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5#ifndef DUNE_GEOMETRY_MULTILINEARGEOMETRY_HH \n-
6#define DUNE_GEOMETRY_MULTILINEARGEOMETRY_HH \n+
5#ifndef DUNE_GEOMETRY_REFERENCEELEMENTIMPLEMENTATION_HH \n+
6#define DUNE_GEOMETRY_REFERENCEELEMENTIMPLEMENTATION_HH \n
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14#include <dune/common/fmatrix.hh> \n-
15#include <dune/common/fvector.hh> \n-
16#include <dune/common/typetraits.hh> \n+
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18#include <dune/common/fmatrix.hh> \n+
19#include <dune/common/fvector.hh> \n+
20#include <dune/common/hybridutilities.hh> \n+
21#include <dune/common/typetraits.hh> \n+
22#include <dune/common/iteratorrange.hh> \n+
23#include <dune/common/math.hh> \n
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61 static ct
tolerance () {
return ct( 16 ) * std::numeric_limits< ct >::epsilon(); }
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127 template<
int mydim,
int cdim >
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130 typedef std::vector< FieldVector< ct, cdim > >
Type;
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149 static const bool v =
false;
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42 template<
class ctype,
int dim >
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43 class ReferenceElementContainer;
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46 template<
class ctype,
int dim >
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47 struct ReferenceElements;
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54 using Dune::Impl::isPrism;
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55 using Dune::Impl::isPyramid;
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56 using Dune::Impl::baseTopologyId;
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57 using Dune::Impl::prismConstruction;
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58 using Dune::Impl::pyramidConstruction;
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59 using Dune::Impl::numTopologies;
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62 unsigned int size (
unsigned int topologyId,
int dim,
int codim );
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73 unsigned int subTopologyId (
unsigned int topologyId,
int dim,
int codim,
unsigned int i );
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80 void subTopologyNumbering (
unsigned int topologyId,
int dim,
int codim,
unsigned int i,
int subcodim,
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81 unsigned int *beginOut,
unsigned int *endOut );
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89 template<
class ct,
int cdim >
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91 checkInside (
unsigned int topologyId,
int dim,
const FieldVector< ct, cdim > &x, ct tolerance, ct factor = ct( 1 ) )
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93 assert( (dim >= 0) && (dim <= cdim) );
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94 assert( topologyId < numTopologies( dim ) );
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98 const ct baseFactor = (isPrism( topologyId, dim ) ? factor : factor - x[ dim-1 ]);
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99 if( (x[ dim-1 ] > -tolerance) && (factor - x[ dim-1 ] > -tolerance) )
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100 return checkInside< ct, cdim >( baseTopologyId( topologyId, dim ), dim-1, x, tolerance, baseFactor );
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113 template<
class ct,
int cdim >
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115 referenceCorners (
unsigned int topologyId,
int dim, FieldVector< ct, cdim > *corners )
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117 assert( (dim >= 0) && (dim <= cdim) );
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118 assert( topologyId < numTopologies( dim ) );
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122 const unsigned int nBaseCorners
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123 = referenceCorners( baseTopologyId( topologyId, dim ), dim-1, corners );
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124 assert( nBaseCorners ==
size( baseTopologyId( topologyId, dim ), dim-1, dim-1 ) );
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125 if( isPrism( topologyId, dim ) )
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127 std::copy( corners, corners + nBaseCorners, corners + nBaseCorners );
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128 for(
unsigned int i = 0; i < nBaseCorners; ++i )
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129 corners[ i+nBaseCorners ][ dim-1 ] = ct( 1 );
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130 return 2*nBaseCorners;
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134 corners[ nBaseCorners ] = FieldVector< ct, cdim >( ct( 0 ) );
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135 corners[ nBaseCorners ][ dim-1 ] = ct( 1 );
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136 return nBaseCorners+1;
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141 *corners = FieldVector< ct, cdim >( ct( 0 ) );
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151 unsigned long referenceVolumeInverse (
unsigned int topologyId,
int dim );
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154 inline ct referenceVolume (
unsigned int topologyId,
int dim )
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156 return ct( 1 ) / ct( referenceVolumeInverse( topologyId, dim ) );
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179 template<
class ct,
int mydim,
int cdim,
class Traits = MultiLinearGeometryTraits< ct > >
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164 template<
class ct,
int cdim >
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166 referenceOrigins (
unsigned int topologyId,
int dim,
int codim, FieldVector< ct, cdim > *origins )
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168 assert( (dim >= 0) && (dim <= cdim) );
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169 assert( topologyId < numTopologies( dim ) );
