3 #ifndef DUNE_MONOMIALBASIS_HH
4 #define DUNE_MONOMIALBASIS_HH
8 #include <dune/common/fvector.hh>
9 #include <dune/common/fmatrix.hh>
11 #include <dune/geometry/topologyfactory.hh>
12 #include <dune/geometry/genericgeometry/topologytypes.hh>
69 template<
class Topology >
70 class MonomialBasisSize;
72 template<
class Topology,
class F >
81 class MonomialBasisSize< GenericGeometry::Point >
88 static This _instance;
94 friend class MonomialBasisSize< GenericGeometry::Prism< Topology > >;
95 friend class MonomialBasisSize< GenericGeometry::Pyramid< Topology > >;
97 mutable unsigned int maxOrder_;
99 mutable unsigned int *sizes_;
101 mutable unsigned int *numBaseFunctions_;
106 numBaseFunctions_( 0 )
111 ~MonomialBasisSize ()
114 delete[] numBaseFunctions_;
117 unsigned int operator() (
const unsigned int order )
const
119 return numBaseFunctions_[ order ];
122 unsigned int maxOrder ()
const
127 void computeSizes (
unsigned int order )
const
129 if (order <= maxOrder_)
135 delete [] numBaseFunctions_;
136 sizes_ =
new unsigned int [ order+1 ];
137 numBaseFunctions_ =
new unsigned int [ order+1 ];
140 numBaseFunctions_[ 0 ] = 1;
141 for(
unsigned int k = 1; k <= order; ++k )
144 numBaseFunctions_[ k ] = 1;
149 template<
class BaseTopology >
150 class MonomialBasisSize< GenericGeometry::Prism< BaseTopology > >
152 typedef MonomialBasisSize< GenericGeometry::Prism< BaseTopology > >
This;
157 static This _instance;
161 typedef GenericGeometry::Prism< BaseTopology >
Topology;
163 friend class MonomialBasisSize< GenericGeometry::Prism< Topology > >;
164 friend class MonomialBasisSize< GenericGeometry::Pyramid< Topology > >;
166 mutable unsigned int maxOrder_;
168 mutable unsigned int *sizes_;
170 mutable unsigned int *numBaseFunctions_;
175 numBaseFunctions_( 0 )
180 ~MonomialBasisSize ()
183 delete[] numBaseFunctions_;
186 unsigned int operator() (
const unsigned int order )
const
188 return numBaseFunctions_[ order ];
191 unsigned int maxOrder()
const
196 void computeSizes (
unsigned int order )
const
198 if (order <= maxOrder_)
204 delete[] numBaseFunctions_;
205 sizes_ =
new unsigned int[ order+1 ];
206 numBaseFunctions_ =
new unsigned int[ order+1 ];
208 MonomialBasisSize<BaseTopology> &baseBasis =
209 MonomialBasisSize<BaseTopology>::instance();
210 baseBasis.computeSizes( order );
211 const unsigned int *
const baseSizes = baseBasis.sizes_;
212 const unsigned int *
const baseNBF = baseBasis.numBaseFunctions_;
215 numBaseFunctions_[ 0 ] = 1;
216 for(
unsigned int k = 1; k <= order; ++k )
218 sizes_[ k ] = baseNBF[ k ] + k*baseSizes[ k ];
219 numBaseFunctions_[ k ] = numBaseFunctions_[ k-1 ] + sizes_[ k ];
224 template<
class BaseTopology >
225 class MonomialBasisSize< GenericGeometry::Pyramid< BaseTopology > >
227 typedef MonomialBasisSize< GenericGeometry::Pyramid< BaseTopology > >
This;
232 static This _instance;
236 typedef GenericGeometry::Pyramid< BaseTopology >
Topology;
238 friend class MonomialBasisSize< GenericGeometry::Prism< Topology > >;
239 friend class MonomialBasisSize< GenericGeometry::Pyramid< Topology > >;
241 mutable unsigned int maxOrder_;
243 mutable unsigned int *sizes_;
245 mutable unsigned int *numBaseFunctions_;
250 numBaseFunctions_( 0 )
255 ~MonomialBasisSize ()
258 delete[] numBaseFunctions_;
261 unsigned int operator() (
const unsigned int order )
const
263 return numBaseFunctions_[ order ];
266 unsigned int maxOrder()
const
271 void computeSizes (
unsigned int order )
const
273 if (order <= maxOrder_)
279 delete[] numBaseFunctions_;
280 sizes_ =
new unsigned int[ order+1 ];
281 numBaseFunctions_ =
new unsigned int[ order+1 ];
283 MonomialBasisSize<BaseTopology> &baseBasis =
284 MonomialBasisSize<BaseTopology>::instance();
