Dune Core Modules (2.5.0)

referenceelements.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3#ifndef DUNE_GEOMETRY_REFERENCEELEMENTS_HH
4#define DUNE_GEOMETRY_REFERENCEELEMENTS_HH
5
6#include <cassert>
7
8#include <algorithm>
9#include <limits>
10#include <tuple>
11#include <utility>
12#include <vector>
13
14#include <dune/common/array.hh>
20#include <dune/common/unused.hh>
21
23#include <dune/geometry/type.hh>
24
25namespace Dune
26{
27
28 // Internal Forward Declarations
29 // -----------------------------
30
31 template< class ctype, int dim >
32 class ReferenceElementContainer;
33
34 template< class ctype, int dim >
35 struct ReferenceElements;
36
37
38
39 namespace Impl
40 {
41
43 unsigned int size ( unsigned int topologyId, int dim, int codim );
44
45
46
54 unsigned int subTopologyId ( unsigned int topologyId, int dim, int codim, unsigned int i );
55
56
57
58 // subTopologyNumbering
59 // --------------------
60
61 void subTopologyNumbering ( unsigned int topologyId, int dim, int codim, unsigned int i, int subcodim,
62 unsigned int *beginOut, unsigned int *endOut );
63
64
65
66
67 // checkInside
68 // -----------
69
70 template< class ct, int cdim >
71 inline bool
72 checkInside ( unsigned int topologyId, int dim, const FieldVector< ct, cdim > &x, ct tolerance, ct factor = ct( 1 ) )
73 {
74 assert( (dim >= 0) && (dim <= cdim) );
75 assert( topologyId < numTopologies( dim ) );
76
77 if( dim > 0 )
78 {
79 const ct baseFactor = (isPrism( topologyId, dim ) ? factor : factor - x[ dim-1 ]);
80 if( (x[ dim-1 ] > -tolerance) && (factor - x[ dim-1 ] > -tolerance) )
81 return checkInside< ct, cdim >( baseTopologyId( topologyId, dim ), dim-1, x, tolerance, baseFactor );
82 else
83 return false;
84 }
85 else
86 return true;
87 }
88
89
90
91 // referenceCorners
92 // ----------------
93
94 template< class ct, int cdim >
95 inline unsigned int
96 referenceCorners ( unsigned int topologyId, int dim, FieldVector< ct, cdim > *corners )
97 {
98 assert( (dim >= 0) && (dim <= cdim) );
99 assert( topologyId < numTopologies( dim ) );
100
101 if( dim > 0 )
102 {
103 const unsigned int nBaseCorners
104 = referenceCorners( baseTopologyId( topologyId, dim ), dim-1, corners );
105 assert( nBaseCorners == size( baseTopologyId( topologyId, dim ), dim-1, dim-1 ) );
106 if( isPrism( topologyId, dim ) )
107 {
108 std::copy( corners, corners + nBaseCorners, corners + nBaseCorners );
109 for( unsigned int i = 0; i < nBaseCorners; ++i )
110 corners[ i+nBaseCorners ][ dim-1 ] = ct( 1 );
111 return 2*nBaseCorners;
112 }
113 else
114 {
115 corners[ nBaseCorners ] = FieldVector< ct, cdim >( ct( 0 ) );
116 corners[ nBaseCorners ][ dim-1 ] = ct( 1 );
117 return nBaseCorners+1;
118 }
119 }
120 else
121 {
122 *corners = FieldVector< ct, cdim >( ct( 0 ) );
123 return 1;
124 }
125 }
126
127
128
129 // referenceVolume
130 // ---------------
131
132 unsigned long referenceVolumeInverse ( unsigned int topologyId, int dim );
133
134 template< class ct >
135 inline ct referenceVolume ( unsigned int topologyId, int dim )
136 {
137 return ct( 1 ) / ct( referenceVolumeInverse( topologyId, dim ) );
138 }
139
140
141
142 // referenceOrigins
143 // ----------------
144
145 template< class ct, int cdim >
146 inline unsigned int
147 referenceOrigins ( unsigned int topologyId, int dim, int codim, FieldVector< ct, cdim > *origins )
148 {
149 assert( (dim >= 0) && (dim <= cdim) );
150 assert( topologyId < numTopologies( dim ) );
151 assert( (codim >= 0) && (codim <= dim) );
152
153 if( codim > 0 )
154 {
155 const unsigned int baseId = baseTopologyId( topologyId, dim );
156 if( isPrism( topologyId, dim ) )
157 {
158 const unsigned int n = (codim < dim ? referenceOrigins( baseId, dim-1, codim, origins ) : 0);
