DUNE-FEM (unstable)

raviartthomassimplexinterpolation.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
4// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS_RAVIARTTHOMASSIMPLEX_RAVIARTTHOMASSIMPLEXINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS_RAVIARTTHOMASSIMPLEX_RAVIARTTHOMASSIMPLEXINTERPOLATION_HH
7
8#include <fstream>
9#include <utility>
10
12
14#include <dune/geometry/referenceelements.hh>
15#include <dune/geometry/type.hh>
17
18#include <dune/localfunctions/common/localkey.hh>
19#include <dune/localfunctions/utility/interpolationhelper.hh>
20#include <dune/localfunctions/utility/polynomialbasis.hh>
21#include <dune/localfunctions/orthonormal/orthonormalbasis.hh>
22
23namespace Dune
24{
25
26 // Internal Forward Declarations
27 // -----------------------------
28
29 template < unsigned int dim, class Field >
30 struct RaviartThomasL2InterpolationFactory;
31
32
33
34 // LocalCoefficientsContainer
35 // --------------------------
36
37 class LocalCoefficientsContainer
38 {
39 typedef LocalCoefficientsContainer This;
40
41 public:
42 template <class Setter>
43 LocalCoefficientsContainer ( const Setter &setter )
44 {
45 setter.setLocalKeys(localKey_);
46 }
47
48 const LocalKey &localKey ( const unsigned int i ) const
49 {
50 assert( i < size() );
51 return localKey_[ i ];
52 }
53
54 std::size_t size () const
55 {
56 return localKey_.size();
57 }
58
59 private:
60 std::vector< LocalKey > localKey_;
61 };
62
63
64
65 // RaviartThomasCoefficientsFactory
66 // --------------------------------
67
68 template < unsigned int dim >
69 struct RaviartThomasCoefficientsFactory
70 {
71 typedef std::size_t Key;
72 typedef const LocalCoefficientsContainer Object;
73
74 template< GeometryType::Id geometryId >
75 static Object *create( const Key &key )
76 {
77 typedef RaviartThomasL2InterpolationFactory< dim, double > InterpolationFactory;
78 if( !supports< geometryId >( key ) )
79 return nullptr;
80 typename InterpolationFactory::Object *interpolation = InterpolationFactory::template create< geometryId >( key );
81 Object *localKeys = new Object( *interpolation );
82 InterpolationFactory::release( interpolation );
83 return localKeys;
84 }
85
86 template< GeometryType::Id geometryId >
87 static bool supports ( const Key &key )
88 {
89 return GeometryType(geometryId).isSimplex();
90 }
91 static void release( Object *object ) { delete object; }
92 };
93
94
95
96 // RTL2InterpolationBuilder
97 // ------------------------
98
99 // L2 Interpolation requires:
100 // - for element
101 // - test basis
102 // - for each face (dynamic)
103 // - test basis
104 // - normal
105 template< unsigned int dim, class Field >
106 struct RTL2InterpolationBuilder
107 {
108 static const unsigned int dimension = dim;
109
110 // for the dofs associated to the element
111 typedef OrthonormalBasisFactory< dimension, Field > TestBasisFactory;
112 typedef typename TestBasisFactory::Object TestBasis;
113
114 // for the dofs associated to the faces
115 typedef OrthonormalBasisFactory< dimension-1, Field > TestFaceBasisFactory;
116 typedef typename TestFaceBasisFactory::Object TestFaceBasis;
117
118 // the normals of the faces
119 typedef FieldVector< Field, dimension > Normal;
120
121 RTL2InterpolationBuilder () = default;
122
123 RTL2InterpolationBuilder ( const RTL2InterpolationBuilder & ) = delete;
124 RTL2InterpolationBuilder ( RTL2InterpolationBuilder && ) = delete;
125
126 ~RTL2InterpolationBuilder ()
127 {
128 TestBasisFactory::release( testBasis_ );
129 for( FaceStructure &f : faceStructure_ )