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170 assert( (codim >= 0) && (codim <= dim) );
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174 const unsigned int baseId = baseTopologyId( topologyId, dim );
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175 if( isPrism( topologyId, dim ) )
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177 const unsigned int n = (codim < dim ? referenceOrigins( baseId, dim-1, codim, origins ) : 0);
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178 const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins+n );
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179 for(
unsigned int i = 0; i < m; ++i )
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181 origins[ n+m+i ] = origins[ n+i ];
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182 origins[ n+m+i ][ dim-1 ] = ct( 1 );
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188 const unsigned int m = referenceOrigins( baseId, dim-1, codim-1, origins );
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191 origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
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192 origins[ m ][ dim-1 ] = ct( 1 );
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196 return m+referenceOrigins( baseId, dim-1, codim, origins+m );
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201 origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
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207 typedef FieldMatrix< ctype, coorddimension, mydimension >
Jacobian;
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211 template<
class ct,
int cdim,
int mydim >
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213 referenceEmbeddings (
unsigned int topologyId,
int dim,
int codim,
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214 FieldVector< ct, cdim > *origins,
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215 FieldMatrix< ct, mydim, cdim > *jacobianTransposeds )
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217 assert( (0 <= codim) && (codim <= dim) && (dim <= cdim) );
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218 assert( (dim - codim <= mydim) && (mydim <= cdim) );
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219 assert( topologyId < numTopologies( dim ) );
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222 static const bool hasSingleGeometryType = Traits::template hasSingleGeometryType< mydimension >::v;
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226 typedef typename std::conditional< hasSingleGeometryType, std::integral_constant< unsigned int, Traits::template hasSingleGeometryType< mydimension >::topologyId >,
unsigned int >
::type TopologyId;
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238 template<
class Corners >
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254 template<
class Corners >
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223 const unsigned int baseId = baseTopologyId( topologyId, dim );
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224 if( isPrism( topologyId, dim ) )
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226 const unsigned int n = (codim < dim ? referenceEmbeddings( baseId, dim-1, codim, origins, jacobianTransposeds ) : 0);
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227 for(
unsigned int i = 0; i < n; ++i )
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228 jacobianTransposeds[ i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
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230 const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins+n, jacobianTransposeds+n );
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231 std::copy( origins+n, origins+n+m, origins+n+m );
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232 std::copy( jacobianTransposeds+n, jacobianTransposeds+n+m, jacobianTransposeds+n+m );
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233 for(
unsigned int i = 0; i < m; ++i )
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234 origins[ n+m+i ][ dim-1 ] = ct( 1 );
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240 const unsigned int m = referenceEmbeddings( baseId, dim-1, codim-1, origins, jacobianTransposeds );
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243 origins[ m ] = FieldVector< ct, cdim >( ct( 0 ) );
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244 origins[ m ][ dim-1 ] = ct( 1 );
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245 jacobianTransposeds[ m ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
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250 const unsigned int n = referenceEmbeddings( baseId, dim-1, codim, origins+m, jacobianTransposeds+m );
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251 for(
unsigned int i = 0; i < n; ++i )
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253 for(
int k = 0; k < dim-1; ++k )
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254 jacobianTransposeds[ m+i ][ dim-codim-1 ][ k ] = -origins[ m+i ][ k ];
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255 jacobianTransposeds[ m+i ][ dim-codim-1 ][ dim-1 ] = ct( 1 );
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263 origins[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
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264 jacobianTransposeds[ 0 ] = FieldMatrix< ct, mydim, cdim >( ct( 0 ) );
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265 for(
int k = 0; k < dim; ++k )
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266 jacobianTransposeds[ 0 ][ k ][ k ] = ct( 1 );
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277 assert( (i >= 0) && (i <
corners()) );
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278 return std::cref(corners_).get()[ i ];
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294 auto cit = begin(std::cref(corners_).get());
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314 const ctype tolerance = Traits::tolerance();
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317 const bool affineMapping = this->
affine();
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321 const GlobalCoordinate dglobal = (*this).global( x ) - globalCoord;