159 const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins+n );
160 for( unsigned int i = 0; i < m; ++i )
161 {
162 origins[ n+m+i ] = origins[ n+i ];
163 origins[ n+m+i ][ dim-1 ] = ct( 1 );
164 }
165 return n+2*m;
166 }
167 else
168 {
169 const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins );
170 if( codim == dim )
171 {
172 origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
173 origins[ m ][ dim-1 ] = ct( 1 );
174 return m+1;
175 }
176 else
177 return m+referenceOrigins( baseId, dim-1, codim, origins+m );
178 }
179 }
180 else
181 {
182 origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
183 return 1;
184 }
185 }
186
187
188
189 // referenceEmbeddings
190 // -------------------
191
192 template< class ct, int cdim, int mydim >
193 inline unsigned int
194 referenceEmbeddings ( unsigned int topologyId, int dim, int codim,
195 FieldVector< ct, cdim > *origins,
196 FieldMatrix< ct, mydim, cdim > *jacobianTransposeds )
197 {
198 assert( (0 <= codim) && (codim <= dim) && (dim <= cdim) );
199 assert( (dim - codim <= mydim) && (mydim <= cdim) );
200 assert( topologyId < numTopologies( dim ) );
201
202 if( codim > 0 )
203 {
204 const unsigned int baseId = baseTopologyId( topologyId, dim );
205 if( isPrism( topologyId, dim ) )
206 {
207 const unsigned int n = (codim < dim ? referenceEmbeddings( baseId, dim-1, codim, origins, jacobianTransposeds ) : 0);
208 for( unsigned int i = 0; i < n; ++i )
209 jacobianTransposeds[ i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
210
211 const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins+n, jacobianTransposeds+n );
212 std::copy( origins+n, origins+n+m, origins+n+m );
213 std::copy( jacobianTransposeds+n, jacobianTransposeds+n+m, jacobianTransposeds+n+m );
214 for( unsigned int i = 0; i < m; ++i )
215 origins[ n+m+i ][ dim-1 ] = ct( 1 );
216
217 return n+2*m;
218 }
219 else
220 {
221 const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins, jacobianTransposeds );
222 if( codim == dim )
223 {
224 origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
225 origins[ m ][ dim-1 ] = ct( 1 );
226 jacobianTransposeds[ m ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
227 return m+1;
228 }
229 else
230 {
231 const unsigned int n = referenceEmbeddings( baseId, dim-1, codim, origins+m, jacobianTransposeds+m );
232 for( unsigned int i = 0; i < n; ++i )
233 {
234 for( int k = 0; k < dim-1; ++k )
235 jacobianTransposeds[ m+i ][ dim-codim-1 ][ k ] = -origins[ m+i ][ k ];
236 jacobianTransposeds[ m+i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
237 }
238 return m+n;
239 }
240 }
241 }
242 else
243 {
244 origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
245 jacobianTransposeds[ 0 ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
246 for( int k = 0; k < dim; ++k )
247 jacobianTransposeds[ 0 ][ k ][ k ] = ct( 1 );
248 return 1;
249 }
250 }
251
252
253
254 // referenceIntegrationOuterNormals
255 // --------------------------------
256
257 template< class ct, int cdim >
258 inline unsigned int
259 referenceIntegrationOuterNormals ( unsigned int topologyId, int dim,
260 const FieldVector< ct, cdim > *origins,
261 FieldVector< ct, cdim > *normals )
262 {
263 assert( (dim > 0) && (dim <= cdim) );
264 assert( topologyId < numTopologies( dim ) );
265
266 if( dim > 1 )
267 {
268 const unsigned int baseId = baseTopologyId( topologyId, dim );
269 if( isPrism( topologyId, dim ) )
270 {
271 const unsigned int numBaseFaces
272 = referenceIntegrationOuterNormals( baseId, dim-1, origins, normals );
273
274 for( unsigned int i = 0; i < 2; ++i )
275 {
276 normals[ numBaseFaces+i ] = FieldVector< ct, cdim >( ct( 0 ) );
