &j) const
	Return the local equation number corresponding to the j-th value stored at the i-th internal data. More...

int	external_local_eqn (const unsigned &i, const unsigned &j)
	Return the local equation number corresponding to the j-th value stored at the i-th external data. More...

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all external data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

virtual void	update_before_internal_fd ()
	Function that is called before the finite differencing of any internal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_internal_fd ()
	Function that is call after the finite differencing of the internal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after a change in any values in the i-th internal data object. More...

virtual void	reset_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	update_before_external_fd ()
	Function that is called before the finite differencing of any external data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_fd ()
	Function that is call after the finite differencing of the external data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after a change in any values in the i-th external data object. More...

virtual void	reset_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the mass matrix matrix. and the residuals vector. Note that this function should NOT initialise the residuals vector or the mass matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is deliberately broken. More...

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the jacobian matrix, mass matrix and the residuals vector. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More...

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Add the elemental contribution to the derivatives of the residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Add the elemental contribution to the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More...

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
	Add the elemental contribution to the derivative of the jacobian matrix, mass matrix and the residuals vector with respect to the passed parameter. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More...

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Fill in contribution to the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Fill in the contribution to the inner products between given pairs of history values. More...

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Fill in the contributions to the vectors that when taken as dot product with other history values give the inner product over the element. More...

Private Attributes
SourceFctPt	Solid_body_force_fct_pt
	Pointer to solid body force function. More...

SourceFctPt	Fluid_body_force_fct_pt
	Pointer to fluid source function. More...

MassSourceFctPt	Mass_source_fct_pt
	Pointer to the mass source function. More...

double *	Youngs_modulus_pt
	Pointer to the nondim Young's modulus. More...

double *	Nu_pt
	Pointer to Poisson's ratio. More...

double *	Lambda_sq_pt
	Timescale ratio (non-dim. density) More...

double *	Density_ratio_pt
	Density ratio. More...

double *	Permeability_pt
	permeability More...

double *	Permeability_ratio_pt
	Ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations. More...

double *	Alpha_pt
	Alpha – the biot parameter. More...

double *	Porosity_pt
	Porosity. More...

bool	Darcy_is_switched_off
	Boolean to record that darcy has been switched off. More...

Static Private Attributes
static double	Default_youngs_modulus_value
	Static default value for Young's modulus (1.0 – for natural scaling, i.e. all stresses have been non-dimensionalised by the same reference Young's modulus. Setting the "non-dimensional" Young's modulus (obtained by de-referencing Youngs_modulus_pt) to a number larger than one means that the material is stiffer than assumed in the non-dimensionalisation. More...

static double	Default_lambda_sq_value = 1.0
	Static default value for timescale ratio. More...

static double	Default_density_ratio_value = 1.0
	Static default value for the density ratio. More...

static double	Default_permeability_value = 1.0
	Static default value for the permeability (1.0 for natural scaling; i.e. timescale is given by L^2/(k^* E) More...

static double	Default_permeability_ratio_value
	Static default value for the ratio of the material's actual permeability to the permeability used to non-dimensionalise the equations. More...

static double	Default_alpha_value = 1.0
	Static default value for alpha, the biot parameter. More...

static double	Default_porosity_value = 1.0
	Static default value for the porosity. More...

Additional Inherited Members
Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false
	Boolean that if set to true allows a negative jacobian in the transform between global and local coordinates (negative surface area = left-handed coordinate system). More...

static bool	Suppress_output_while_checking_for_inverted_elements
	Static boolean to suppress output while checking for inverted elements. More...

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data
	Static boolean to suppress warnings about repeated internal data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_external_data = true
	Static boolean to suppress warnings about repeated external data. Defaults to true. More...

static double	Default_fd_jacobian_step = 1.0e-8
	Double used for the default finite difference step in elemental jacobian calculations. More...

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeneralisedElement
int	Non_halo_proc_ID
	Non-halo processor ID for Data; -1 if it's not a halo. More...

bool	Must_be_kept_as_halo
	Does this element need to be kept as a halo element during a distribute? More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt
	Timestepper (used to handle access to geometry at previous timesteps) More...

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default return value for required_nvalue(n) which gives the number of "data" values required by the element at node n; for example, solving a Poisson equation would required only one "data" value at each node. The defaults is set to zero, because a general element is problem-less. More...

static const double	Node_location_tolerance = 1.0e-14
	Default value for the tolerance to be used when locating nodes via local coordinates. More...

static const unsigned	N2deriv [] = {0, 1, 3, 6}
	Static array that holds the number of second derivatives as a function of the dimension of the element. More...

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix
	Empty dense matrix used as a dummy argument to combined residual and jacobian functions in the case when only the residuals are being assembled. More...

static std::deque< double * >	Dof_pt_deque
	Static storage for deque used to add_global_equation_numbers when pointers to the dofs in each element are not required. More...

Detailed Description

Class implementing the generic maths of the axisym poroelasticity equations: axisym linear elasticity coupled with axisym Darcy equations (using Raviart-Thomas elements with both edge and internal degrees of freedom) including inertia in both.

Definition at line 48 of file axisym_poroelasticity_elements.h.

Member Typedef Documentation

◆ MassSourceFctPt

typedef void(* oomph::AxisymmetricPoroelasticityEquations::MassSourceFctPt) (const double &time, const Vector< double > &x, double &f)

Mass source function pointer typedef.

Definition at line 59 of file axisym_poroelasticity_elements.h.

◆ SourceFctPt

typedef void(* oomph::AxisymmetricPoroelasticityEquations::SourceFctPt) (const double &time, const Vector< double > &x, Vector< double > &f)

Source function pointer typedef.

Definition at line 54 of file axisym_poroelasticity_elements.h.

Constructor & Destructor Documentation

◆ AxisymmetricPoroelasticityEquations()

oomph::AxisymmetricPoroelasticityEquations::AxisymmetricPoroelasticityEquations ( )

inline

Constructor.

Definition at line 64 of file axisym_poroelasticity_elements.h.

Member Function Documentation

◆ alpha()

const double& oomph::AxisymmetricPoroelasticityEquations::alpha ( ) const

inline

Access function for alpha, the Biot parameter.

Definition at line 171 of file axisym_poroelasticity_elements.h.

References Alpha_pt.

Referenced by fill_in_generic_residual_contribution().