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322 const bool invertible =
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323 MatrixHelper::template xTRightInvA< mydimension, coorddimension >(
jacobianTransposed( x ), dglobal, dx );
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331 if ( affineMapping )
break;
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332 }
while( dx.two_norm2() > tolerance );
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382 auto cit = begin(std::cref(corners_).get());
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383 jacobianTransposed< false >(
topologyId(), std::integral_constant< int, mydimension >(), cit,
ctype( 1 ),
local,
ctype( 1 ), jt );
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276 template<
class ct,
int cdim >
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278 referenceIntegrationOuterNormals (
unsigned int topologyId,
int dim,
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279 const FieldVector< ct, cdim > *origins,
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280 FieldVector< ct, cdim > *normals )
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282 assert( (dim > 0) && (dim <= cdim) );
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283 assert( topologyId < numTopologies( dim ) );
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287 const unsigned int baseId = baseTopologyId( topologyId, dim );
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288 if( isPrism( topologyId, dim ) )
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290 const unsigned int numBaseFaces
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291 = referenceIntegrationOuterNormals( baseId, dim-1, origins, normals );
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293 for(
unsigned int i = 0; i < 2; ++i )
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295 normals[ numBaseFaces+i ] = FieldVector< ct, cdim >( ct( 0 ) );
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296 normals[ numBaseFaces+i ][ dim-1 ] = ct( 2*
int( i )-1 );
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299 return numBaseFaces+2;
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303 normals[ 0 ] = FieldVector< ct, cdim >( ct( 0 ) );
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304 normals[ 0 ][ dim-1 ] = ct( -1 );
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306 const unsigned int numBaseFaces
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307 = referenceIntegrationOuterNormals( baseId, dim-1, origins+1, normals+1 );
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308 for(
unsigned int i = 1; i <= numBaseFaces; ++i )
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309 normals[ i ][ dim-1 ] = normals[ i ]*origins[ i ];
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311 return numBaseFaces+1;
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316 for(
unsigned int i = 0; i < 2; ++i )
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318 normals[ i ] = FieldVector< ct, cdim >( ct( 0 ) );
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319 normals[ i ][ 0 ] = ct( 2*
int( i )-1 );
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326 template<
class ct,
int cdim >
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328 referenceIntegrationOuterNormals (
unsigned int topologyId,
int dim,
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329 FieldVector< ct, cdim > *normals )
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331 assert( (dim > 0) && (dim <= cdim) );
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333 FieldVector< ct, cdim > *origins
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334 =
new FieldVector< ct, cdim >[
size( topologyId, dim, 1 ) ];
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335 referenceOrigins( topologyId, dim, 1, origins );
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337 const unsigned int numFaces
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338 = referenceIntegrationOuterNormals( topologyId, dim, origins, normals );
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339 assert( numFaces ==
size( topologyId, dim, 1 ) );
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371 template<
class ctype_,
int dim >
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372 class ReferenceElementImplementation
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378 using ctype = ctype_;
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381 using CoordinateField = ctype;
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384 using Coordinate = Dune::FieldVector<ctype,dim>;
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387 static constexpr int dimension = dim;
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390 typedef ctype Volume;
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394 friend class Impl::ReferenceElementContainer< ctype, dim >;
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396 struct SubEntityInfo;
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398 template<
int codim >
struct CreateGeometries;
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402 template<
int codim >
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406 typedef AffineGeometry< ctype, dim-codim, dim > Geometry;
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410 ReferenceElementImplementation (
const ReferenceElementImplementation& ) =
delete;
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432 return topologyId( std::integral_constant< bool, hasSingleGeometryType >() );
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435 template<
bool add,
int dim,
class CornerIterator >
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439 template<
bool add,
class CornerIterator >
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444 template<
bool add,
int rows,
int dim,
class CornerIterator >
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447 const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt );
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448 template<
bool add,
int rows,
class CornerIterator >