277 normals[ numBaseFaces+i ][ dim-1 ] = ct( 2*int( i )-1 );
278 }
279
280 return numBaseFaces+2;
281 }
282 else
283 {
284 normals[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
285 normals[ 0 ][ dim-1 ] = ct( -1 );
286
287 const unsigned int numBaseFaces
288 = referenceIntegrationOuterNormals( baseId, dim-1, origins+1, normals+1 );
289 for( unsigned int i = 1; i <= numBaseFaces; ++i )
290 normals[ i ][ dim-1 ] = normals[ i ]*origins[ i ];
291
292 return numBaseFaces+1;
293 }
294 }
295 else
296 {
297 for( unsigned int i = 0; i < 2; ++i )
298 {
299 normals[ i ] = FieldVector< ct, cdim >( ct( 0 ) );
300 normals[ i ][ 0 ] = ct( 2*int( i )-1 );
301 }
302
303 return 2;
304 }
305 }
306
307 template< class ct, int cdim >
308 inline unsigned int
309 referenceIntegrationOuterNormals ( unsigned int topologyId, int dim,
310 FieldVector< ct, cdim > *normals )
311 {
312 assert( (dim > 0) && (dim <= cdim) );
313
314 FieldVector< ct, cdim > *origins
315 = new FieldVector< ct, cdim >[ size( topologyId, dim, 1 ) ];
316 referenceOrigins( topologyId, dim, 1, origins );
317
318 const unsigned int numFaces
319 = referenceIntegrationOuterNormals( topologyId, dim, origins, normals );
320 assert( numFaces == size( topologyId, dim, 1 ) );
321
322 delete[] origins;
323
324 return numFaces;
325 }
326
327 } // namespace Impl
328
329
330
331 // ReferenceElement
332 // ----------------
333
352 template< class ctype, int dim >
354 {
356
357 friend class ReferenceElementContainer< ctype, dim >;
358
359 struct SubEntityInfo;
360
361 // make copy constructor private
362 ReferenceElement ( const This & );
363
364 ReferenceElement () {}
365
366 template< int codim > struct CreateGeometries;
367
368 public:
370 template< int codim >
371 struct Codim
372 {
374 typedef AffineGeometry< ctype, dim-codim, dim > Geometry;
375 };
376
381 int size ( int c ) const
382 {
383 assert( (c >= 0) && (c <= dim) );
384 return info_[ c ].size();
385 }
386
398 int size ( int i, int c, int cc ) const
399 {
400 assert( (i >= 0) && (i < size( c )) );
401 return info_[ c ][ i ].size( cc );
402 }
403
417 int subEntity ( int i, int c, int ii, int cc ) const
418 {
419 assert( (i >= 0) && (i < size( c )) );
420 return info_[ c ][ i ].number( ii, cc );
421 }
422
431 const GeometryType &type ( int i, int c ) const
432 {
433 assert( (i >= 0) && (i < size( c )) );
434 return info_[ c ][ i ].type();
435 }
436
438 const GeometryType &type () const { return type( 0, 0 ); }
439
449 const FieldVector< ctype, dim > &position( int i, int c ) const
450 {
451 assert( (c >= 0) && (c <= dim) );
452 return baryCenters_[ c ][ i ];
453 }
454
462 bool checkInside ( const FieldVector< ctype, dim > &local ) const
463 {
464 const ctype tolerance = ctype( 64 ) * std::numeric_limits< ctype >::epsilon();
465 return Impl::template checkInside< ctype, dim >( type().id(), dim, local, tolerance );
466 }
467
479 template< int codim >
480 typename Codim< codim >::Geometry geometry ( int i ) const
481 {
482 return std::get< codim >( geometries_ )[ i ];
483 }
484
486 ctype volume () const
487 {
488 return volume_;
489 }
490
499 {
500 assert( (face >= 0) && (face < int( integrationNormals_.size() )) );
501 return integrationNormals_[ face ];
502 }
503
504 private:
505 void initialize ( unsigned int topologyId )
506 {
507 assert( topologyId < Impl::numTopologies( dim ) );
508
509 // set up subentities
510 for( int codim = 0; codim <= dim; ++codim )
511 {
512 const unsigned int size = Impl::size( topologyId, dim, codim );
513 info_[ codim ].resize( size );
514 for( unsigned int i = 0; i < size; ++i )
515 info_[ codim ][ i ].initialize( topologyId, codim, i );
516 }
517
518 // compute corners
