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/type.hh>
69 template<
class Topology >
72 template<
class Topology,
class F >
86 static This &instance ()
88 static This _instance;
92 typedef Impl::Point 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< Impl::Prism< BaseTopology > >
152 typedef MonomialBasisSize< Impl::Prism< BaseTopology > > This;
155 static This &instance ()
157 static This _instance;
161 typedef Impl::Prism< BaseTopology > Topology;
163 friend class MonomialBasisSize< Impl::Prism< Topology > >;
164 friend class MonomialBasisSize< Impl::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< Impl::Pyramid< BaseTopology > >
227 typedef MonomialBasisSize< Impl::Pyramid< BaseTopology > > This;
230 static This &instance ()
232 static This _instance;
236 typedef Impl::Pyramid< BaseTopology > Topology;
238 friend class MonomialBasisSize< Impl::Prism< Topology > >;
239 friend class MonomialBasisSize< Impl::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 >
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 ];
333 const F *
const drend = rit + mySize.sizes_[ d ] - mySize.sizes_[ d-1 ];
334 for( ; rit != drend ; ++rit, ++wit )
338 for (
unsigned int j=1; j<d; ++j)
340 const F *
const drend = rit + mySize.sizes_[ d-j ] - mySize.sizes_[ d-j-1 ];
341 for( ; rit != drend ; ++prit, ++rit, ++wit )
342 *wit = F(j) * *prit + z * *rit;
344 *wit = F(d) * *prit + z * *rit;
345 ++prit, ++rit, ++wit;
346 assert(derivEnd == rit);
347 rit += size.sizes_[d] - mySize.sizes_[d];
348 prit += size.sizes_[d-1] - mySize.sizes_[d-1];
349 const F *
const emptyWitEnd = wit + size.sizes_[d] - mySize.sizes_[d];
350 for ( ; wit != emptyWitEnd; ++wit )
362 template<
class Topology,
class F >
374 static const unsigned int dimDomain = Topology::dimension;
384 void evaluate ( const unsigned int deriv, const unsigned int order,
385 const FieldVector< Field, dimD > &x,
386 const unsigned int block, const unsigned int *const offsets,
387 Field *const values ) const
390 F *
const end = values + block;
391 for(
Field *it = values+1 ; it != end; ++it )
395 void integrate (
const unsigned int order,
396 const unsigned int *
const offsets,
397 Field *
const values )
const
403 template<
class BaseTopology,
class F >
412 static const unsigned int dimDomain = Topology::dimension;
430 void evaluate (
const unsigned int deriv,
const unsigned int order,
431 const FieldVector< Field, dimD > &x,
432 const unsigned int block,
const unsigned int *
const offsets,
433 Field *
const values )
const
436 const BaseSize &size = BaseSize::instance();
438 const Field &z = x[ dimDomain-1 ];
441 baseBasis_.evaluate( deriv, order, x, block, offsets, values );
443 Field *row0 = values;
444 for(
unsigned int k = 1; k <= order; ++k )
446 Field *row1 = values + block*offsets[ k-1 ];
447 Field *wit = row1 + block*size.sizes_[ k ];
448 Helper::copy( deriv, wit, row1, k*size.sizes_[ k ], z );
449 Helper::copy( deriv, wit, row0, size( k-1 ), z );
454 void integrate (
const unsigned int order,
455 const unsigned int *
const offsets,
456 Field *
const values )
const
458 const BaseSize &size = BaseSize::instance();
459 const Size &mySize = Size::instance();
461 baseBasis_.integrate( order, offsets, values );
462 const unsigned int *
const baseSizes = size.sizes_;
464 Field *row0 = values;
465 for(
unsigned int k = 1; k <= order; ++k )
467 Field *