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451 const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt );
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453 template<
int dim,
class CornerIterator >
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455 template<
class CornerIterator >
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462 auto cit = begin(std::cref(corners_).get());
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463 return affine(
topologyId(), std::integral_constant< int, mydimension >(), cit, jacobianT );
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470 static unsigned int toUnsignedInt(
unsigned int i) {
return i; }
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471 template<
unsigned int v>
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472 static unsigned int toUnsignedInt(std::integral_constant<unsigned int,v> ) {
return v; }
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474 unsigned int topologyId ( std::integral_constant< bool, false > )
const {
return refElement().type().id(); }
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477 typename Traits::template CornerStorage< mydimension, coorddimension >::Type corners_;
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413 ReferenceElementImplementation& operator= (
const ReferenceElementImplementation& ) =
delete;
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416 ReferenceElementImplementation () =
default;
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422 int size (
int c )
const \n+
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424 assert( (c >= 0) && (c <= dim) );
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425 return info_[ c ].size();
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439 int size (
int i,
int c,
int cc )
const \n+
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441 assert( (i >= 0) && (i <
size( c )) );
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442 return info_[ c ][ i ].size( cc );
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458 int subEntity (
int i,
int c,
int ii,
int cc )
const \n+
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460 assert( (i >= 0) && (i <
size( c )) );
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461 return info_[ c ][ i ].number( ii, cc );
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479 auto subEntities (
int i,
int c,
int cc )
const \n+
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481 assert( (i >= 0) && (i <
size( c )) );
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482 return info_[ c ][ i ].numbers( cc );
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485 template<
class ct,
int mydim,
int cdim,
class Traits >
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487 :
public FieldMatrix< ctype, coorddimension, mydimension >
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489 typedef FieldMatrix< ctype, coorddimension, mydimension > Base;
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494 detInv_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jt,
static_cast< Base &
>( *
this ) );
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499 detInv_ = MatrixHelper::template sqrtDetAAT< mydimension, coorddimension >( jt );
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493 const GeometryType &type (
int i,
int c )
const \n+
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495 assert( (i >= 0) && (i <
size( c )) );
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496 return info_[ c ][ i ].type();
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500 const GeometryType &type ()
const {
return type( 0, 0 ); }
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523 template<
class ct,
int mydim,
int cdim,
class Traits = MultiLinearGeometryTraits< ct > >
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511 const Coordinate &position(
int i,
int c )
const \n+
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513 assert( (c >= 0) && (c <= dim) );
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514 return baryCenters_[ c ][ i ];
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524 bool checkInside (
const Coordinate &local )
const \n+
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526 const ctype tolerance = ctype( 64 ) * std::numeric_limits< ctype >::epsilon();
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527 return Impl::template checkInside< ctype, dim >( type().
id(), dim, local, tolerance );
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550 template<
class CornerStorage >
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553 affine_(
Base::
affine( jacobianTransposed_ ) ),
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554 jacobianInverseTransposedComputed_( false ),
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555 integrationElementComputed_( false )
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\n-
\n-
558 template<
class CornerStorage >
\n-
\n-
\n-
560 :
Base( gt, cornerStorage ),
\n-
561 affine_(
Base::
affine( jacobianTransposed_ ) ),
\n-
562 jacobianInverseTransposedComputed_( false ),
\n-
563 integrationElementComputed_( false )
\n-
\n-
\n+
541 template<
int codim >
\n+
542 typename Codim< codim >::Geometry geometry (
int i )
const \n+
\n+
544 return std::get< codim >( geometries_ )[ i ];
\n+
\n+
\n+
548 Volume volume ()
const \n+
\n+
\n+
\n+
\n+
560 const Coordinate &integrationOuterNormal (
int face )
const \n+
\n+
562 assert( (face >= 0) && (face <
int( integrationNormals_.size() )) );
\n+
563 return integrationNormals_[ face ];
\n+
\n
\n-
\n-
\n-
\n+
\n+
567 void initialize (
unsigned int topologyId )
\n+
\n+
569 assert( topologyId < Impl::numTopologies( dim ) );
\n
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
609 if( jacobianInverseTransposedComputed_ )
\n-
\n-
\n-
612 MatrixHelper::template xTRightInvA< mydimension, coorddimension >( jacobianTransposed_,
global -
corner( 0 ),
local );
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
637 if( !integrationElementComputed_ )
\n-
\n-
\n-
640 integrationElementComputed_ =
true;
\n-
\n-
642 return jacobianInverseTransposed_.