519 const unsigned int numVertices = size( dim );
520 baryCenters_[ dim ].resize( numVertices );
521 Impl::referenceCorners( topologyId, dim, &(baryCenters_[ dim ][ 0 ]) );
522
523 // compute barycenters
524 for( int codim = 0; codim < dim; ++codim )
525 {
526 baryCenters_[ codim ].resize( size(codim) );
527 for( int i = 0; i < size( codim ); ++i )
528 {
529 baryCenters_[ codim ][ i ] = FieldVector< ctype, dim >( ctype( 0 ) );
530 const unsigned int numCorners = size( i, codim, dim );
531 for( unsigned int j = 0; j < numCorners; ++j )
532 baryCenters_[ codim ][ i ] += baryCenters_[ dim ][ subEntity( i, codim, j, dim ) ];
533 baryCenters_[ codim ][ i ] *= ctype( 1 ) / ctype( numCorners );
534 }
535 }
536
537 // compute reference element volume
538 volume_ = Impl::template referenceVolume< ctype >( topologyId, dim );
539
540 // compute integration outer normals
541 if( dim > 0 )
542 {
543 integrationNormals_.resize( size( 1 ) );
544 Impl::referenceIntegrationOuterNormals( topologyId, dim, &(integrationNormals_[ 0 ]) );
545 }
546
547 // set up geometries
549 }
550
551 template< int... codim >
552 static std::tuple< std::vector< typename Codim< codim >::Geometry >... >
553 makeGeometryTable ( std::integer_sequence< int, codim... > );
554
556 typedef decltype( makeGeometryTable( std::make_integer_sequence< int, dim+1 >() ) ) GeometryTable;
557
559 ctype volume_;
560
561 std::vector< FieldVector< ctype, dim > > baryCenters_[ dim+1 ];
562 std::vector< FieldVector< ctype, dim > > integrationNormals_;
563
565 GeometryTable geometries_;
566
567 std::vector< SubEntityInfo > info_[ dim+1 ];
568 };
569
571 template< class ctype, int dim >
572 struct ReferenceElement< ctype, dim >::SubEntityInfo
573 {
575 : numbering_( nullptr )
576 {
577 std::fill( offset_.begin(), offset_.end(), 0 );
578 }
579
580 SubEntityInfo ( const SubEntityInfo &other )
581 : offset_( other.offset_ ),
582 type_( other.type_ )
583 {
584 numbering_ = allocate();
585 std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
586 }
587
588 ~SubEntityInfo () { deallocate( numbering_ ); }
589
590 const SubEntityInfo &operator= ( const SubEntityInfo &other )
591 {
592 type_ = other.type_;
593 offset_ = other.offset_;
594
595 deallocate( numbering_ );
596 numbering_ = allocate();
597 std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
598
599 return *this;
600 }
601
602 int size ( int cc ) const
603 {
604 assert( (cc >= codim()) && (cc <= dim) );
605 return (offset_[ cc+1 ] - offset_[ cc ]);
606 }
607
608 int number ( int ii, int cc ) const
609 {
610 assert( (ii >= 0) && (ii < size( cc )) );
611 return numbering_[ offset_[ cc ] + ii ];
612 }
613
614 const GeometryType &type () const { return type_; }
615
616 void initialize ( unsigned int topologyId, int codim, unsigned int i )
617 {
618 const unsigned int subId = Impl::subTopologyId( topologyId, dim, codim, i );
619 type_ = GeometryType( subId, dim-codim );
620
621 // compute offsets
622 for( int cc = 0; cc <= codim; ++cc )
623 offset_[ cc ] = 0;
624 for( int cc = codim; cc <= dim; ++cc )
625 offset_[ cc+1 ] = offset_[ cc ] + Impl::size( subId, dim-codim, cc-codim );
626
627 // compute subnumbering
628 deallocate( numbering_ );
629 numbering_ = allocate();
630 for( int cc = codim; cc <= dim; ++cc )
631 Impl::subTopologyNumbering( topologyId, dim, codim, i, cc-codim, numbering_+offset_[ cc ], numbering_+offset_[ cc+1 ] );
632 }
633
634 protected:
635 int codim () const { return dim - type().dim(); }
636
637 unsigned int *allocate () { return (capacity() != 0 ? new unsigned int[ capacity() ] : nullptr); }
638 void deallocate ( unsigned int *ptr ) { delete[] ptr; }
639 unsigned int capacity () const { return offset_[ dim+1 ]; }