130 TestFaceBasisFactory::release( f.basis_ );
131 }
132
133 GeometryType type () const { return geometry_; }
134
135 std::size_t order () const { return order_; }
136
137 // number of faces
138 unsigned int faceSize () const { return faceSize_; }
139
140 // basis associated to the element
141 TestBasis *testBasis () const { return testBasis_; }
142
143 // basis associated to face f
144 TestFaceBasis *testFaceBasis ( unsigned int f ) const { assert( f < faceSize() ); return faceStructure_[ f ].basis_; }
145
146 // normal of face f
147 const Normal normal ( unsigned int f ) const { assert( f < faceSize() ); return faceStructure_[ f ].normal_; }
148
149 template< GeometryType::Id geometryId >
150 void build ( std::size_t order )
151 {
152 constexpr GeometryType geometry = geometryId;
153 geometry_ = geometry;
154 order_ = order;
155
156 testBasis_ = (order > 0 ? TestBasisFactory::template create< geometry >( order-1 ) : nullptr);
157
158 const auto &refElement = ReferenceElements< Field, dimension >::general( type() );
159 faceSize_ = refElement.size( 1 );
160 faceStructure_.reserve( faceSize_ );
161 for( unsigned int face = 0; face < faceSize_; ++face )
162 {
163 /* For simplices or cubes of arbitrary dimension you could just use
164 *
165 * ```
166 * GeometryType faceGeometry = Impl::getBase(geometry_);
167 * TestFaceBasis *faceBasis = TestFaceBasisFactory::template create< faceGeometry >( order );
168 * ```
169 *
170 * For i.e. Prisms and Pyramids in 3d this does not work because they contain squares and triangles as faces.
171 * And depending on the dynamic face index a different face geometry is needed.
172 *
173 */
174 TestFaceBasis *faceBasis = Impl::toGeometryTypeIdConstant<dimension-1>(refElement.type( face, 1 ), [&](auto faceGeometryTypeId) {
175 return TestFaceBasisFactory::template create< decltype(faceGeometryTypeId)::value >( order );
176 });
177 faceStructure_.emplace_back( faceBasis, refElement.integrationOuterNormal( face ) );
178 }
179 assert( faceStructure_.size() == faceSize_ );
180 }
181
182 private:
183 struct FaceStructure
184 {
185 FaceStructure( TestFaceBasis *tfb, const Normal n )
186 : basis_( tfb ), normal_( n )
187 {}
188
189 TestFaceBasis *basis_;
191 };
192
193 std::vector< FaceStructure > faceStructure_;
194 TestBasis *testBasis_ = nullptr;
195 GeometryType geometry_;
196 unsigned int faceSize_;
197 std::size_t order_;
198 };
199
200
201
202 // RaviartThomasL2Interpolation
203 // ----------------------------
204
210 template< unsigned int dimension, class F>
212 : public InterpolationHelper< F ,dimension >
213 {
215 typedef InterpolationHelper<F,dimension> Base;
216
217 public:
218 typedef F Field;
219 typedef RTL2InterpolationBuilder<dimension,Field> Builder;
221 : order_(0),
222 size_(0)
223 {}
224
225 template< class Function, class Vector,
226 decltype(std::declval<Vector>().size(),bool{}) = true,
227 decltype(std::declval<Vector>().resize(0u),bool{}) = true>
228 void interpolate ( const Function &function, Vector &coefficients ) const
229 {
230 coefficients.resize(size());
231 typename Base::template Helper<Function,Vector,true> func( function,coefficients );
232 interpolate(func);
233 }
234
235 template< class Basis, class Matrix,
236 decltype(std::declval<Matrix>().rows(),bool{}) = true,
237 decltype(std::declval<Matrix>().cols(),bool{}) = true,
238 decltype(std::declval<Matrix>().resize(0u,0u),bool{}) = true>
239 void interpolate ( const Basis &basis, Matrix &matrix ) const
240 {
241 matrix.resize( size(), basis.size() );