detInv();
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
669 return jacobianTransposed_;
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
684 if( !jacobianInverseTransposedComputed_ )
\n-
\n-
686 jacobianInverseTransposed_.
setup( jacobianTransposed_ );
\n-
687 jacobianInverseTransposedComputed_ =
true;
\n-
688 integrationElementComputed_ =
true;
\n-
\n-
690 return jacobianInverseTransposed_;
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
725 mutable bool affine_ : 1;
\n-
\n-
727 mutable bool jacobianInverseTransposedComputed_ : 1;
\n-
728 mutable bool integrationElementComputed_ : 1;
\n-
\n-
\n-
\n+
\n+
572 for(
int codim = 0; codim <= dim; ++codim )
\n+
\n+
574 const unsigned int size = Impl::size( topologyId, dim, codim );
\n+
575 info_[ codim ].resize( size );
\n+
576 for(
unsigned int i = 0; i <
size; ++i )
\n+
577 info_[ codim ][ i ].initialize( topologyId, codim, i );
\n+
\n+
\n+
\n+
581 const unsigned int numVertices =
size( dim );
\n+
582 baryCenters_[ dim ].resize( numVertices );
\n+
583 Impl::referenceCorners( topologyId, dim, &(baryCenters_[ dim ][ 0 ]) );
\n+
\n+
\n+
586 for(
int codim = 0; codim < dim; ++codim )
\n+
\n+
588 baryCenters_[ codim ].resize(
size(codim) );
\n+
589 for(
int i = 0; i <
size( codim ); ++i )
\n+
\n+
591 baryCenters_[ codim ][ i ] = Coordinate( ctype( 0 ) );
\n+
592 const unsigned int numCorners =
size( i, codim, dim );
\n+
593 for(
unsigned int j = 0; j < numCorners; ++j )
\n+
594 baryCenters_[ codim ][ i ] += baryCenters_[ dim ][ subEntity( i, codim, j, dim ) ];
\n+
595 baryCenters_[ codim ][ i ] *= ctype( 1 ) / ctype( numCorners );
\n+
\n+
\n+
\n+
\n+
600 volume_ = Impl::template referenceVolume< ctype >( topologyId, dim );
\n+
\n+
\n+
\n+
\n+
605 integrationNormals_.resize(
size( 1 ) );
\n+
606 Impl::referenceIntegrationOuterNormals( topologyId, dim, &(integrationNormals_[ 0 ]) );
\n+
\n+
\n+
\n+
610 Hybrid::forEach( std::make_index_sequence< dim+1 >{}, [ & ](
auto i ){ CreateGeometries< i >::apply( *
this, geometries_ ); } );
\n+
\n+
\n+
613 template<
int... codim >
\n+
614 static std::tuple< std::vector< typename Codim< codim >::Geometry >... >
\n+
615 makeGeometryTable ( std::integer_sequence< int, codim... > );
\n+
\n+
618 typedef decltype( makeGeometryTable( std::make_integer_sequence< int, dim+1 >() ) ) GeometryTable;
\n+
\n+
\n+
\n+
623 std::vector< Coordinate > baryCenters_[ dim+1 ];
\n+
624 std::vector< Coordinate > integrationNormals_;
\n+
\n+
627 GeometryTable geometries_;
\n+
\n+