286 baseBasis.computeSizes( order );
288 const unsigned int *
const baseNBF = baseBasis.numBaseFunctions_;
290 numBaseFunctions_[ 0 ] = 1;
291 for(
unsigned int k = 1; k <= order; ++k )
293 sizes_[ k ] = baseNBF[ k ];
294 numBaseFunctions_[ k ] = numBaseFunctions_[ k-1 ] + sizes_[ k ];
305 template<
int mydim,
int dim,
class F >
308 typedef MonomialBasisSize< typename GenericGeometry::SimplexTopology< mydim >::type >
MySize;
309 typedef MonomialBasisSize< typename GenericGeometry::SimplexTopology< dim >::type >
Size;
311 static void copy (
const unsigned int deriv, F *&wit, F *&rit,
312 const unsigned int numBaseFunctions,
const F &z )
315 MySize &mySize = MySize::instance();
316 Size &size = Size::instance();
318 const F *
const rend = rit + size( deriv )*numBaseFunctions;
319 for( ; rit != rend; )
326 for(
unsigned d = 1; d <= deriv; ++d )
329 const F *
const derivEnd = rit + mySize.sizes_[ d ];
331 const F *
const drend = rit + mySize.sizes_[ d ] - mySize.sizes_[ d-1 ];
332 for( ; rit != drend ; ++rit, ++wit )
334 for (
unsigned int j=1; j<d; ++j)
336 const F *
const drend = rit + mySize.sizes_[ d-j ] - mySize.sizes_[ d-j-1 ];
337 for( ; rit != drend ; ++prit, ++rit, ++wit )
338 *wit = F(j) * *prit + z * *rit;
340 *wit = F(d) * *prit + z * *rit;
341 ++prit, ++rit, ++wit;
342 assert(derivEnd == rit);
343 rit += size.sizes_[d] - mySize.sizes_[d];
344 prit += size.sizes_[d-1] - mySize.sizes_[d-1];
345 const F *
const emptyWitEnd = wit + size.sizes_[d] - mySize.sizes_[d];
346 for ( ; wit != emptyWitEnd; ++wit )
358 template<
class Topology,
class F >
370 static const unsigned int dimDomain = Topology::dimension;
380 void evaluate ( const unsigned int deriv, const unsigned int order,
381 const FieldVector< Field, dimD > &x,
382 const unsigned int block, const unsigned int *const offsets,
383 Field *const values ) const
386 F *
const end = values + block;
387 for(
Field *it = values+1 ; it != end; ++it )
391 void integrate (
const unsigned int order,
392 const unsigned int *
const offsets,
393 Field *
const values )
const
399 template<
class BaseTopology,
class F >
405 typedef GenericGeometry::Prism< BaseTopology >
Topology;
408 static const unsigned int dimDomain = Topology::dimension;
417 typedef MonomialBasisSize< BaseTopology > BaseSize;
418 typedef MonomialBasisSize< Topology > Size;
426 void evaluate (
const unsigned int deriv,
const unsigned int order,
427 const FieldVector< Field, dimD > &x,
428 const unsigned int block,
const unsigned int *
const offsets,
429 Field *
const values )
const
432 const BaseSize &size = BaseSize::instance();
434 const Field &z = x[ dimDomain-1 ];
437 baseBasis_.evaluate( deriv, order, x, block, offsets, values );
439 Field *row0 = values;
440 for(
unsigned int k = 1; k <= order; ++k )
442 Field *row1 = values + block*offsets[ k-1 ];
443 Field *wit = row1 + block*size.sizes_[ k ];
444 Helper::copy( deriv, wit, row1, k*size.sizes_[ k ], z );
445 Helper::copy( deriv, wit, row0, size( k-1 ), z );
450 void integrate (
const unsigned int order,
451 const unsigned int *
const offsets,
452 Field *
const values )
const
454 const BaseSize &size = BaseSize::instance();
455 const Size &mySize = Size::instance();
457 baseBasis_.integrate( order, offsets, values );
458 const unsigned int *
const baseSizes = size.sizes_;
460 Field *row0 = values;
461 for(
unsigned int k = 1; k <= order; ++k )
463 Field *
const row1begin = values + offsets[ k-1 ];
464 Field *
const row1End = row1begin + mySize.sizes_[ k ];
465 assert( (
unsigned int)(row1End - values) <= offsets[ k ] );
467 Field *row1 = row1begin;
468 Field *it = row1begin + baseSizes[ k ];
469 for(
unsigned int j = 1; j <= k; ++j )
471 Field *
const end = it + baseSizes[ k ];