◆ alpha_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::alpha_pt ( )

inline

Access function for pointer to alpha, the Biot parameter.

Definition at line 177 of file axisym_poroelasticity_elements.h.

References Alpha_pt.

◆ compute_error() [1/2]

void oomph::AxisymmetricPoroelasticityEquations::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		Vector< double > &	error,
		Vector< double > &	norm
	)

virtual

Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for p.

Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for u and p.

Reimplemented from oomph::FiniteElement.

Definition at line 308 of file axisym_poroelasticity_elements.cc.

References i, oomph::FiniteElement::integral_pt(), interpolated_div_q(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ compute_error() [2/2]

void oomph::AxisymmetricPoroelasticityEquations::compute_error	(	std::ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		Vector< double > &	error,
		Vector< double > &	norm
	)

virtual

Compute the error between the FE solution and the exact solution using the H(div) norm for q and L^2 norm for p. Unsteady version.

Compute the error between the FE solution and the exact solution using the H(div) norm for u and L^2 norm for p. Unsteady version.

Reimplemented from oomph::FiniteElement.

Definition at line 415 of file axisym_poroelasticity_elements.cc.

References i, oomph::FiniteElement::integral_pt(), interpolated_div_q(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ d2u_dt2()

double oomph::AxisymmetricPoroelasticityEquations::d2u_dt2	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

d^2u/dt^2 at local node n

Definition at line 912 of file axisym_poroelasticity_elements.h.

References i, oomph::TimeStepper::is_steady(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::node_pt(), oomph::TimeStepper::ntstorage(), t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), u_index_axisym_poroelasticity(), and oomph::TimeStepper::weight().

Referenced by fill_in_generic_residual_contribution().

◆ darcy_is_switched_off()

bool oomph::AxisymmetricPoroelasticityEquations::darcy_is_switched_off ( )

inline

Is Darcy flow switched off?

Definition at line 1008 of file axisym_poroelasticity_elements.h.

References Darcy_is_switched_off.

◆ density_ratio()

const double& oomph::AxisymmetricPoroelasticityEquations::density_ratio ( ) const

inline

Access function for the density ratio (fluid to solid)

Definition at line 130 of file axisym_poroelasticity_elements.h.

References Density_ratio_pt.

Referenced by fill_in_generic_residual_contribution().

◆ density_ratio_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::density_ratio_pt ( )

inline

Access function for pointer to the density ratio (fluid to solid)

Definition at line 136 of file axisym_poroelasticity_elements.h.

References Density_ratio_pt.

◆ dq_edge_dt()

double oomph::AxisymmetricPoroelasticityEquations::dq_edge_dt ( const unsigned & n ) const

inline

dq_edge/dt for the n-th edge degree of freedom

Definition at line 942 of file axisym_poroelasticity_elements.h.

References oomph::TimeStepper::is_steady(), oomph::FiniteElement::node_pt(), oomph::TimeStepper::ntstorage(), q_edge(), q_edge_node_number(), t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), and oomph::TimeStepper::weight().

Referenced by fill_in_generic_residual_contribution().

◆ dq_internal_dt()

double oomph::AxisymmetricPoroelasticityEquations::dq_internal_dt ( const unsigned & n ) const

inline

dq_internal/dt for the n-th internal degree of freedom

Definition at line 970 of file axisym_poroelasticity_elements.h.

References oomph::GeneralisedElement::internal_data_pt(), oomph::TimeStepper::is_steady(), oomph::TimeStepper::ntstorage(), q_internal(), q_internal_index(), t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), and oomph::TimeStepper::weight().

Referenced by fill_in_generic_residual_contribution().

◆ du_dt()

double oomph::AxisymmetricPoroelasticityEquations::du_dt	(	const unsigned &	n,
		const unsigned &	i
	)		const

inline

du/dt at local node n

Definition at line 882 of file axisym_poroelasticity_elements.h.

References i, oomph::TimeStepper::is_steady(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::node_pt(), oomph::TimeStepper::ntstorage(), t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), u_index_axisym_poroelasticity(), and oomph::TimeStepper::weight().

Referenced by fill_in_generic_residual_contribution(), interpolated_div_du_dt(), interpolated_du_dt(), output(), point_output_data(), and scalar_value_paraview().

◆ edge_flux_interpolation_point()

virtual Vector<double> oomph::AxisymmetricPoroelasticityEquations::edge_flux_interpolation_point	(	const unsigned &	edge,
		const unsigned &	j
	)		const

pure virtual

Returns the local coordinate of the jth flux_interpolation point along the specified edge.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ edge_flux_interpolation_point_global()

virtual void oomph::AxisymmetricPoroelasticityEquations::edge_flux_interpolation_point_global	(	const unsigned &	edge,
		const unsigned &	j,
		Vector< double > &	x
	)		const

pure virtual

Compute the global coordinates of the jth flux_interpolation point along an edge.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ face_index_of_edge()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::face_index_of_edge ( const unsigned & j ) const

pure virtual

Return the face index associated with specified edge.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ face_index_of_q_edge_basis_fct()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::face_index_of_q_edge_basis_fct ( const unsigned & j ) const

pure virtual

Return the face index associated with j-th edge flux degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ face_local_coordinate_of_flux_interpolation_point()

virtual void oomph::AxisymmetricPoroelasticityEquations::face_local_coordinate_of_flux_interpolation_point	(	const unsigned &	edge,
		const unsigned &	n,
		Vector< double > &	s
	)		const

pure virtual

Compute the face element coordinates of the nth flux interpolation point along an edge.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ fill_in_contribution_to_jacobian()

void oomph::AxisymmetricPoroelasticityEquations::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Fill in the Jacobian matrix for the Newton method.

Reimplemented from oomph::GeneralisedElement.

Definition at line 469 of file axisym_poroelasticity_elements.h.

References fill_in_generic_residual_contribution().

◆ fill_in_contribution_to_residuals()

void oomph::AxisymmetricPoroelasticityEquations::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Fill in contribution to residuals for the Darcy equations.

Reimplemented from oomph::GeneralisedElement.

Definition at line 462 of file axisym_poroelasticity_elements.h.

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution().

◆ fill_in_generic_residual_contribution()

void oomph::AxisymmetricPoroelasticityEquations::fill_in_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		bool	flag
	)

protectedvirtual

Fill in residuals and, if flag==true, jacobian.