242 typename Base::template Helper<Basis,Matrix,false> func( basis,matrix );
243 interpolate(func);
244 }
245
246 std::size_t order() const
247 {
248 return order_;
249 }
250 std::size_t size() const
251 {
252 return size_;
253 }
254 template <GeometryType::Id geometryId>
255 void build( std::size_t order )
256 {
257 size_ = 0;
258 order_ = order;
259 builder_.template build<geometryId>(order_);
260 if (builder_.testBasis())
261 size_ += dimension*builder_.testBasis()->size();
262 for ( unsigned int f=0; f<builder_.faceSize(); ++f )
263 if (builder_.testFaceBasis(f))
264 size_ += builder_.testFaceBasis(f)->size();
265 }
266
267 void setLocalKeys(std::vector< LocalKey > &keys) const
268 {
269 keys.resize(size());
270 unsigned int row = 0;
271 for (unsigned int f=0; f<builder_.faceSize(); ++f)
272 {
273 if (builder_.faceSize())
274 for (unsigned int i=0; i<builder_.testFaceBasis(f)->size(); ++i,++row)
275 keys[row] = LocalKey(f,1,i);
276 }
277 if (builder_.testBasis())
278 for (unsigned int i=0; i<builder_.testBasis()->size()*dimension; ++i,++row)
279 keys[row] = LocalKey(0,0,i);
280 assert( row == size() );
281 }
282
283 protected:
284 template< class Func, class Container, bool type >
285 void interpolate ( typename Base::template Helper<Func,Container,type> &func ) const
286 {
287 const Dune::GeometryType geoType = builder_.type();
288
289 std::vector< Field > testBasisVal;
290
291 for (unsigned int i=0; i<size(); ++i)
292 for (unsigned int j=0; j<func.size(); ++j)
293 func.set(i,j,0);
294
295 unsigned int row = 0;
296
297 // boundary dofs:
298 typedef Dune::QuadratureRule<Field, dimension-1> FaceQuadrature;
299 typedef Dune::QuadratureRules<Field, dimension-1> FaceQuadratureRules;
300
301 const auto &refElement = Dune::ReferenceElements< Field, dimension >::general( geoType );
302
303 for (unsigned int f=0; f<builder_.faceSize(); ++f)
304 {
305 if (!builder_.testFaceBasis(f))
306 continue;
307 testBasisVal.resize(builder_.testFaceBasis(f)->size());
308
309 const auto &geometry = refElement.template geometry< 1 >( f );
310 const Dune::GeometryType subGeoType( geometry.type().id(), dimension-1 );
311 const FaceQuadrature &faceQuad = FaceQuadratureRules::rule( subGeoType, 2*order_+2 );
312
313 const unsigned int quadratureSize = faceQuad.size();
314 for( unsigned int qi = 0; qi < quadratureSize; ++qi )
315 {
316 if (dimension>1)
317 builder_.testFaceBasis(f)->template evaluate<0>(faceQuad[qi].position(),testBasisVal);
318 else
319 testBasisVal[0] = 1.;
320 fillBnd( row, testBasisVal,
321 func.evaluate( geometry.global( faceQuad[qi].position() ) ),
322 builder_.normal(f), faceQuad[qi].weight(),
323 func);
324 }
325
326 row += builder_.testFaceBasis(f)->size();
327 }
328 // element dofs
329 if (builder_.testBasis())
330 {
331 testBasisVal.resize(builder_.testBasis()->size());
332
335 const Quadrature &elemQuad = QuadratureRules::rule( geoType, 2*order_+1 );
336
337 const unsigned int quadratureSize = elemQuad.size();
338 for( unsigned int qi = 0; qi < quadratureSize; ++qi )
339 {
340 builder_.testBasis()->template evaluate<0>(elemQuad[qi].position(),testBasisVal);
341 fillInterior( row, testBasisVal,
342 func.evaluate(elemQuad[qi].position()),
343 elemQuad[qi].weight(),
344 func );
345 }
346
347 row += builder_.testBasis()->size()*dimension;
348 }
349 assert(row==size());
350 }
351
352 private:
362 template <class MVal, class RTVal,class Matrix>
363 void fillBnd (unsigned int startRow,
364 const MVal &mVal,
365 const RTVal &rtVal,
366 const FieldVector<Field,dimension> &normal,
367 const Field &weight,
