Tpoisson_elements.h
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26// Header file for TPoisson elements
27#ifndef OOMPH_TPOISSON_ELEMENTS_HEADER
28#define OOMPH_TPOISSON_ELEMENTS_HEADER
29
30
31// Config header generated by autoconfig
32#ifdef HAVE_CONFIG_H
33#include <oomph-lib-config.h>
34#endif
35
36
37// OOMPH-LIB headers
38#include "../generic/nodes.h"
39#include "../generic/oomph_utilities.h"
40#include "../generic/Telements.h"
41#include "../generic/error_estimator.h"
42#include "poisson_elements.h"
43
44namespace oomph
45{
46 /// //////////////////////////////////////////////////////////////////////
47 /// //////////////////////////////////////////////////////////////////////
48 // TPoissonElement
49 /// /////////////////////////////////////////////////////////////////////
50 /// /////////////////////////////////////////////////////////////////////
51
52
53 //======================================================================
54 /// TPoissonElement<DIM,NNODE_1D> elements are isoparametric triangular
55 /// DIM-dimensional Poisson elements with NNODE_1D nodal points along each
56 /// element edge. Inherits from TElement and PoissonEquations
57 //======================================================================
58 template<unsigned DIM, unsigned NNODE_1D>
59 class TPoissonElement : public virtual TElement<DIM, NNODE_1D>,
60 public virtual PoissonEquations<DIM>,
61 public virtual ElementWithZ2ErrorEstimator
62 {
63 public:
64 /// Constructor: Call constructors for TElement and
65 /// Poisson equations
66 TPoissonElement() : TElement<DIM, NNODE_1D>(), PoissonEquations<DIM>() {}
67
68
69 /// Broken copy constructor
71
72 /// Broken assignment operator
74
75 /// Access function for Nvalue: # of `values' (pinned or dofs)
76 /// at node n (always returns the same value at every node, 1)
77 inline unsigned required_nvalue(const unsigned& n) const
78 {
79 return Initial_Nvalue;
80 }
81
82 /// Output function:
83 /// x,y,u or x,y,z,u
84 void output(std::ostream& outfile)
85 {
87 }
88
89 /// Output function:
90 /// x,y,u or x,y,z,u at n_plot^DIM plot points
91 void output(std::ostream& outfile, const unsigned& n_plot)
92 {
93 PoissonEquations<DIM>::output(outfile, n_plot);
94 }
95
96
97 /// C-style output function:
98 /// x,y,u or x,y,z,u
99 void output(FILE* file_pt)
100 {
102 }
103
104
105 /// C-style output function:
106 /// x,y,u or x,y,z,u at n_plot^DIM plot points
107 void output(FILE* file_pt, const unsigned& n_plot)
108 {
109 PoissonEquations<DIM>::output(file_pt, n_plot);
110 }
111
112
113 /// Output function for an exact solution:
114 /// x,y,u_exact
115 void output_fct(std::ostream& outfile,
116 const unsigned& n_plot,
118 {
119 PoissonEquations<DIM>::output_fct(outfile, n_plot, exact_soln_pt);
120 }
121
122
123 /// Output function for a time-dependent exact solution.
124 /// x,y,u_exact (calls the steady version)
125 void output_fct(std::ostream& outfile,
126 const unsigned& n_plot,
127 const double& time,
129 {
130 PoissonEquations<DIM>::output_fct(outfile, n_plot, time, exact_soln_pt);
131 }
132
133 protected:
134 /// Shape, test functions & derivs. w.r.t. to global coords. Return
135 /// Jacobian.
137 Shape& psi,
138 DShape& dpsidx,
139 Shape& test,
140 DShape& dtestdx) const;
141
142
143 /// Shape, test functions & derivs. w.r.t. to global coords. Return
144 /// Jacobian.
146 const unsigned& ipt,
147 Shape& psi,
148 DShape& dpsidx,
149 Shape& test,
150 DShape& dtestdx) const;
151
152 /// Shape/test functions and derivs w.r.t. to global coords at
153 /// integration point ipt; return Jacobian of mapping (J). Also compute
154 /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
156 const unsigned& ipt,
157 Shape& psi,
158 DShape& dpsidx,
159 RankFourTensor<double>& d_dpsidx_dX,
160 Shape& test,
161 DShape& dtestdx,
162 RankFourTensor<double>& d_dtestdx_dX,
163 DenseMatrix<double>& djacobian_dX) const;
164
165 /// Order of recovery shape functions for Z2 error estimation:
166 /// Same order as shape functions.
