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>
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" as . More... | |
typedef void(* | UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &) |
Function pointer for function that computes Vector-valued time-dependent function as . 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) = 2D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = 3D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = d2psids(i,3) = d2psids(i,4) = d2psids(i,5) = . 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) = 2D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = 3D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = d2psids(i,3) = d2psids(i,4) = d2psids(i,5) = . 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) = 2D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = 3D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = d2psidx(i,3) = d2psidx(i,4) = d2psidx(i,5) = . 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) = 2D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = 3D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = d2psidx(i,3) = d2psidx(i,4) = d2psidx(i,5) = . 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 ¤t_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 ¤t_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 unsigned | nvertex_node () const |
Return the number of vertex nodes in this element. Broken virtual function in "pure" finite elements. More... | |
virtual Node * | vertex_node_pt (const unsigned &j) const |
Pointer to the j-th vertex node in the element. Broken virtual function in "pure" finite elements. 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: . 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 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 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 . 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 . 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 . 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 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 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 ¤t_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 ¶meter_pt, Vector< double > &dres_dparam) |
Calculate the derivatives of the residuals with respect to a parameter. More... | |
virtual void | get_djacobian_dparameter (double *const ¶meter_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 ¶meter_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: = 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: = 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: = drdzeta(alpha,i). = 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 | 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 of the derivative of the shape functions 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 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 , 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) = 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 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 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 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 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 ¶meter_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 ¶meter_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 ¶meter_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_any_repeated_data = false |
Static boolean to suppress warnings about repeated data. Defaults to false. More... | |
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... | |
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.
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.
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.
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inline |
Constructor.
Definition at line 64 of file axisym_poroelasticity_elements.h.
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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().
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inline |
Access function for pointer to alpha, the Biot parameter.
Definition at line 177 of file axisym_poroelasticity_elements.h.
References Alpha_pt.
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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().
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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().
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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().
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Is Darcy flow switched off?
Definition at line 1008 of file axisym_poroelasticity_elements.h.
References Darcy_is_switched_off.
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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().
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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.
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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().
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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().
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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().
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Returns the local coordinate of the jth flux_interpolation point along the specified edge.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
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pure virtual |
Compute the global coordinates of the jth flux_interpolation point along an edge.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
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pure virtual |
Return the face index associated with specified edge.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
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pure virtual |
Return the face index associated with j-th edge flux degree of freedom.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
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pure virtual |
Compute the face element coordinates of the nth flux interpolation point along an edge.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
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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().
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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().
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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().
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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().
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Access function: Pointer to fluid force function.
Definition at line 207 of file axisym_poroelasticity_elements.h.
References Fluid_body_force_fct_pt.
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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.
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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().
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pure virtual |
Compute the pressure basis.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >, oomph::TAxisymmetricPoroelasticityElement< ORDER >, and oomph::TAxisymmetricPoroelasticityElement< ORDER >.
Referenced by interpolated_p().
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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().
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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().
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inlinevirtual |
Z2 flux (use Darcy flux)
Implements oomph::ElementWithZ2ErrorEstimator.
Definition at line 1275 of file axisym_poroelasticity_elements.h.
References interpolated_q(), and s.
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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().
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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.
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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().
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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().
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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().
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Calculate the FE representation of p and return it.
Definition at line 869 of file axisym_poroelasticity_elements.h.
References interpolated_p(), and s.
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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().
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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.
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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.
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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.
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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().
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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().
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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().
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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().
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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().
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Access function for pointer to timescale ratio (nondim density)
Definition at line 124 of file axisym_poroelasticity_elements.h.
References Lambda_sq_pt.
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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().
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Access function: Pointer to mass source function.
Definition at line 219 of file axisym_poroelasticity_elements.h.
References Mass_source_fct_pt.
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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.
|
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 >.
|
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().
|
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().
|
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().
|
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().
|
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.
|
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().
|
inline |
Access function for pointer to Poisson's ratio.
Definition at line 112 of file axisym_poroelasticity_elements.h.
References Nu_pt.
|
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.
|
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().
|
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().
|
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().
|
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().
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.
|
pure virtual |
Return pointer to the Data object that stores the pressure values.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
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().
|
pure virtual |
Return the jth pressure value.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
Referenced by fill_in_generic_residual_contribution(), and interpolated_p().
|
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().
|
inline |
Access function for pointer to the nondim permeability.
Definition at line 148 of file axisym_poroelasticity_elements.h.
References Permeability_pt.
|
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().
|
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.
|
pure virtual |
Pin the jth pressure value and set it to p.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
Referenced by switch_off_darcy().
|
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().
|
pure virtual |
Pin the jth internal q value and set it to specified value.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
Referenced by switch_off_darcy().
|
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.
|
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().
|
inline |
Access function for pointer to the porosity.
Definition at line 189 of file axisym_poroelasticity_elements.h.
References Porosity_pt.
|
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().
|
pure virtual |
Return the values of the j-th edge (flux) degree of freedom at time history level t.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Return vector of pointers to the Data objects that store the edge flux values.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Return the nodal index at which the jth edge unknown is stored.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
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().
|
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().
|
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().
|
pure virtual |
Return the values of the j-th internal degree of freedom at time history level t.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Return pointer to the Data object that stores the internal flux values.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
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().
|
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().
|
pure virtual |
Number of values required at node n.
Reimplemented from oomph::FiniteElement.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
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.
|
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.
|
pure virtual |
Scale the edge basis to allow arbitrary edge mappings.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
Referenced by transform_basis().
|
inlinevirtual |
Self test.
Reimplemented from oomph::FiniteElement.
Definition at line 1044 of file axisym_poroelasticity_elements.h.
|
pure virtual |
Set the jth pressure value.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Set the values of the j-th edge (flux) degree of freedom.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Set the values of the j-th edge (flux) degree of freedom at time history level t.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Set the values of the j-th internal degree of freedom.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
pure virtual |
Set the values of the j-th internal degree of freedom at time history level t.
Implemented in oomph::TAxisymmetricPoroelasticityElement< ORDER >.
|
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().
|
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 >.
|
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().
|
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().
|
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.
|
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.
|
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().
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().
|
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().
|
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().
|
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().
|
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.
|
private |
Alpha – the biot parameter.
Definition at line 1348 of file axisym_poroelasticity_elements.h.
Referenced by alpha(), and alpha_pt().
|
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().
|
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.
|
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.
|
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.
|
staticprivate |
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.
|
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.
|
staticprivate |
Static default value for the porosity.
Definition at line 1383 of file axisym_poroelasticity_elements.h.
|
staticprivate |
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.
|
private |
Density ratio.
Definition at line 1338 of file axisym_poroelasticity_elements.h.
Referenced by density_ratio(), and density_ratio_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().
|
private |
Timescale ratio (non-dim. density)
Definition at line 1335 of file axisym_poroelasticity_elements.h.
Referenced by lambda_sq(), and lambda_sq_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().
|
private |
Pointer to Poisson's ratio.
Definition at line 1332 of file axisym_poroelasticity_elements.h.
|
private |
permeability
Definition at line 1341 of file axisym_poroelasticity_elements.h.
Referenced by permeability(), and permeability_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().
|
private |
Porosity.
Definition at line 1351 of file axisym_poroelasticity_elements.h.
Referenced by porosity(), and porosity_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().
|
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().