Definition at line 522 of file axisym_poroelasticity_elements.cc.

References alpha(), d2u_dt2(), density_ratio(), dq_edge_dt(), dq_internal_dt(), du_dt(), fluid_body_force(), i, oomph::FiniteElement::integral_pt(), oomph::GeneralisedElement::internal_data_pt(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::interpolated_x(), oomph::Integral::knot(), lambda_sq(), mass_source(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::node_pt(), np_basis(), nq_basis(), nq_basis_edge(), nu(), oomph::Integral::nweight(), p_local_eqn(), p_value(), permeability(), permeability_ratio(), porosity(), q_edge(), q_edge_local_eqn(), q_edge_node_number(), q_internal(), q_internal_index(), q_internal_local_eqn(), oomph::FiniteElement::raw_nodal_value(), s, shape_basis_test_local_at_knot(), solid_body_force(), oomph::Time::time(), oomph::TimeStepper::time_pt(), oomph::Data::time_stepper_pt(), u_index_axisym_poroelasticity(), oomph::Integral::weight(), oomph::TimeStepper::weight(), and youngs_modulus().

Referenced by fill_in_contribution_to_jacobian(), and fill_in_contribution_to_residuals().

◆ fluid_body_force()

void oomph::AxisymmetricPoroelasticityEquations::fluid_body_force	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	b
	)		const

inline

Indirect access to the fluid body force function - returns 0 if no forcing function has been set.

Definition at line 254 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::dim(), Fluid_body_force_fct_pt, and i.

Referenced by fill_in_generic_residual_contribution().

◆ fluid_body_force_fct_pt() [1/2]

SourceFctPt& oomph::AxisymmetricPoroelasticityEquations::fluid_body_force_fct_pt ( )

inline

Access function: Pointer to fluid force function.

Definition at line 207 of file axisym_poroelasticity_elements.h.

References Fluid_body_force_fct_pt.

◆ fluid_body_force_fct_pt() [2/2]

SourceFctPt oomph::AxisymmetricPoroelasticityEquations::fluid_body_force_fct_pt ( ) const

inline

Access function: Pointer to fluid force function (const version)

Definition at line 213 of file axisym_poroelasticity_elements.h.

References Fluid_body_force_fct_pt.

◆ get_div_q_basis_local()

virtual void oomph::AxisymmetricPoroelasticityEquations::get_div_q_basis_local	(	const Vector< double > &	s,
		Shape &	div_q_basis_ds
	)		const

pure virtual

Compute the local form of the q basis and dbasis/ds at local coordinate s.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by interpolated_div_q().

◆ get_p_basis()

virtual void oomph::AxisymmetricPoroelasticityEquations::get_p_basis	(	const Vector< double > &	s,
		Shape &	p_basis
	)		const

pure virtual

Compute the pressure basis.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by interpolated_p().

◆ get_q_basis()

void oomph::AxisymmetricPoroelasticityEquations::get_q_basis	(	const Vector< double > &	s,
		Shape &	q_basis
	)		const

inline

Compute the transformed basis at local coordinate s.

Definition at line 386 of file axisym_poroelasticity_elements.h.

References get_q_basis_local(), oomph::FiniteElement::nnode(), nq_basis(), and transform_basis().

Referenced by interpolated_q().

◆ get_q_basis_local()

virtual void oomph::AxisymmetricPoroelasticityEquations::get_q_basis_local	(	const Vector< double > &	s,
		Shape &	q_basis
	)		const

pure virtual

Comute the local form of the q basis at local coordinate s.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by get_q_basis().

◆ get_Z2_flux()

void oomph::AxisymmetricPoroelasticityEquations::get_Z2_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)

inlinevirtual

Z2 flux (use Darcy flux)

Implements oomph::ElementWithZ2ErrorEstimator.

Definition at line 1275 of file axisym_poroelasticity_elements.h.

References interpolated_q(), and s.

◆ interpolated_div_du_dt()

double oomph::AxisymmetricPoroelasticityEquations::interpolated_div_du_dt	(	const Vector< double > &	s,
		Vector< double > &	div_dudt_components
	)		const

inline

Calculate the FE representation of the divergence of the skeleton velocity, div(du/dt), and its components: 1/r diff(r*du_r/dt,r) and diff(du_z/dt,z).

Definition at line 479 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::dshape_eulerian(), du_dt(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nnode(), and s.

Referenced by point_output_data().

◆ interpolated_div_q() [1/2]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_div_q ( const Vector< double > & s ) const

inline

Calculate the FE representation of div q and return it.

Definition at line 834 of file axisym_poroelasticity_elements.h.

References interpolated_div_q(), and s.

◆ interpolated_div_q() [2/2]

void oomph::AxisymmetricPoroelasticityEquations::interpolated_div_q	(	const Vector< double > &	s,
		double &	div_q
	)		const

inline

Calculate the FE representation of div u.

Definition at line 782 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::dshape_local(), e, get_div_q_basis_local(), interpolated_q(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::local_to_eulerian_mapping(), oomph::FiniteElement::nnode(), nq_basis(), nq_basis_edge(), q_edge(), q_internal(), and s.

Referenced by compute_error(), interpolated_div_q(), output(), point_output_data(), and scalar_value_paraview().

◆ interpolated_div_u()

double oomph::AxisymmetricPoroelasticityEquations::interpolated_div_u	(	const Vector< double > &	s,
		Vector< double > &	div_u_components
	)		const

inline

Calculate the FE representation of the divergence of the skeleton displ, div(u), and its components: 1/r diff(r*u_r,r) and diff(u_z,z).

Definition at line 527 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::dshape_eulerian(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, and u_index_axisym_poroelasticity().

Referenced by point_output_data().

◆ interpolated_du_dt()

void oomph::AxisymmetricPoroelasticityEquations::interpolated_du_dt	(	const Vector< double > &	s,
		Vector< double > &	du_dt
	)		const

inline

Calculate the FE representation of du_dt.

Definition at line 663 of file axisym_poroelasticity_elements.h.

References du_dt(), i, oomph::FiniteElement::nnode(), s, and oomph::FiniteElement::shape().

Referenced by output(), point_output_data(), and scalar_value_paraview().

◆ interpolated_p() [1/2]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_p ( const Vector< double > & s ) const

inline

Calculate the FE representation of p and return it.

Definition at line 869 of file axisym_poroelasticity_elements.h.

