spectral_poisson_elements.h
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25// LIC//====================================================================
26// Header file for Spectral Poisson elements
27#ifndef OOMPH_SPECTRAL_POISSON_ELEMENTS_HEADER
28#define OOMPH_SPECTRAL_POISSON_ELEMENTS_HEADER
29
30// Config header generated by autoconfig
31#ifdef HAVE_CONFIG_H
32#include <oomph-lib-config.h>
33#endif
34
35// OOMPH-LIB headers
36#include "poisson_elements.h"
37#include "../generic/Qspectral_elements.h"
38
39namespace oomph
40{
41 //======================================================================
42 /// QSpectralPoissonElement elements are linear/quadrilateral/brick-shaped
43 /// Poisson elements with isoparametric spectral interpolation for the
44 /// function. Note that the implementation is PoissonEquations<DIM> does
45 /// not use sum factorisation for the evaluation of the residuals and is,
46 /// therefore, not optimal for higher dimensions.
47 //======================================================================
48 template<unsigned DIM, unsigned NNODE_1D>
50 : public virtual QSpectralElement<DIM, NNODE_1D>,
51 public virtual PoissonEquations<DIM>
52 {
53 private:
54 /// Static array of ints to hold number of variables at
55 /// nodes: Initial_Nvalue[n]
56 static const unsigned Initial_Nvalue;
57
58 public:
59 /// Constructor: Call constructors for QSpectralElement and
60 /// Poisson equations
62 : QSpectralElement<DIM, NNODE_1D>(), PoissonEquations<DIM>()
63 {
64 }
65
66 /// Broken copy constructor
68 const QSpectralPoissonElement<DIM, NNODE_1D>& dummy) = delete;
69
70 /// Broken assignment operator
71 // Commented out broken assignment operator because this can lead to a
72 // conflict warning when used in the virtual inheritence hierarchy.
73 // Essentially the compiler doesn't realise that two separate
74 // implementations of the broken function are the same and so, quite
75 // rightly, it shouts.
76 /*void operator=(const QSpectralPoissonElement<DIM,NNODE_1D>&) =
77 delete;*/
78
79 /// Required # of `values' (pinned or dofs)
80 /// at node n
81 inline unsigned required_nvalue(const unsigned& n) const
82 {
83 return Initial_Nvalue;
84 }
85
86 /// Output function:
87 /// x,y,u or x,y,z,u
88 void output(std::ostream& outfile)
89 {
91 }
92
93 /// Output function:
94 /// x,y,u or x,y,z,u at n_plot^DIM plot points
95 void output(std::ostream& outfile, const unsigned& n_plot)
96 {
97 PoissonEquations<DIM>::output(outfile, n_plot);
98 }
99
100
101 /// C-style output function:
102 /// x,y,u or x,y,z,u
103 void output(FILE* file_pt)
104 {
106 }
107
108
109 /// C-style output function:
110 /// x,y,u or x,y,z,u at n_plot^DIM plot points
111 void output(FILE* file_pt, const unsigned& n_plot)
112 {
113 PoissonEquations<DIM>::output(file_pt, n_plot);
114 }
115
116
117 /// Output function for an exact solution:
118 /// x,y,u_exact or x,y,z,u_exact at n_plot^DIM plot points
119 void output_fct(std::ostream& outfile,
120 const unsigned& n_plot,
122 {
123 PoissonEquations<DIM>::output_fct(outfile, n_plot, exact_soln_pt);
124 }
125
126
127 /// Output function for a time-dependent exact solution.
128 /// x,y,u_exact or x,y,z,u_exact at n_plot^DIM plot points
129 /// (Calls the steady version)
130 void output_fct(std::ostream& outfile,
131 const unsigned& n_plot,
132 const double& time,
134 {
135 PoissonEquations<DIM>::output_fct(outfile, n_plot, time, exact_soln_pt);
136 }
137
138
139 protected:
140 /// Shape, test functions & derivs. w.r.t. to global coords. Return
141 /// Jacobian.
143 Shape& psi,
144 DShape& dpsidx,
145 Shape& test,
146 DShape& dtestdx) const;
147
148
149 /// Shape, test functions & derivs. w.r.t. to global coords. at
150 /// integration point ipt. Return Jacobian.
152 const unsigned& ipt,
153 Shape& psi,
154 DShape& dpsidx,
155 Shape& test,
156 DShape& dtestdx) const;
157
158 /// Shape/test functions and derivs w.r.t. to global coords at
159 /// integration point ipt; return Jacobian of mapping (J). Also compute
160 /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
162 const unsigned& ipt,
163 Shape& psi,
164 DShape& dpsidx,
165 RankFourTensor<double>& d_dpsidx_dX,
166 Shape& test,
167 DShape& dtestdx,
168 RankFourTensor<double>& d_dtestdx_dX,
169 DenseMatrix<double>& djacobian_dX) const;
170 };
171
172
173 // Inline functions:
174
175
176 //======================================================================
177 /// Define the shape functions and test functions and derivatives
178 /// w.r.t. global coordinates and return Jacobian of mapping.