const row1begin = values + offsets[ k-1 ];
468 Field *
const row1End = row1begin + mySize.sizes_[ k ];
469 assert( (
unsigned int)(row1End - values) <= offsets[ k ] );
471 Field *row1 = row1begin;
472 Field *it = row1begin + baseSizes[ k ];
473 for(
unsigned int j = 1; j <= k; ++j )
475 Field *
const end = it + baseSizes[ k ];
476 assert( (
unsigned int)(end - values) <= offsets[ k ] );
477 for( ; it != end; ++row1, ++it )
478 *it = (Field( j ) / Field( j+1 )) * (*row1);
480 for( ; it != row1End; ++row0, ++it )
481 *it = (Field( k ) / Field( k+1 )) * (*row0);
487 template<
class BaseTopology,
class F >
496 static const unsigned int dimDomain = Topology::dimension;
514 void evaluateSimplexBase (
const unsigned int deriv,
const unsigned int order,
515 const FieldVector< Field, dimD > &x,
516 const unsigned int block,
const unsigned int *
const offsets,
518 const BaseSize &size )
const
520 baseBasis_.evaluate( deriv, order, x, block, offsets, values );
524 void evaluatePyramidBase (
const unsigned int deriv,
const unsigned int order,
525 const FieldVector< Field, dimD > &x,
526 const unsigned int block,
const unsigned int *
const offsets,
528 const BaseSize &size )
const
530 Field omz = Unity< Field >() - x[ dimDomain-1 ];
532 if( Zero< Field >() < omz )
534 const Field invomz = Unity< Field >() / omz;
535 FieldVector< Field, dimD > y;
536 for(
unsigned int i = 0; i < dimDomain-1; ++i )
537 y[ i ] = x[ i ] * invomz;
540 baseBasis_.evaluate( deriv, order, y, block, offsets, values );
543 for(
unsigned int k = 1; k <= order; ++k )
545 Field *it = values + block*offsets[ k-1 ];
546 Field *
const end = it + block*size.sizes_[ k ];
547 for( ; it != end; ++it )
555 *values = Unity< Field >();
556 for(
unsigned int k = 1; k <= order; ++k )
558 Field *it = values + block*offsets[ k-1 ];
559 Field *
const end = it + block*size.sizes_[ k ];
560 for( ; it != end; ++it )
561 *it = Zero< Field >();
567 void evaluate (
const unsigned int deriv,
const unsigned int order,
568 const FieldVector< Field, dimD > &x,
569 const unsigned int block,
const unsigned int *
const offsets,
570 Field *
const values )
const
572 typedef MonomialBasisHelper< dimDomain, dimD, Field > Helper;
573 const BaseSize &size = BaseSize::instance();
576 evaluateSimplexBase( deriv, order, x, block, offsets, values, size );
578 evaluatePyramidBase( deriv, order, x, block, offsets, values, size );
580 Field *row0 = values;
581 for(
unsigned int k = 1; k <= order; ++k )
583 Field *row1 = values + block*offsets[ k-1 ];
584 Field *wit = row1 + block*size.sizes_[ k ];
585 Helper::copy( deriv, wit, row0, size( k-1 ), x[ dimDomain-1 ] );
590 void integrate (
const unsigned int order,
591 const unsigned int *
const offsets,
592 Field *
const values )
const
594 const BaseSize &size = BaseSize::instance();
597 baseBasis_.integrate( order, offsets, values );
599 const unsigned int *
const baseSizes = size.sizes_;
602 Field *
const col0End = values + baseSizes[ 0 ];
603 for( Field *it = values; it != col0End; ++it )
604 *it *= Field( 1 ) / Field(
int(dimDomain) );
607 Field *row0 = values;
608 for(
unsigned int k = 1; k <= order; ++k )
610 const Field factor = (Field( 1 ) / Field( k + dimDomain ));
612 Field *
const row1 = values+offsets[ k-1 ];
613 Field *
const col0End = row1 + baseSizes[ k ];
615 for( ; it != col0End; ++it )
617 for(
unsigned int i = 1; i <= k; ++i )
619 Field *