References interpolated_p(), and s.

◆ interpolated_p() [2/2]

void oomph::AxisymmetricPoroelasticityEquations::interpolated_p	(	const Vector< double > &	s,
		double &	p
	)		const

inline

Calculate the FE representation of p.

Definition at line 847 of file axisym_poroelasticity_elements.h.

References get_p_basis(), np_basis(), p_value(), and s.

Referenced by compute_error(), fill_in_generic_residual_contribution(), interpolated_p(), output(), point_output_data(), and scalar_value_paraview().

◆ interpolated_q() [1/4]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_q	(	const unsigned &	t,
		const Vector< double > &	s,
		const unsigned	i
	)		const

inline

Calculate the FE representation of the i-th component of q at time level t (t=0: current)

Definition at line 757 of file axisym_poroelasticity_elements.h.

References get_q_basis(), i, nq_basis(), nq_basis_edge(), q_edge(), q_internal(), s, and t.

◆ interpolated_q() [2/4]

void oomph::AxisymmetricPoroelasticityEquations::interpolated_q	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	q
	)		const

inline

Calculate the FE representation of q at time level t (t=0: current)

Definition at line 711 of file axisym_poroelasticity_elements.h.

References get_q_basis(), i, nq_basis(), nq_basis_edge(), q_edge(), q_internal(), s, and t.

◆ interpolated_q() [3/4]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_q	(	const Vector< double > &	s,
		const unsigned	i
	)		const

inline

Calculate the FE representation of the i-th component of q.

Definition at line 734 of file axisym_poroelasticity_elements.h.

References get_q_basis(), i, nq_basis(), nq_basis_edge(), q_edge(), q_internal(), and s.

◆ interpolated_q() [4/4]

void oomph::AxisymmetricPoroelasticityEquations::interpolated_q	(	const Vector< double > &	s,
		Vector< double > &	q
	)		const

inline

Calculate the FE representation of q.

Definition at line 689 of file axisym_poroelasticity_elements.h.

References get_q_basis(), i, nq_basis(), nq_basis_edge(), q_edge(), q_internal(), and s.

Referenced by compute_error(), fill_in_generic_residual_contribution(), get_Z2_flux(), interpolated_div_q(), output(), point_output_data(), and scalar_value_paraview().

◆ interpolated_u() [1/3]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_u	(	const unsigned &	t,
		const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

Calculate the FE representation of the i-th component of u at time level t (t=0: current)

Definition at line 633 of file axisym_poroelasticity_elements.h.

References i, interpolated_u(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), t, and u_index_axisym_poroelasticity().

◆ interpolated_u() [2/3]

double oomph::AxisymmetricPoroelasticityEquations::interpolated_u	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

Calculate the FE representation of the i-th component of u.

Definition at line 604 of file axisym_poroelasticity_elements.h.

References i, interpolated_u(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and u_index_axisym_poroelasticity().

◆ interpolated_u() [3/3]

void oomph::AxisymmetricPoroelasticityEquations::interpolated_u	(	const Vector< double > &	s,
		Vector< double > &	disp
	)		const

inline

Calculate the FE representation of u.

Definition at line 576 of file axisym_poroelasticity_elements.h.

References i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and u_index_axisym_poroelasticity().

Referenced by compute_error(), fill_in_generic_residual_contribution(), interpolated_u(), output(), point_output_data(), and scalar_value_paraview().

◆ lambda_sq()

const double& oomph::AxisymmetricPoroelasticityEquations::lambda_sq ( ) const

inline

Access function for timescale ratio (nondim density)

Definition at line 118 of file axisym_poroelasticity_elements.h.

References Lambda_sq_pt.

Referenced by fill_in_generic_residual_contribution().

◆ lambda_sq_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::lambda_sq_pt ( )

inline

Access function for pointer to timescale ratio (nondim density)

Definition at line 124 of file axisym_poroelasticity_elements.h.

References Lambda_sq_pt.

◆ mass_source()

void oomph::AxisymmetricPoroelasticityEquations::mass_source	(	const double &	time,
		const Vector< double > &	x,
		double &	b
	)		const

inline

Indirect access to the mass source function - returns 0 if no mass source function has been set.

Definition at line 276 of file axisym_poroelasticity_elements.h.

References Mass_source_fct_pt.

Referenced by fill_in_generic_residual_contribution().

◆ mass_source_fct_pt() [1/2]

MassSourceFctPt& oomph::AxisymmetricPoroelasticityEquations::mass_source_fct_pt ( )

inline

Access function: Pointer to mass source function.

Definition at line 219 of file axisym_poroelasticity_elements.h.

References Mass_source_fct_pt.

◆ mass_source_fct_pt() [2/2]

MassSourceFctPt oomph::AxisymmetricPoroelasticityEquations::mass_source_fct_pt ( ) const

inline

Access function: Pointer to mass source function (const version)

Definition at line 225 of file axisym_poroelasticity_elements.h.

References Mass_source_fct_pt.

◆ nedge_flux_interpolation_point()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::nedge_flux_interpolation_point ( ) const

pure virtual

Returns the number of flux_interpolation points along each edge of the element.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ np_basis()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::np_basis ( ) const

pure virtual

Return the total number of pressure basis functions.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution(), interpolated_p(), and switch_off_darcy().

◆ nq_basis()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::nq_basis ( ) const

inlinevirtual

Return the total number of computational basis functions for q.

Definition at line 365 of file axisym_poroelasticity_elements.h.

References nq_basis_edge(), and nq_basis_internal().

Referenced by fill_in_generic_residual_contribution(), get_q_basis(), interpolated_div_q(), interpolated_q(), oomph::TAxisymmetricPoroelasticityElement< ORDER >::shape_basis_test_local(), and transform_basis().

◆ nq_basis_edge()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::nq_basis_edge ( ) const

pure virtual

Return the number of edge basis functions for q.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution(), interpolated_div_q(), interpolated_q(), nq_basis(), and switch_off_darcy().

◆ nq_basis_internal()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::nq_basis_internal ( ) const

pure virtual

Return the number of internal basis functions for q.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by nq_basis(), and switch_off_darcy().

◆ nscalar_paraview()

unsigned oomph::AxisymmetricPoroelasticityEquations::nscalar_paraview ( ) const

inlinevirtual

Number of scalars/fields output by this element. Reimplements broken virtual function in base class.