179 ///
180 /// Galerkin: Test functions = shape functions
181 //======================================================================
182 template<unsigned DIM, unsigned NNODE_1D>
185 Shape& psi,
186 DShape& dpsidx,
187 Shape& test,
188 DShape& dtestdx) const
189 {
190 // Call the geometrical shape functions and derivatives
191 double J = this->dshape_eulerian(s, psi, dpsidx);
192
193 // Loop over the test functions and derivatives and set them equal to the
194 // shape functions
195 unsigned nnod = this->nnode();
196 for (unsigned i = 0; i < nnod; i++)
197 {
198 test[i] = psi[i];
199 for (unsigned j = 0; j < DIM; j++)
200 {
201 dtestdx(i, j) = dpsidx(i, j);
202 }
203 }
204
205 // Return the jacobian
206 return J;
207 }
208
209 //======================================================================
210 /// Define the shape functions and test functions and derivatives
211 /// w.r.t. global coordinates and return Jacobian of mapping.
212 ///
213 /// Galerkin: Test functions = shape functions
214 //======================================================================
215 template<unsigned DIM, unsigned NNODE_1D>
218 Shape& psi,
219 DShape& dpsidx,
220 Shape& test,
221 DShape& dtestdx) const
222 {
223 // Call the geometrical shape functions and derivatives
224 double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
225
226 // Set the pointers of the test functions
227 test = psi;
228 dtestdx = dpsidx;
229
230 // Return the jacobian
231 return J;
232 }
233
234 //======================================================================
235 /// Define the shape functions (psi) and test functions (test) and
236 /// their derivatives w.r.t. global coordinates (dpsidx and dtestdx)
237 /// and return Jacobian of mapping (J). Additionally compute the
238 /// derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.
239 ///
240 /// Galerkin: Test functions = shape functions
241 //======================================================================
242 template<unsigned DIM, unsigned NNODE_1D>
245 const unsigned& ipt,
246 Shape& psi,
247 DShape& dpsidx,
248 RankFourTensor<double>& d_dpsidx_dX,
249 Shape& test,
250 DShape& dtestdx,
251 RankFourTensor<double>& d_dtestdx_dX,
252 DenseMatrix<double>& djacobian_dX) const
253 {
254 // Call the geometrical shape functions and derivatives
255 const double J = this->dshape_eulerian_at_knot(
256 ipt, psi, dpsidx, djacobian_dX, d_dpsidx_dX);
257
258 // Set the pointers of the test functions
259 test = psi;
260 dtestdx = dpsidx;
261 d_dtestdx_dX = d_dpsidx_dX;
262
263 // Return the jacobian
264 return J;
265 }
266
267 /// /////////////////////////////////////////////////////////////////////
268 /// /////////////////////////////////////////////////////////////////////
269 /// /////////////////////////////////////////////////////////////////////
270
271
272 //=======================================================================
273 /// Face geometry for the QSpectralPoissonElement elements: The spatial
274 /// dimension of the face elements is one lower than that of the
275 /// bulk element but they have the same number of points
276 /// along their 1D edges.
277 //=======================================================================
278 template<unsigned DIM, unsigned NNODE_1D>
280 : public virtual QSpectralElement<DIM - 1, NNODE_1D>
281 {
282 public:
283 /// Constructor: Call the constructor for the
284 /// appropriate lower-dimensional QElement
285 FaceGeometry() : QSpectralElement<DIM - 1, NNODE_1D>() {}
286 };
287
288
289 //=======================================================================
290 /// Face geometry for the 1D QPoissonElement elements: Point elements
291 //=======================================================================
292 template<unsigned NNODE_1D>
294 : public virtual PointElement
295 {
296 public:
297 /// Constructor: Call the constructor for the
298 /// appropriate lower-dimensional QElement
300 };
301
302} // namespace oomph
303
304#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
FaceGeometry()
Constructor: Call the constructor for the appropriate lower-dimensional QElement.
FaceGeometry()
Constructor: Call the constructor for the appropriate lower-dimensional QElement.
//////////////////////////////////////////////////////////////////// ////////////////////////////////...
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
/////////////////////////////////////////////////////////////////////// /////////////////////////////...
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 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.
General QLegendreElement class.
QSpectralPoissonElement elements are linear/quadrilateral/brick-shaped Poisson elements with isoparam...
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.
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 or x,y,z,u_exact at n_plot^DIM plot points.
QSpectralPoissonElement()
Constructor: Call constructors for QSpectralElement and Poisson equations.
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. at integration point ipt....
QSpectralPoissonElement(const QSpectralPoissonElement< DIM, NNODE_1D > &dummy)=delete
Broken copy constructor.
unsigned required_nvalue(const unsigned &n) const
Broken assignment operator.
void output(std::ostream &outfile)
Output function: x,y,u or x,y,z,u.
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 or x,y,z,u_exact at n_plot^DIM plot ...
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.
static const unsigned Initial_Nvalue
Static array of ints to hold number of variables at nodes: Initial_Nvalue[n].
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.
void output(FILE *file_pt)
C-style output function: x,y,u or x,y,z,u.
////////////////////////////////////////////////////////////////// //////////////////////////////////...
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
//////////////////////////////////////////////////////////////////// ////////////////////////////////...