629 std::vector< SubEntityInfo > info_[ dim+1 ];
\n+
\n+
\n+
633 template<
class ctype,
int dim >
\n+
634 struct ReferenceElementImplementation< ctype, dim >::SubEntityInfo
\n+
\n+
\n+
\n+
\n+
639 static constexpr std::size_t maxSubEntityCount()
\n+
\n+
641 std::size_t maxCount=0;
\n+
642 for(std::size_t codim=0; codim<=dim; ++codim)
\n+
643 maxCount = std::max(maxCount,
binomial(std::size_t(dim),codim)*(1 << codim));
\n+
\n+
\n+
\n+
647 using SubEntityFlags = std::bitset<maxSubEntityCount()>;
\n+
\n+
\n+
650 :
public Dune::IteratorRange<const unsigned int*>
\n+
\n+
652 using Base =
typename Dune::IteratorRange<const unsigned int*>;
\n+
\n+
\n+
\n+
656 using iterator = Base::iterator;
\n+
657 using const_iterator = Base::const_iterator;
\n+
\n+
659 SubEntityRange(
const iterator& begin,
const iterator& end,
const SubEntityFlags& contains) :
\n+
\n+
661 containsPtr_(&contains),
\n+
\n+
\n+
\n+
\n+
\n+
667 containsPtr_(nullptr),
\n+
\n+
\n+
\n+
671 std::size_t
size()
const \n+
\n+
\n+
\n+
\n+
676 bool contains(std::size_t i)
const \n+
\n+
678 return (*containsPtr_)[i];
\n+
\n+
\n+
\n+
682 const SubEntityFlags* containsPtr_;
\n+
\n+
\n+
\n+
\n+
687 using NumberRange =
typename Dune::IteratorRange<const unsigned int*>;
\n+
\n+
\n+
690 : numbering_( nullptr )
\n+
\n+
692 std::fill( offset_.begin(), offset_.end(), 0 );
\n+
\n+
\n+
695 SubEntityInfo (
const SubEntityInfo &other )
\n+
696 : offset_( other.offset_ ),
\n+
697 type_( other.type_ ),
\n+
698 containsSubentity_( other.containsSubentity_ )
\n+
\n+
700 numbering_ = allocate();
\n+
701 std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
\n+
\n+
\n+
704 ~SubEntityInfo () { deallocate( numbering_ ); }
\n+
\n+
706 const SubEntityInfo &operator= (
const SubEntityInfo &other )
\n+
\n+
\n+
709 offset_ = other.offset_;
\n+
\n+
711 deallocate( numbering_ );
\n+
712 numbering_ = allocate();
\n+
713 std::copy( other.numbering_, other.numbering_ + capacity(), numbering_ );
\n+
\n+
715 containsSubentity_ = other.containsSubentity_;
\n+
\n+
\n+
\n+
\n+
720 int size (
int cc )
const \n+
\n+
722 assert( (cc >= 0) && (cc <= dim) );
\n+
723 return (offset_[ cc+1 ] - offset_[ cc ]);
\n+
\n+
\n+
726 int number (
int ii,
int cc )
const \n+
\n+
728 assert( (ii >= 0) && (ii <
size( cc )) );
\n+
729 return numbering_[ offset_[ cc ] + ii ];
\n+
\n
\n-
\n-
\n-
\n-
\n-
736 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
737 inline typename MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverseTransposed
\n-
\n-
\n-
\n-
\n-
741 jit.