Reimplemented from oomph::FiniteElement.

Definition at line 1052 of file axisym_poroelasticity_elements.h.

◆ nu()

const double& oomph::AxisymmetricPoroelasticityEquations::nu ( ) const

inline

Access function for Poisson's ratio.

Definition at line 96 of file axisym_poroelasticity_elements.h.

References Nu_pt.

Referenced by fill_in_generic_residual_contribution().

◆ nu_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::nu_pt ( )

inline

Access function for pointer to Poisson's ratio.

Definition at line 112 of file axisym_poroelasticity_elements.h.

References Nu_pt.

◆ num_Z2_flux_terms()

unsigned oomph::AxisymmetricPoroelasticityEquations::num_Z2_flux_terms ( )

inlinevirtual

Number off flux terms for Z2 error estimator (use Darcy flux)

Implements oomph::ElementWithZ2ErrorEstimator.

Definition at line 1269 of file axisym_poroelasticity_elements.h.

◆ output() [1/2]

void oomph::AxisymmetricPoroelasticityEquations::output ( std::ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Definition at line 1221 of file axisym_poroelasticity_elements.h.

Referenced by oomph::TAxisymmetricPoroelasticityElement< ORDER >::output().

◆ output() [2/2]

void oomph::AxisymmetricPoroelasticityEquations::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

virtual

Output FE representation of soln: x,y,u1,u2,div_q,p at Nplot^2 plot points.

Output FE representation of soln: x,y,u1,u2,q1,q2,div_q,p at Nplot^2 plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Definition at line 145 of file axisym_poroelasticity_elements.cc.

References du_dt(), oomph::FiniteElement::get_s_plot(), i, interpolated_div_q(), interpolated_du_dt(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [1/2]

void oomph::AxisymmetricPoroelasticityEquations::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output FE representation of exact soln: x,y,u1,u2,div_q,p at Nplot^2 plot points. Unsteady version.

Output FE representation of exact soln at Nplot^2 plot points. Unsteady version.

Reimplemented from oomph::FiniteElement.

Definition at line 256 of file axisym_poroelasticity_elements.cc.

References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [2/2]

void oomph::AxisymmetricPoroelasticityEquations::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output FE representation of exact soln: x,y,u1,u2,div_q,p at Nplot^2 plot points.

Output FE representation of exact soln at Nplot^2 plot points.

Reimplemented from oomph::FiniteElement.

Definition at line 205 of file axisym_poroelasticity_elements.cc.

References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_with_projected_flux()

void oomph::AxisymmetricPoroelasticityEquations::output_with_projected_flux	(	std::ostream &	outfile,
		const unsigned &	nplot,
		const Vector< double >	unit_normal
	)

Output incl. projection of fluxes into direction of the specified unit vector.

◆ p_data_pt()

virtual Data* oomph::AxisymmetricPoroelasticityEquations::p_data_pt ( ) const

pure virtual

Return pointer to the Data object that stores the pressure values.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ p_local_eqn()

virtual int oomph::AxisymmetricPoroelasticityEquations::p_local_eqn ( const unsigned & j ) const

pure virtual

Return the equation number of the j-th pressure degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution().

◆ p_value()

virtual double oomph::AxisymmetricPoroelasticityEquations::p_value ( const unsigned & j ) const

pure virtual

Return the jth pressure value.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution(), and interpolated_p().

◆ permeability()

const double& oomph::AxisymmetricPoroelasticityEquations::permeability ( ) const

inline

Access function for the nondim permeability.

Definition at line 142 of file axisym_poroelasticity_elements.h.

References Permeability_pt.

Referenced by fill_in_generic_residual_contribution().

◆ permeability_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::permeability_pt ( )

inline

Access function for pointer to the nondim permeability.

Definition at line 148 of file axisym_poroelasticity_elements.h.

References Permeability_pt.

◆ permeability_ratio()

const double& oomph::AxisymmetricPoroelasticityEquations::permeability_ratio ( ) const

inline

Access function for the ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations.

Definition at line 157 of file axisym_poroelasticity_elements.h.

References Permeability_ratio_pt.

Referenced by fill_in_generic_residual_contribution().

◆ permeability_ratio_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::permeability_ratio_pt ( )

inline

Access function for pointer to ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations.

Definition at line 165 of file axisym_poroelasticity_elements.h.

References Permeability_ratio_pt.

◆ pin_p_value()

virtual void oomph::AxisymmetricPoroelasticityEquations::pin_p_value	(	const unsigned &	j,
		const double &	p
	)

pure virtual

Pin the jth pressure value and set it to p.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by switch_off_darcy().

◆ pin_q_edge_value()

virtual void oomph::AxisymmetricPoroelasticityEquations::pin_q_edge_value	(	const unsigned &	j,
		const double &	value
	)

pure virtual

Pin the j-th edge (flux) degree of freedom and set it to specified value.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by switch_off_darcy().

◆ pin_q_internal_value()

virtual void oomph::AxisymmetricPoroelasticityEquations::pin_q_internal_value	(	const unsigned &	j,
		const double &	value
	)

pure virtual

Pin the jth internal q value and set it to specified value.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by switch_off_darcy().

◆ point_output_data()

void oomph::AxisymmetricPoroelasticityEquations::point_output_data	(	const Vector< double > &	s,
		Vector< double > &	data
	)

inlinevirtual

Output solution in data vector at local cordinates s: r,z,u_r,u_z,q_r,q_z,div_q,p,durdt,duzdt.

Reimplemented from oomph::FiniteElement.

Definition at line 1174 of file axisym_poroelasticity_elements.h.

References du_dt(), i, interpolated_div_du_dt(), interpolated_div_q(), interpolated_div_u(), interpolated_du_dt(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::interpolated_x(), and s.

◆ porosity()

const double& oomph::AxisymmetricPoroelasticityEquations::porosity ( ) const

inline

Access function for the porosity.

Definition at line 183 of file axisym_poroelasticity_elements.h.

References Porosity_pt.

Referenced by fill_in_generic_residual_contribution().

◆ porosity_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::porosity_pt ( )

inline

Access function for pointer to the porosity.

Definition at line 189 of file axisym_poroelasticity_elements.h.

References Porosity_pt.