472 assert( (
unsigned int)(end - values) <= offsets[ k ] );
473 for( ; it != end; ++row1, ++it )
474 *it = (Field( j ) / Field( j+1 )) * (*row1);
476 for( ; it != row1End; ++row0, ++it )
477 *it = (Field( k ) / Field( k+1 )) * (*row0);
483 template<
class BaseTopology,
class F >
484 class MonomialBasisImpl< GenericGeometry::Pyramid< BaseTopology >, F >
486 typedef MonomialBasisImpl< GenericGeometry::Pyramid< BaseTopology >, F >
This;
489 typedef GenericGeometry::Pyramid< BaseTopology >
Topology;
492 static const unsigned int dimDomain = Topology::dimension;
498 friend class MonomialBasisImpl< GenericGeometry::Prism< Topology >,
Field >;
499 friend class MonomialBasisImpl< GenericGeometry::Pyramid< Topology >, Field >;
501 typedef MonomialBasisSize< BaseTopology > BaseSize;
502 typedef MonomialBasisSize< Topology > Size;
504 MonomialBasisImpl< BaseTopology, Field > baseBasis_;
510 void evaluateSimplexBase (
const unsigned int deriv,
const unsigned int order,
511 const FieldVector< Field, dimD > &x,
512 const unsigned int block,
const unsigned int *
const offsets,
514 const BaseSize &size )
const
516 baseBasis_.
evaluate( deriv, order, x, block, offsets, values );
520 void evaluatePyramidBase (
const unsigned int deriv,
const unsigned int order,
521 const FieldVector< Field, dimD > &x,
522 const unsigned int block,
const unsigned int *
const offsets,
524 const BaseSize &size )
const
526 Field omz = Unity< Field >() - x[ dimDomain-1 ];
528 if( Zero< Field >() < omz )
530 const Field invomz = Unity< Field >() / omz;
531 FieldVector< Field, dimD > y;
532 for(
unsigned int i = 0; i < dimDomain-1; ++i )
533 y[ i ] = x[ i ] * invomz;
536 baseBasis_.evaluate( deriv, order, y, block, offsets, values );
539 for(
unsigned int k = 1; k <= order; ++k )
541 Field *it = values + block*offsets[ k-1 ];
542 Field *
const end = it + block*size.sizes_[ k ];
543 for( ; it != end; ++it )
551 *values = Unity< Field >();
552 for(
unsigned int k = 1; k <= order; ++k )
554 Field *it = values + block*offsets[ k-1 ];
555 Field *
const end = it + block*size.sizes_[ k ];
556 for( ; it != end; ++it )
557 *it = Zero< Field >();
563 void evaluate (
const unsigned int deriv,
const unsigned int order,
564 const FieldVector< Field, dimD > &x,
565 const unsigned int block,
const unsigned int *
const offsets,
566 Field *
const values )
const
568 typedef MonomialBasisHelper< dimDomain, dimD, Field > Helper;
569 const BaseSize &size = BaseSize::instance();
572 evaluateSimplexBase( deriv, order, x, block, offsets, values, size );
574 evaluatePyramidBase( deriv, order, x, block, offsets, values, size );
576 Field *row0 = values;
577 for(
unsigned int k = 1; k <= order; ++k )
579 Field *row1 = values + block*offsets[ k-1 ];
580 Field *wit = row1 + block*size.sizes_[ k ];
581 Helper::copy( deriv, wit, row0, size( k-1 ), x[ dimDomain-1 ] );
586 void integrate (
const unsigned int order,
587 const unsigned int *
const offsets,
588 Field *
const values )
const
590 const BaseSize &size = BaseSize::instance();
593 baseBasis_.integrate( order, offsets, values );
595 const unsigned int *
const baseSizes = size.sizes_;
597 Field *
const col0End = values + baseSizes[ 0 ];
598 for( Field *it = values; it != col0End; ++it )
599 *it *= Field( 1 ) / Field(
int(dimDomain) );
600 Field *row0 = values;
602 for(
unsigned int k = 1; k <= order; ++k )
604 const Field factor = (Field( 1 ) / Field( k + dimDomain ));
606 Field *
const row1 = values+offsets[ k-1 ];
607 Field *
const col0End = row1 + baseSizes[ k ];
609 for( ; it != col0End; ++it )
611 for(
unsigned int i = 1; i <= k; ++i )
613 Field *
const end = it + baseSizes[ k-i ];
614 assert( (
unsigned int)(end - values) <= offsets[ k ] );