setup( jacobianTransposed( local ) );
\n-
\n-
\n-
\n-
\n-
\n-
746 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
747 template<
bool add,
int dim,
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
\n-
\n-
753 const ctype xn = df*x[ dim-1 ];
\n-
\n+
732 auto numbers (
int cc )
const \n+
\n+
734 return SubEntityRange( numbering_ + offset_[ cc ], numbering_ + offset_[ cc+1 ], containsSubentity_[cc]);
\n+
\n+
\n+
737 const GeometryType &type ()
const {
return type_; }
\n+
\n+
739 void initialize (
unsigned int topologyId,
int codim,
unsigned int i )
\n+
\n+
741 const unsigned int subId = Impl::subTopologyId( topologyId, dim, codim, i );
\n+
742 type_ = GeometryType( subId, dim-codim );
\n+
\n+
\n+
745 for(
int cc = 0; cc <= codim; ++cc )
\n+
\n+
747 for(
int cc = codim; cc <= dim; ++cc )
\n+
748 offset_[ cc+1 ] = offset_[ cc ] + Impl::size( subId, dim-codim, cc-codim );
\n+
\n+
\n+
751 deallocate( numbering_ );
\n+
752 numbering_ = allocate();
\n+
753 for(
int cc = codim; cc <= dim; ++cc )
\n+
754 Impl::subTopologyNumbering( topologyId, dim, codim, i, cc-codim, numbering_+offset_[ cc ], numbering_+offset_[ cc+1 ] );
\n
\n-
756 if( Impl::isPrism( toUnsignedInt(topologyId), mydimension, mydimension-dim ) )
\n-
\n-
\n-
759 global< add >( topologyId, std::integral_constant< int, dim-1 >(), cit, df, x, rf*cxn, y );
\n-
\n-
761 global< true >( topologyId, std::integral_constant< int, dim-1 >(), cit, df, x, rf*xn, y );
\n-
\n-
\n-
\n-
765 assert( Impl::isPyramid( toUnsignedInt(topologyId), mydimension, mydimension-dim ) );
\n-
\n-
767 if( cxn > Traits::tolerance() || cxn < -Traits::tolerance() )
\n-
768 global< add >( topologyId, std::integral_constant< int, dim-1 >(), cit, df/cxn, x, rf*cxn, y );
\n-
\n-
770 global< add >( topologyId, std::integral_constant< int, dim-1 >(), cit, df, x,
ctype( 0 ), y );
\n-
\n-
772 y.axpy( rf*xn, *cit );
\n-
\n-
\n-
\n-
\n-
\n-
777 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
778 template<
bool add,
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
786 for(
int i = 0; i < coorddimension; ++i )
\n-
787 y[ i ] = (add ? y[ i ] + rf*origin[ i ] : rf*origin[ i ]);
\n-
\n-
\n-
\n+
\n+
757 for(std::size_t cc=0; cc<= dim; ++cc)
\n+
\n+
759 containsSubentity_[cc].reset();
\n+
760 for(std::size_t idx=0; idx<std::size_t(
size(cc)); ++idx)
\n+
761 containsSubentity_[cc][number(idx,cc)] =
true;
\n+
\n+
\n+
\n+
\n+
766 int codim ()
const {
return dim - type().dim(); }
\n+
\n+
768 unsigned int *allocate () {
return (capacity() != 0 ?
new unsigned int[ capacity() ] : nullptr); }
\n+
769 void deallocate (
unsigned int *ptr ) {
delete[] ptr; }
\n+
770 unsigned int capacity ()
const {
return offset_[ dim+1 ]; }
\n+
\n+
\n+
773 unsigned int *numbering_;
\n+
774 std::array< unsigned int, dim+2 > offset_;
\n+
\n+
776 std::array< SubEntityFlags, dim+1> containsSubentity_;
\n+
\n+
\n+
\n+
780 template<
class ctype,
int dim >
\n+
781 template<
int codim >
\n+
782 struct ReferenceElementImplementation< ctype, dim >::CreateGeometries
\n+
\n+
\n+
785 static typename ReferenceElements< ctype, dim-cc >::ReferenceElement
\n+
786 subRefElement(
const ReferenceElementImplementation< ctype, dim > &refElement,
int i, std::integral_constant< int, cc > )
\n+
\n+
\n+
\n
\n-
791 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
792 template<
bool add,
int rows,
int dim,
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
796 const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt )
\n-
\n-
798 assert( rows >= dim );
\n-
\n-
800 const ctype xn = df*x[ dim-1 ];
\n-
\n-
\n-
\n-
804 if( Impl::isPrism( toUnsignedInt(topologyId), mydimension, mydimension-dim ) )
\n-
\n-
\n-
807 jacobianTransposed< add >( topologyId, std::integral_constant< int, dim-1 >(), cit2, df, x, rf*cxn, jt );
\n-
\n-
809 jacobianTransposed< true >( topologyId, std::integral_constant< int, dim-1 >(), cit2, df, x, rf*xn, jt );
\n-
\n-
811 global< add >( topologyId, std::integral_constant< int, dim-1 >(), cit, df, x, -rf, jt[ dim-1 ] );
\n-
812 global< true >( topologyId, std::integral_constant< int, dim-1 >(), cit, df, x, rf, jt[ dim-1 ] );
\n-
\n-
\n-
\n-
816 assert( Impl::isPyramid( toUnsignedInt(topologyId), mydimension, mydimension-dim ) );
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
858 ctype dfcxn = (cxn > Traits::tolerance() || cxn < -Traits::tolerance()) ?