◆ q_edge() [1/2]

virtual double oomph::AxisymmetricPoroelasticityEquations::q_edge ( const unsigned & j ) const

pure virtual

Return the values of the j-th edge (flux) degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by dq_edge_dt(), fill_in_generic_residual_contribution(), interpolated_div_q(), and interpolated_q().

◆ q_edge() [2/2]

virtual double oomph::AxisymmetricPoroelasticityEquations::q_edge	(	const unsigned &	t,
		const unsigned &	j
	)		const

pure virtual

Return the values of the j-th edge (flux) degree of freedom at time history level t.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ q_edge_data_pt()

virtual Vector<Data*> oomph::AxisymmetricPoroelasticityEquations::q_edge_data_pt ( ) const

pure virtual

Return vector of pointers to the Data objects that store the edge flux values.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ q_edge_index()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::q_edge_index ( const unsigned & j ) const

pure virtual

Return the nodal index at which the jth edge unknown is stored.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ q_edge_local_eqn()

virtual int oomph::AxisymmetricPoroelasticityEquations::q_edge_local_eqn ( const unsigned & j ) const

pure virtual

Return the equation number of the j-th edge (flux) degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution().

◆ q_edge_node_number()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::q_edge_node_number ( const unsigned & j ) const

pure virtual

Return the number of the node where the jth edge unknown is stored.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by dq_edge_dt(), and fill_in_generic_residual_contribution().

◆ q_internal() [1/2]

virtual double oomph::AxisymmetricPoroelasticityEquations::q_internal ( const unsigned & j ) const

pure virtual

Return the values of the j-th internal degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by dq_internal_dt(), fill_in_generic_residual_contribution(), interpolated_div_q(), and interpolated_q().

◆ q_internal() [2/2]

virtual double oomph::AxisymmetricPoroelasticityEquations::q_internal	(	const unsigned &	t,
		const unsigned &	j
	)		const

pure virtual

Return the values of the j-th internal degree of freedom at time history level t.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ q_internal_data_pt()

virtual Data* oomph::AxisymmetricPoroelasticityEquations::q_internal_data_pt ( ) const

pure virtual

Return pointer to the Data object that stores the internal flux values.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ q_internal_index()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::q_internal_index ( ) const

pure virtual

Return the index of the internal data where the q internal degrees of freedom are stored.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by dq_internal_dt(), fill_in_generic_residual_contribution(), and set_q_internal_timestepper().

◆ q_internal_local_eqn()

virtual int oomph::AxisymmetricPoroelasticityEquations::q_internal_local_eqn ( const unsigned & j ) const

pure virtual

Return the equation number of the j-th internal degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution().

◆ required_nvalue()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::required_nvalue ( const unsigned & n ) const

pure virtual

Number of values required at node n.

Reimplemented from oomph::FiniteElement.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ scalar_name_paraview()

std::string oomph::AxisymmetricPoroelasticityEquations::scalar_name_paraview ( const unsigned & i ) const

inlinevirtual

Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements.

Reimplemented from oomph::FiniteElement.

Definition at line 1121 of file axisym_poroelasticity_elements.h.

References i.

◆ scalar_value_paraview()

void oomph::AxisymmetricPoroelasticityEquations::scalar_value_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

Definition at line 1059 of file axisym_poroelasticity_elements.h.

References du_dt(), oomph::FiniteElement::get_s_plot(), i, interpolated_div_q(), interpolated_du_dt(), interpolated_p(), interpolated_q(), interpolated_u(), oomph::FiniteElement::nplot_points_paraview(), and s.

◆ scale_basis()

virtual void oomph::AxisymmetricPoroelasticityEquations::scale_basis ( Shape & basis ) const

pure virtual

Scale the edge basis to allow arbitrary edge mappings.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by transform_basis().

◆ self_test()

unsigned oomph::AxisymmetricPoroelasticityEquations::self_test ( )

inlinevirtual

Self test.

Reimplemented from oomph::FiniteElement.

Definition at line 1044 of file axisym_poroelasticity_elements.h.

◆ set_p_value()

virtual void oomph::AxisymmetricPoroelasticityEquations::set_p_value	(	const unsigned &	j,
		const double &	value
	)

pure virtual

Set the jth pressure value.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ set_q_edge() [1/2]

virtual void oomph::AxisymmetricPoroelasticityEquations::set_q_edge	(	const unsigned &	j,
		const double &	value
	)

pure virtual

Set the values of the j-th edge (flux) degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ set_q_edge() [2/2]

virtual void oomph::AxisymmetricPoroelasticityEquations::set_q_edge	(	const unsigned &	t,
		const unsigned &	j,
		const double &	value
	)

pure virtual

Set the values of the j-th edge (flux) degree of freedom at time history level t.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ set_q_internal() [1/2]

virtual void oomph::AxisymmetricPoroelasticityEquations::set_q_internal	(	const unsigned &	j,
		const double &	value
	)

pure virtual

Set the values of the j-th internal degree of freedom.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ set_q_internal() [2/2]

virtual void oomph::AxisymmetricPoroelasticityEquations::set_q_internal	(	const unsigned &	t,
		const unsigned &	j,
		const double &	value
	)

pure virtual

Set the values of the j-th internal degree of freedom at time history level t.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ set_q_internal_timestepper()

void oomph::AxisymmetricPoroelasticityEquations::set_q_internal_timestepper ( TimeStepper *const time_stepper_pt )

inline

Set the timestepper of the q internal data object.

Definition at line 1000 of file axisym_poroelasticity_elements.h.

References oomph::GeneralisedElement::internal_data_pt(), q_internal_index(), oomph::Data::set_time_stepper(), and oomph::GeomObject::time_stepper_pt().

◆ shape_basis_test_local()

virtual double oomph::AxisymmetricPoroelasticityEquations::shape_basis_test_local	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsi,
		Shape &	u_basis,
		Shape &	u_test,
		DShape &	du_basis_dx,
		DShape &	du_test_dx,
		Shape &	q_basis,
		Shape &	q_test,
		Shape &	p_basis,
		Shape &	p_test,
		Shape &	div_q_basis_ds,
		Shape &	div_q_test_ds
	)		const

protectedpure virtual

Compute the geometric basis, and the q, p and divergence basis functions and test functions at local coordinate s.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

◆ shape_basis_test_local_at_knot()

virtual double oomph::AxisymmetricPoroelasticityEquations::shape_basis_test_local_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsi,
		Shape &	u_basis,
		Shape &	u_test,
		DShape &	du_basis_dx,
		DShape &	du_test_dx,
		Shape &	q_basis,
		Shape &	q_test,
		Shape &	p_basis,
		Shape &	p_test,
		Shape &	div_q_basis_ds,
		Shape &	div_q_test_ds
	)		const

protectedpure virtual

Compute the geometric basis, and the q, p and divergence basis functions and test functions at integration point ipt.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by fill_in_generic_residual_contribution().