368 Matrix &matrix) const
369 {
370 const unsigned int endRow = startRow+mVal.size();
371 typename RTVal::const_iterator rtiter = rtVal.begin();
372 for ( unsigned int col = 0; col < rtVal.size() ; ++rtiter,++col)
373 {
374 Field cFactor = (*rtiter)*normal;
375 typename MVal::const_iterator miter = mVal.begin();
376 for (unsigned int row = startRow;
377 row!=endRow; ++miter, ++row )
378 {
379 matrix.add(row,col, (weight*cFactor)*(*miter) );
380 }
381 assert( miter == mVal.end() );
382 }
383 }
392 template <class MVal, class RTVal,class Matrix>
393 void fillInterior (unsigned int startRow,
394 const MVal &mVal,
395 const RTVal &rtVal,
396 Field weight,
397 Matrix &matrix) const
398 {
399 const unsigned int endRow = startRow+mVal.size()*dimension;
400 typename RTVal::const_iterator rtiter = rtVal.begin();
401 for ( unsigned int col = 0; col < rtVal.size() ; ++rtiter,++col)
402 {
403 typename MVal::const_iterator miter = mVal.begin();
404 for (unsigned int row = startRow;
405 row!=endRow; ++miter,row+=dimension )
406 {
407 for (unsigned int i=0; i<dimension; ++i)
408 {
409 matrix.add(row+i,col, (weight*(*miter))*(*rtiter)[i] );
410 }
411 }
412 assert( miter == mVal.end() );
413 }
414 }
415
416 Builder builder_;
417 std::size_t order_;
418 std::size_t size_;
419 };
420
421 template < unsigned int dim, class Field >
422 struct RaviartThomasL2InterpolationFactory
423 {
424 typedef RTL2InterpolationBuilder<dim,Field> Builder;
425 typedef const RaviartThomasL2Interpolation<dim,Field> Object;
426 typedef std::size_t Key;
427 typedef typename std::remove_const<Object>::type NonConstObject;
428
429 template <GeometryType::Id geometryId>
430 static Object *create( const Key &key )
431 {
432 if ( !supports<geometryId>(key) )
433 return 0;
434 NonConstObject *interpol = new NonConstObject();
435 interpol->template build<geometryId>(key);
436 return interpol;
437 }
438 template< GeometryType::Id geometryId >
439 static bool supports ( const Key &key )
440 {
441 return GeometryType(geometryId).isSimplex();
442 }
443 static void release( Object *object ) { delete object; }
444 };
445
446} // namespace Dune
447
448#endif // #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS_RAVIARTTHOMASSIMPLEX_RAVIARTTHOMASSIMPLEXINTERPOLATION_HH
Iterator begin()
begin iterator
Definition: densevector.hh:347
Unique label for each type of entities that can occur in DUNE grids.
Definition: type.hh:114
Describe position of one degree of freedom.
Definition: localkey.hh:24
A generic dynamic dense matrix.
Definition: matrix.hh:561
Abstract base class for quadrature rules.
Definition: quadraturerules.hh:214
A container for all quadrature rules of dimension dim
Definition: quadraturerules.hh:260
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:326
An L2-based interpolation for Raviart Thomas.
Definition: raviartthomassimplexinterpolation.hh:213
A few common exception classes.
GeometryType
Type representing VTK's entity geometry types.
Definition: common.hh:132
Dune namespace.
Definition: alignedallocator.hh:13
constexpr std::integral_constant< std::size_t, sizeof...(II)> size(std::integer_sequence< T, II... >)
Return the size of the sequence.
Definition: integersequence.hh:75
static const ReferenceElement & general(const GeometryType &type)
get general reference elements
Definition: referenceelements.hh:156
A unique label for each type of element that can occur in a grid.
Helper classes to provide indices for geometrytypes for use in a vector.
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