615 for( ; it != end; ++row0, ++it )
616 *it = (*row0) * (Field( i ) * factor);
628 template<
class Topology,
class F >
630 :
public MonomialBasisImpl< Topology, F >
633 typedef MonomialBasisImpl< Topology, F > Base;
645 typedef MonomialBasisSize<Topology>
Size;
650 size_(
Size::instance())
655 const unsigned int *
sizes (
unsigned int order )
const
657 size_.computeSizes( order );
658 return size_.numBaseFunctions_;
663 return sizes( order_ );
666 const unsigned int size ()
const
668 size_.computeSizes( order_ );
669 return size_( order_ );
672 const unsigned int derivSize (
const unsigned int deriv )
const
674 typedef typename GenericGeometry::SimplexTopology< dimension >::type SimplexTopology;
675 MonomialBasisSize< SimplexTopology >::instance().computeSizes( deriv );
676 return MonomialBasisSize< SimplexTopology >::instance() ( deriv );
690 Field *
const values )
const
695 template <
unsigned int deriv>
697 Field *
const values )
const
702 template<
unsigned int deriv,
class Vector >
704 Vector &values )
const
706 evaluate<deriv>(x,&(values[0]));
708 template<
unsigned int deriv, DerivativeLayout layout >
710 Derivatives<Field,dimension,1,deriv,layout> *values )
const
712 evaluate<deriv>(x,&(values->block()));
714 template<
unsigned int deriv >
716 FieldVector<
Field,Derivatives<Field,dimension,1,deriv,value>::size> *values )
const
721 template<
class Vector >
723 Vector &values )
const
725 evaluate<0>(x,&(values[0]));
728 template<
class DVector,
class RVector >
729 void evaluate (
const DVector &x, RVector &values )
const
731 assert( DVector::dimension ==
dimension);
735 evaluate<0>( bx, values );
742 template <
class Vector>
749 This& operator=(
const This&);
759 template<
int dim,
class F >
761 :
public MonomialBasis< typename GenericGeometry::SimplexTopology< dim >::type, F >
767 typedef typename GenericGeometry::SimplexTopology< dim >::type
Topology;
780 template<
int dim,
class F >
782 :
public MonomialBasis< typename GenericGeometry::CubeTopology< dim >::type, F >
788 typedef typename GenericGeometry::CubeTopology< dim >::type
Topology;
801 template<
int dim,
class F >
821 virtual const unsigned int *
sizes ( )
const = 0;
823 const unsigned int size ( )
const
839 Field *
const values )
const = 0;
840 template <
unsigned int deriv >
842 Field *
const values )
const
846 template <
unsigned int deriv,
int size >
848 Dune::FieldVector<Field,size> *
const values )
const
850 evaluate( deriv, x, &(values[0][0]) );
852 template<
unsigned int deriv, DerivativeLayout layout >
854 Derivatives<Field,dimension,1,deriv,layout> *values )
const
856 evaluate<deriv>(x,&(values->block()));
858 template <
unsigned int deriv,
class Vector>
860 Vector &values )
const
862 evaluate<deriv>( x, &(values[ 0 ]) );
864 template<
class Vector >
866 Vector &values )
const
868 evaluate<0>(x,values);
870 template<
class DVector,
class RVector >
871 void evaluate (
const DVector &x, RVector &values )
const
873 assert( DVector::dimension ==
dimension);
877 evaluate<0>( bx, values );
879 template<
unsigned int deriv,
class DVector,
class RVector >
880 void evaluate (
const DVector &x, RVector &values )
const
882 assert( DVector::dimension ==
dimension);
886 evaluate<deriv>( bx, values );
890 template <
class Vector>
900 template<
class Topology,
class F >
912 :
Base(Topology::id,order), basis_(order)
921 Field *
const values )
const
939 template<
int dim,
class F >
940 struct MonomialBasisFactory;
942 template<
int dim,
class F >
951 template<
int dim,
class F >
962 template <
int dd,
class FF >
968 template<
class Topology >
980 template<
int dim,
class SF >
982 :
public TopologySingletonFactory< MonomialBasisFactory< dim, SF > >
986 template <
int dd,
class FF >