168 {
169 return (NNODE_1D - 1);
170 }
171
172 /// Number of 'flux' terms for Z2 error estimation
174 {
175 return DIM;
176 }
177
178 /// Get 'flux' for Z2 error recovery: Standard flux.from Poisson equations
180 {
181 this->get_flux(s, flux);
182 }
183
184 /// Number of vertex nodes in the element
185 unsigned nvertex_node() const
186 {
188 }
189
190 /// Pointer to the j-th vertex node in the element
191 Node* vertex_node_pt(const unsigned& j) const
192 {
194 }
195
196 private:
197 /// Static unsigned that holds the (same) number of variables at every node
198 static const unsigned Initial_Nvalue;
199 };
200
201
202 // Inline functions:
203
204
205 //======================================================================
206 /// Define the shape functions and test functions and derivatives
207 /// w.r.t. global coordinates and return Jacobian of mapping.
208 ///
209 /// Galerkin: Test functions = shape functions
210 //======================================================================
211 template<unsigned DIM, unsigned NNODE_1D>
213 const Vector<double>& s,
214 Shape& psi,
215 DShape& dpsidx,
216 Shape& test,
217 DShape& dtestdx) const
218 {
219 unsigned n_node = this->nnode();
220
221 // Call the geometrical shape functions and derivatives
222 double J = this->dshape_eulerian(s, psi, dpsidx);
223
224 // Loop over the test functions and derivatives and set them equal to the
225 // shape functions
226 for (unsigned i = 0; i < n_node; i++)
227 {
228 test[i] = psi[i];
229 dtestdx(i, 0) = dpsidx(i, 0);
230 dtestdx(i, 1) = dpsidx(i, 1);
231 }
232
233 // Return the jacobian
234 return J;
235 }
236
237
238 //======================================================================
239 /// Define the shape functions and test functions and derivatives
240 /// w.r.t. global coordinates and return Jacobian of mapping.
241 ///
242 /// Galerkin: Test functions = shape functions
243 //======================================================================
244 template<unsigned DIM, unsigned NNODE_1D>
247 Shape& psi,
248 DShape& dpsidx,
249 Shape& test,
250 DShape& dtestdx) const
251 {
252 // Call the geometrical shape functions and derivatives
253 double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
254
255 // Set the pointers of the test functions
256 test = psi;
257 dtestdx = dpsidx;
258
259 // Return the jacobian
260 return J;
261 }
262
263
264 //======================================================================
265 /// Define the shape functions (psi) and test functions (test) and
266 /// their derivatives w.r.t. global coordinates (dpsidx and dtestdx)
267 /// and return Jacobian of mapping (J). Additionally compute the
268 /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
269 ///
270 /// Galerkin: Test functions = shape functions
271 //======================================================================
272 template<unsigned DIM, unsigned NNODE_1D>
275 const unsigned& ipt,
276 Shape& psi,
277 DShape& dpsidx,
278 RankFourTensor<double>& d_dpsidx_dX,
279 Shape& test,
280 DShape& dtestdx,
281 RankFourTensor<double>& d_dtestdx_dX,
282 DenseMatrix<double>& djacobian_dX) const
283 {
284 // Call the geometrical shape functions and derivatives
285 const double J = this->dshape_eulerian_at_knot(
286 ipt, psi, dpsidx, djacobian_dX, d_dpsidx_dX);
287
288 // Set the pointers of the test functions
289 test = psi;
290 dtestdx = dpsidx;
291 d_dtestdx_dX = d_dpsidx_dX;
292
293 // Return the jacobian
294 return J;
295 }
296
297
298 //=======================================================================
299 /// Face geometry for the TPoissonElement elements: The spatial
300 /// dimension of the face elements is one lower than that of the
301 /// bulk element but they have the same number of points
302 /// along their 1D edges.