◆ solid_body_force()

void oomph::AxisymmetricPoroelasticityEquations::solid_body_force	(	const double &	time,
		const Vector< double > &	x,
		Vector< double > &	b
	)		const

inline

Indirect access to the solid body force function - returns 0 if no forcing function has been set.

Definition at line 232 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::dim(), i, and Solid_body_force_fct_pt.

Referenced by fill_in_generic_residual_contribution().

◆ solid_body_force_fct_pt() [1/2]

SourceFctPt& oomph::AxisymmetricPoroelasticityEquations::solid_body_force_fct_pt ( )

inline

Access function: Pointer to solid body force function.

Definition at line 195 of file axisym_poroelasticity_elements.h.

References Solid_body_force_fct_pt.

◆ solid_body_force_fct_pt() [2/2]

SourceFctPt oomph::AxisymmetricPoroelasticityEquations::solid_body_force_fct_pt ( ) const

inline

Access function: Pointer to solid body force function (const version)

Definition at line 201 of file axisym_poroelasticity_elements.h.

References Solid_body_force_fct_pt.

◆ switch_off_darcy()

void oomph::AxisymmetricPoroelasticityEquations::switch_off_darcy ( )

inline

Switch off Darcy flow.

Definition at line 1015 of file axisym_poroelasticity_elements.h.

References Darcy_is_switched_off, np_basis(), nq_basis_edge(), nq_basis_internal(), pin_p_value(), pin_q_edge_value(), and pin_q_internal_value().

◆ transform_basis() [1/2]

double oomph::AxisymmetricPoroelasticityEquations::transform_basis	(	const Vector< double > &	s,
		const Shape &	q_basis_local,
		Shape &	psi,
		DShape &	dpsi,
		Shape &	q_basis
	)		const

Performs a div-conserving transformation of the vector basis functions from the reference element to the actual element.

Definition at line 80 of file axisym_poroelasticity_elements.cc.

References oomph::FiniteElement::dshape_local(), i, oomph::FiniteElement::local_to_eulerian_mapping(), nq_basis(), scale_basis(), and oomph::FiniteElement::transform_derivatives().

Referenced by get_q_basis(), oomph::TAxisymmetricPoroelasticityElement< ORDER >::shape_basis_test_local(), and transform_basis().

◆ transform_basis() [2/2]

double oomph::AxisymmetricPoroelasticityEquations::transform_basis	(	const Vector< double > &	s,
		const Shape &	q_basis_local,
		Shape &	psi,
		Shape &	q_basis
	)		const

inline

Performs a div-conserving transformation of the vector basis functions from the reference element to the actual element.

Definition at line 451 of file axisym_poroelasticity_elements.h.

References oomph::FiniteElement::nnode(), s, and transform_basis().

◆ u_index_axisym_poroelasticity()

virtual unsigned oomph::AxisymmetricPoroelasticityEquations::u_index_axisym_poroelasticity ( const unsigned & j ) const

pure virtual

Return the nodal index of the j-th solid displacement unknown.

Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.

Referenced by d2u_dt2(), du_dt(), fill_in_generic_residual_contribution(), interpolated_div_u(), and interpolated_u().

◆ youngs_modulus()

const double& oomph::AxisymmetricPoroelasticityEquations::youngs_modulus ( ) const

inline

Access function to non-dim Young's modulus (ratio of actual Young's modulus to reference stress used to non-dim the equations. (const version)

Definition at line 83 of file axisym_poroelasticity_elements.h.

References Youngs_modulus_pt.

Referenced by fill_in_generic_residual_contribution().

◆ youngs_modulus_pt()

double*& oomph::AxisymmetricPoroelasticityEquations::youngs_modulus_pt ( )

inline

Pointer to non-dim Young's modulus (ratio of actual Young's modulus to reference stress used to non-dim the equations.

Definition at line 90 of file axisym_poroelasticity_elements.h.

References Youngs_modulus_pt.

Member Data Documentation

◆ Alpha_pt

double* oomph::AxisymmetricPoroelasticityEquations::Alpha_pt

private

Alpha – the biot parameter.

Definition at line 1348 of file axisym_poroelasticity_elements.h.

Referenced by alpha(), and alpha_pt().

◆ Darcy_is_switched_off

bool oomph::AxisymmetricPoroelasticityEquations::Darcy_is_switched_off

private

Boolean to record that darcy has been switched off.

Definition at line 1354 of file axisym_poroelasticity_elements.h.

Referenced by darcy_is_switched_off(), and switch_off_darcy().

◆ Default_alpha_value

double oomph::AxisymmetricPoroelasticityEquations::Default_alpha_value = 1.0

staticprivate

Static default value for alpha, the biot parameter.

Static default value for alpha, the Biot parameter.

Definition at line 1380 of file axisym_poroelasticity_elements.h.

◆ Default_density_ratio_value

double oomph::AxisymmetricPoroelasticityEquations::Default_density_ratio_value = 1.0

staticprivate

Static default value for the density ratio.

Static default value for the density ratio (fluid to solid)

Definition at line 1368 of file axisym_poroelasticity_elements.h.

◆ Default_lambda_sq_value

double oomph::AxisymmetricPoroelasticityEquations::Default_lambda_sq_value = 1.0

staticprivate

Static default value for timescale ratio.

Static default value for timescale ratio (1.0)

Definition at line 1365 of file axisym_poroelasticity_elements.h.

◆ Default_permeability_ratio_value

double oomph::AxisymmetricPoroelasticityEquations::Default_permeability_ratio_value

staticprivate

Initial value:

=

1.0

Static default value for the ratio of the material's actual permeability to the permeability used to non-dimensionalise the equations.

Static default value for ratio of the material's actual permeability to the permeability used in the non-dimensionalisastion of the equations.

Definition at line 1377 of file axisym_poroelasticity_elements.h.