640
641 private:
642 unsigned int *numbering_;
643 std::array< unsigned int, dim+2 > offset_;
644 GeometryType type_;
645 };
646
647
648 template< class ctype, int dim >
649 template< int codim >
650 struct ReferenceElement< ctype, dim >::CreateGeometries
651 {
652 template< int cc >
653 static const ReferenceElement< ctype, dim-cc > &
654 subRefElement( const ReferenceElement< ctype, dim > &refElement, int i, std::integral_constant< int, cc > )
655 {
656 return ReferenceElements< ctype, dim-cc >::general( refElement.type( i, cc ) );
657 }
658
659 static const ReferenceElement< ctype, dim > &
660 subRefElement( const ReferenceElement< ctype, dim > &refElement, int i, std::integral_constant< int, 0 > )
661 {
663 return refElement;
664 }
665
666 static void apply ( const ReferenceElement< ctype, dim > &refElement, GeometryTable &geometries )
667 {
668 const int size = refElement.size( codim );
669 std::vector< FieldVector< ctype, dim > > origins( size );
670 std::vector< FieldMatrix< ctype, dim - codim, dim > > jacobianTransposeds( size );
671 Impl::referenceEmbeddings( refElement.type().id(), dim, codim, &(origins[ 0 ]), &(jacobianTransposeds[ 0 ]) );
672
673 std::get< codim >( geometries ).reserve( size );
674 for( int i = 0; i < size; ++i )
675 {
676 typename Codim< codim >::Geometry geometry( subRefElement( refElement, i, std::integral_constant< int, codim >() ), origins[ i ], jacobianTransposeds[ i ] );
677 std::get< codim >( geometries ).push_back( geometry );
678 }
679 }
680 };
681
682
683
684 // ReferenceElementContainer
685 // -------------------------
686
687 template< class ctype, int dim >
688 class ReferenceElementContainer
689 {
690 static const unsigned int numTopologies = (1u << dim);
691
692 public:
693 typedef ReferenceElement< ctype, dim > value_type;
694 typedef const value_type *const_iterator;
695
696 ReferenceElementContainer ()
697 {
698 for( unsigned int topologyId = 0; topologyId < numTopologies; ++topologyId )
699 values_[ topologyId ].initialize( topologyId );
700 }
701
702 const value_type &operator() ( const GeometryType &type ) const
703 {
704 assert( type.dim() == dim );
705 return values_[ type.id() ];
706 }
707
708 const value_type &simplex () const
709 {
710 return values_[ Impl::SimplexTopology< dim >::type::id ];
711 }
712
713 const value_type &cube () const
714 {
715 return values_[ Impl::CubeTopology< dim >::type::id ];
716 }
717
718 const value_type &pyramid () const
719 {
720 return values_[ Impl::PyramidTopology< dim >::type::id ];
721 }
722
723 const value_type &prism () const
724 {
725 return values_[ Impl::PrismTopology< dim >::type::id ];
726 }
727
728 const_iterator begin () const { return values_; }
729 const_iterator end () const { return values_ + numTopologies; }
730
731 private:
732 value_type values_[ numTopologies ];
733 };
734
735
736
737 // ReferenceElements
738 // ------------------------
739
750 template< class ctype, int dim >
752 {
754
756 static const ReferenceElement< ctype, dim > &
757 general ( const GeometryType &type )
758 {
759 return container() ( type );
760 }
761
764 {
765 return container().simplex();
766 }
767
770 {
771 return container().cube();
772 }
773
774 static Iterator begin () { return container().begin(); }
775 static Iterator end () { return container().end(); }
776
777 private:
778 DUNE_EXPORT static const ReferenceElementContainer< ctype, dim > &container ()
779 {
780 static ReferenceElementContainer< ctype, dim > container;
781 return container;
782 }
783 };
784
785} // namespace Dune
786
787#endif // #ifndef DUNE_GEOMETRY_REFERENCEELEMENTS_HH
An implementation of the Geometry interface for affine geometries.