303 //=======================================================================
304 template<unsigned DIM, unsigned NNODE_1D>
305 class FaceGeometry<TPoissonElement<DIM, NNODE_1D>>
306 : public virtual TElement<DIM - 1, NNODE_1D>
307 {
308 public:
309 /// Constructor: Call the constructor for the
310 /// appropriate lower-dimensional TElement
311 FaceGeometry() : TElement<DIM - 1, NNODE_1D>() {}
312 };
313
314 //=======================================================================
315 /// Face geometry for the 1D TPoissonElement elements: Point elements
316 //=======================================================================
317 template<unsigned NNODE_1D>
318 class FaceGeometry<TPoissonElement<1, NNODE_1D>> : public virtual PointElement
319 {
320 public:
321 /// Constructor: Call the constructor for the
322 /// appropriate lower-dimensional TElement
324 };
325
326
327} // namespace oomph
328
329#endif
static char t char * s
Definition: cfortran.h:568
cstr elem_len * i
Definition: cfortran.h:603
A Class for the derivatives of shape functions The class design is essentially the same as Shape,...
Definition: shape.h:278
Base class for finite elements that can compute the quantities that are required for the Z2 error est...
FaceGeometry()
Constructor: Call the constructor for the appropriate lower-dimensional TElement.
FaceGeometry()
Constructor: Call the constructor for the appropriate lower-dimensional TElement.
//////////////////////////////////////////////////////////////////// ////////////////////////////////...
Definition: elements.h:4998
void(* SteadyExactSolutionFctPt)(const Vector< double > &, Vector< double > &)
Function pointer for function that computes vector-valued steady "exact solution" as .
Definition: elements.h:1759
void(* UnsteadyExactSolutionFctPt)(const double &, const Vector< double > &, Vector< double > &)
Function pointer for function that computes Vector-valued time-dependent function as .
Definition: elements.h:1765
Nodes are derived from Data, but, in addition, have a definite (Eulerian) position in a space of a gi...
Definition: nodes.h:906
/////////////////////////////////////////////////////////////////////// /////////////////////////////...
Definition: elements.h:3439
A class for all isoparametric elements that solve the Poisson equations.
void output(std::ostream &outfile)
Output with default number of plot points.
void get_flux(const Vector< double > &s, Vector< double > &flux) const
Get flux: flux[i] = du/dx_i.
void output_fct(std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
Output exact soln: x,y,u_exact or x,y,z,u_exact at n_plot^DIM plot points.
////////////////////////////////////////////////////////////////// //////////////////////////////////...
Definition: matrices.h:1701
A Class for shape functions. In simple cases, the shape functions have only one index that can be tho...
Definition: shape.h:76
General TElement class.
Definition: Telements.h:1208
//////////////////////////////////////////////////////////////////////
void output_fct(std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
Output function for a time-dependent exact solution. x,y,u_exact (calls the steady version)
void output(FILE *file_pt)
C-style output function: x,y,u or x,y,z,u.
void output(std::ostream &outfile)
Output function: x,y,u or x,y,z,u.
TPoissonElement()
Constructor: Call constructors for TElement and Poisson equations.
void output_fct(std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
Output function for an exact solution: x,y,u_exact.
unsigned num_Z2_flux_terms()
Number of 'flux' terms for Z2 error estimation.
unsigned nvertex_node() const
Number of vertex nodes in the element.
void output(std::ostream &outfile, const unsigned &n_plot)
Output function: x,y,u or x,y,z,u at n_plot^DIM plot points.
double dshape_and_dtest_eulerian_at_knot_poisson(const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
Shape, test functions & derivs. w.r.t. to global coords. Return Jacobian.
void output(FILE *file_pt, const unsigned &n_plot)
C-style output function: x,y,u or x,y,z,u at n_plot^DIM plot points.
double dshape_and_dtest_eulerian_poisson(const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
Shape, test functions & derivs. w.r.t. to global coords. Return Jacobian.
unsigned required_nvalue(const unsigned &n) const
Access function for Nvalue: # of ‘values’ (pinned or dofs) at node n (always returns the same value a...
Node * vertex_node_pt(const unsigned &j) const
Pointer to the j-th vertex node in the element.
void operator=(const TPoissonElement< DIM, NNODE_1D > &)=delete
Broken assignment operator.
TPoissonElement(const TPoissonElement< DIM, NNODE_1D > &dummy)=delete
Broken copy constructor.
void get_Z2_flux(const Vector< double > &s, Vector< double > &flux)
Get 'flux' for Z2 error recovery: Standard flux.from Poisson equations.
static const unsigned Initial_Nvalue
Static unsigned that holds the (same) number of variables at every node.
unsigned nrecovery_order()
Order of recovery shape functions for Z2 error estimation: Same order as shape functions.
//////////////////////////////////////////////////////////////////// ////////////////////////////////...