◆ Default_permeability_value

double oomph::AxisymmetricPoroelasticityEquations::Default_permeability_value = 1.0

staticprivate

Static default value for the permeability (1.0 for natural scaling; i.e. timescale is given by L^2/(k^* E)

Static default value for permeability (1.0 for natural scaling i.e. timescale is given by L^2/(k^* E)

Definition at line 1372 of file axisym_poroelasticity_elements.h.

◆ Default_porosity_value

double oomph::AxisymmetricPoroelasticityEquations::Default_porosity_value = 1.0

staticprivate

Static default value for the porosity.

Definition at line 1383 of file axisym_poroelasticity_elements.h.

◆ Default_youngs_modulus_value

double oomph::AxisymmetricPoroelasticityEquations::Default_youngs_modulus_value

staticprivate

Initial value:

=

1.0

Static default value for Young's modulus (1.0 – for natural scaling, i.e. all stresses have been non-dimensionalised by the same reference Young's modulus. Setting the "non-dimensional" Young's modulus (obtained by de-referencing Youngs_modulus_pt) to a number larger than one means that the material is stiffer than assumed in the non-dimensionalisation.

Definition at line 1362 of file axisym_poroelasticity_elements.h.

◆ Density_ratio_pt

double* oomph::AxisymmetricPoroelasticityEquations::Density_ratio_pt

private

Density ratio.

Definition at line 1338 of file axisym_poroelasticity_elements.h.

Referenced by density_ratio(), and density_ratio_pt().

◆ Fluid_body_force_fct_pt

SourceFctPt oomph::AxisymmetricPoroelasticityEquations::Fluid_body_force_fct_pt

private

Pointer to fluid source function.

Definition at line 1323 of file axisym_poroelasticity_elements.h.

Referenced by fluid_body_force(), and fluid_body_force_fct_pt().

◆ Lambda_sq_pt

double* oomph::AxisymmetricPoroelasticityEquations::Lambda_sq_pt

private

Timescale ratio (non-dim. density)

Definition at line 1335 of file axisym_poroelasticity_elements.h.

Referenced by lambda_sq(), and lambda_sq_pt().

◆ Mass_source_fct_pt

MassSourceFctPt oomph::AxisymmetricPoroelasticityEquations::Mass_source_fct_pt

private

Pointer to the mass source function.

Definition at line 1326 of file axisym_poroelasticity_elements.h.

Referenced by mass_source(), and mass_source_fct_pt().

◆ Nu_pt

double* oomph::AxisymmetricPoroelasticityEquations::Nu_pt

private

Pointer to Poisson's ratio.

Definition at line 1332 of file axisym_poroelasticity_elements.h.

Referenced by nu(), and nu_pt().

◆ Permeability_pt

double* oomph::AxisymmetricPoroelasticityEquations::Permeability_pt

private

permeability

Definition at line 1341 of file axisym_poroelasticity_elements.h.

Referenced by permeability(), and permeability_pt().

◆ Permeability_ratio_pt

double* oomph::AxisymmetricPoroelasticityEquations::Permeability_ratio_pt

private

Ratio of the material's actual permeability to the permeability used in the non-dimensionalisation of the equations.

Definition at line 1345 of file axisym_poroelasticity_elements.h.

Referenced by permeability_ratio(), and permeability_ratio_pt().

◆ Porosity_pt

double* oomph::AxisymmetricPoroelasticityEquations::Porosity_pt

private

Porosity.

Definition at line 1351 of file axisym_poroelasticity_elements.h.

Referenced by porosity(), and porosity_pt().

◆ Solid_body_force_fct_pt

SourceFctPt oomph::AxisymmetricPoroelasticityEquations::Solid_body_force_fct_pt

private

Pointer to solid body force function.

Definition at line 1320 of file axisym_poroelasticity_elements.h.

Referenced by solid_body_force(), and solid_body_force_fct_pt().

◆ Youngs_modulus_pt

double* oomph::AxisymmetricPoroelasticityEquations::Youngs_modulus_pt

private

Pointer to the nondim Young's modulus.

Definition at line 1329 of file axisym_poroelasticity_elements.h.

Referenced by youngs_modulus(), and youngs_modulus_pt().

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ MassSourceFctPt

◆ SourceFctPt

Constructor & Destructor Documentation

◆ AxisymmetricPoroelasticityEquations()

Member Function Documentation

◆ alpha()

◆ alpha_pt()

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ d2u_dt2()

◆ darcy_is_switched_off()

◆ density_ratio()

◆ density_ratio_pt()

◆ dq_edge_dt()

◆ dq_internal_dt()

◆ du_dt()

◆ edge_flux_interpolation_point()

◆ edge_flux_interpolation_point_global()

◆ face_index_of_edge()

◆ face_index_of_q_edge_basis_fct()

◆ face_local_coordinate_of_flux_interpolation_point()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution()

◆ fluid_body_force()

◆ fluid_body_force_fct_pt() [1/2]

◆ fluid_body_force_fct_pt() [2/2]

◆ get_div_q_basis_local()

◆ get_p_basis()

◆ get_q_basis()

◆ get_q_basis_local()

◆ get_Z2_flux()

◆ interpolated_div_du_dt()

◆ interpolated_div_q() [1/2]

◆ interpolated_div_q() [2/2]

◆ interpolated_div_u()

◆ interpolated_du_dt()

◆ interpolated_p() [1/2]

◆ interpolated_p() [2/2]

◆ interpolated_q() [1/4]

◆ interpolated_q() [2/4]

◆ interpolated_q() [3/4]

◆ interpolated_q() [4/4]

◆ interpolated_u() [1/3]

◆ interpolated_u() [2/3]

◆ interpolated_u() [3/3]

◆ lambda_sq()

◆ lambda_sq_pt()

◆ mass_source()

◆ mass_source_fct_pt() [1/2]

◆ mass_source_fct_pt() [2/2]

◆ nedge_flux_interpolation_point()

◆ np_basis()

◆ nq_basis()

◆ nq_basis_edge()

◆ nq_basis_internal()

◆ nscalar_paraview()

◆ nu()

◆ nu_pt()

◆ num_Z2_flux_terms()

◆ output() [1/2]

◆ output() [2/2]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ output_with_projected_flux()

◆ p_data_pt()

◆ p_local_eqn()

◆ p_value()

◆ permeability()

◆ permeability_pt()

◆ permeability_ratio()

◆ permeability_ratio_pt()