Fallback implementation of the std::array class (a static array)
Implementation of the Geometry interface for affine geometries.
Definition: affinegeometry.hh:461
Unique label for each type of entities that can occur in DUNE grids.
Definition: type.hh:268
unsigned int dim() const
Return dimension of the type.
Definition: type.hh:565
This class provides access to geometric and topological properties of a reference element.
Definition: referenceelements.hh:354
int size(int c) const
number of subentities of codimension c
Definition: referenceelements.hh:381
int size(int i, int c, int cc) const
number of subentities of codimension cc of subentity (i,c)
Definition: referenceelements.hh:398
const FieldVector< ctype, dim > & position(int i, int c) const
position of the barycenter of entity (i,c)
Definition: referenceelements.hh:449
ctype volume() const
obtain the volume of the reference element
Definition: referenceelements.hh:486
int subEntity(int i, int c, int ii, int cc) const
obtain number of ii-th subentity with codim cc of (i,c)
Definition: referenceelements.hh:417
bool checkInside(const FieldVector< ctype, dim > &local) const
check if a coordinate is in the reference element
Definition: referenceelements.hh:462
const GeometryType & type(int i, int c) const
obtain the type of subentity (i,c)
Definition: referenceelements.hh:431
Codim< codim >::Geometry geometry(int i) const
obtain the embedding of subentity (i,codim) into the reference element
Definition: referenceelements.hh:480
const FieldVector< ctype, dim > & integrationOuterNormal(int face) const
obtain the integration outer normal of the reference element
Definition: referenceelements.hh:498
const GeometryType & type() const
obtain the type of this reference element
Definition: referenceelements.hh:438
Implements a matrix constructed from a given type representing a field and compile-time given number ...
A static for loop for template meta-programming.
Implements a vector constructed from a given type representing a field and a compile-time given size.
Dune namespace.
Definition: alignment.hh:11
A static loop using TMP.
Definition: forloop.hh:67
Collection of types depending on the codimension.
Definition: referenceelements.hh:372
AffineGeometry< ctype, dim-codim, dim > Geometry
type of geometry embedding a subentity into the reference element
Definition: referenceelements.hh:374
topological information about the subentities of a reference element
Definition: referenceelements.hh:573
Class providing access to the singletons of the reference elements.
Definition: referenceelements.hh:752
static const ReferenceElement< ctype, dim > & simplex()
get simplex reference elements
Definition: referenceelements.hh:763
static const ReferenceElement< ctype, dim > & cube()
get hypercube reference elements
Definition: referenceelements.hh:769
static const ReferenceElement< ctype, dim > & general(const GeometryType &type)
get general reference elements
Definition: referenceelements.hh:757
A unique label for each type of element that can occur in a grid.
Traits for type conversions and type information.
Definition of the DUNE_UNUSED macro for the case that config.h is not available.
#define DUNE_UNUSED_PARAMETER(parm)
A macro to mark intentionally unused function parameters with.
Definition: unused.hh:18
Definition of macros controlling symbol visibility at the ABI level.
#define DUNE_EXPORT
Export a symbol as part of the public ABI.
Definition: visibility.hh:18
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