const end = it + baseSizes[ k-i ];
620 assert( (
unsigned int)(end - values) <= offsets[ k ] );
621 for( ; it != end; ++row0, ++it )
622 *it = (*row0) * (Field( i ) * factor);
634 template<
class Topology,
class F >
636 :
public MonomialBasisImpl< Topology, F >
638 typedef MonomialBasis< Topology, F > This;
639 typedef MonomialBasisImpl< Topology, F > Base;
656 size_(
Size::instance())
663 size_.computeSizes(
order );
664 return size_.numBaseFunctions_;
669 return sizes( order_ );
674 size_.computeSizes( order_ );
675 return size_( order_ );
678 unsigned int derivSize (
const unsigned int deriv )
const
680 typedef typename Impl::SimplexTopology< dimension >::type SimplexTopology;
696 Field *
const values )
const
698 Base::evaluate( deriv, order_, x,
derivSize( deriv ),
sizes( order_ ), values );
701 template <
unsigned int deriv>
703 Field *
const values )
const
708 template<
unsigned int deriv,
class Vector >
710 Vector &values )
const
712 evaluate<deriv>(x,&(values[0]));
714 template<
unsigned int deriv, DerivativeLayout layout >
718 evaluate<deriv>(x,&(values->block()));
720 template<
unsigned int deriv >
727 template<
class Vector >
729 Vector &values )
const
731 evaluate<0>(x,&(values[0]));
734 template<
class DVector,
class RVector >
735 void evaluate (
const DVector &x, RVector &values )
const
737 assert( DVector::dimension ==
dimension);
741 evaluate<0>( bx, values );
746 Base::integrate( order_,
sizes( order_ ), values );
748 template <
class Vector>
755 This& operator=(
const This&);
765 template<
int dim,
class F >
767 :
public MonomialBasis< typename Impl::SimplexTopology< dim >::type, F >
773 typedef typename Impl::SimplexTopology< dim >::type
Topology;
786 template<
int dim,
class F >
788 :
public MonomialBasis< typename Impl::CubeTopology< dim >::type, F >
794 typedef typename Impl::CubeTopology< dim >::type
Topology;
807 template<
int dim,
class F >
827 virtual const unsigned int *
sizes ( )
const = 0;
845 Field *
const values )
const = 0;
846 template <
unsigned int deriv >
848 Field *
const values )
const
852 template <
unsigned int deriv,
int size >
854 Dune::FieldVector<Field,size> *
const values )
const
856 evaluate( deriv, x, &(values[0][0]) );
858 template<
unsigned int deriv, DerivativeLayout layout >
862 evaluate<deriv>(x,&(values->block()));
864 template <
unsigned int deriv,
class Vector>
866 Vector &values )
const
868 evaluate<deriv>( x, &(values[ 0 ]) );
870 template<
class Vector >
872 Vector &values )
const
874 evaluate<0>(x,values);
876 template<
class DVector,
class RVector >
877 void evaluate (
const DVector &x, RVector &values )
const
879 assert( DVector::dimension ==
dimension);
883 evaluate<0>( bx, values );
885 template<
unsigned int deriv,
class DVector,
class RVector >
886 void evaluate (
const DVector &x, RVector &values )
const
888 assert( DVector::dimension ==
dimension);
892 evaluate<deriv>( bx, values );
896 template <
class Vector>
906 template<
class Topology,
class F >
927 Field *
const values )
const
945 template<
int dim,
class F >
948 template<
int dim,
class F >
957 template<
int dim,
class F >
959 public TopologyFactory< MonomialBasisFactoryTraits<dim,F> >
968 template <
int dd,
class FF >
974 template<
class Topology >
986 template<
int dim,
class SF >
988 :
public TopologySingletonFactory< MonomialBasisFactory< dim, SF > >
992 template <
int dd,
class FF >