ctype(df / cxn) :
ctype(0);
\n-
\n-
\n-
\n-
\n-
863 global< add >( topologyId, std::integral_constant< int, dim-1 >(), cit, dfcxn, x, -rf, jt[ dim-1 ] );
\n-
\n-
865 jt[ dim-1 ].axpy( rf, *cit );
\n-
\n-
\n-
\n-
\n-
870 FieldMatrix<
ctype, dim-1, coorddimension > jt2;
\n-
\n-
872 jacobianTransposed< false >( topologyId, std::integral_constant< int, dim-1 >(), cit2, dfcxn, x, rf, jt2 );
\n-
\n-
\n-
\n-
876 for(
int j = 0; j < dim-1; ++j )
\n-
\n-
\n-
879 jt[ dim-1 ].axpy( dfcxn*x[ j ], jt2[ j ] );
\n-
\n-
\n-
\n-
\n-
\n-
885 jacobianTransposed< false >( topologyId, std::integral_constant< int, dim-1 >(), cit2, dfcxn, x, rf, jt );
\n-
\n-
887 for(
int j = 0; j < dim-1; ++j )
\n-
888 jt[ dim-1 ].axpy( dfcxn*x[ j ], jt[ j ] );
\n-
\n-
\n-
\n-
\n-
\n-
893 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
894 template<
bool add,
int rows,
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
898 const ctype &, FieldMatrix< ctype, rows, cdim > & )
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
905 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
906 template<
int dim,
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
\n-
911 if( !affine( topologyId, std::integral_constant< int, dim-1 >(), cit, jt ) )
\n-
\n-
\n-
\n-
915 if( Impl::isPrism( toUnsignedInt(topologyId), mydimension, mydimension-dim ) )
\n-
\n-
\n-
918 if( !affine( topologyId, std::integral_constant< int, dim-1 >(), cit, jtTop ) )
\n-
\n-
\n-
\n-
\n-
923 for(
int i = 0; i < dim-1; ++i )
\n-
924 norm += (jtTop[ i ] - jt[ i ]).two_norm2();
\n-
925 if( norm >= Traits::tolerance() )
\n-
\n-
\n-
\n-
\n-
930 jt[ dim-1 ] = orgTop - orgBottom;
\n-
\n-
\n-
\n-
\n-
934 template<
class ct,
int mydim,
int cdim,
class Traits >
\n-
935 template<
class CornerIterator >
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n-
\n+
\n+
792 subRefElement(
const ReferenceElementImplementation< ctype, dim > &refElement,
\n+
793 [[maybe_unused]]
int i, std::integral_constant<int, 0>)
\n+
\n+
\n+
\n+
\n+
798 static void apply (
const ReferenceElementImplementation< ctype, dim > &refElement, GeometryTable &geometries )
\n+
\n+
800 const int size = refElement.size( codim );
\n+
801 std::vector< FieldVector< ctype, dim > > origins( size );
\n+
802 std::vector< FieldMatrix< ctype, dim - codim, dim > > jacobianTransposeds( size );
\n+
803 Impl::referenceEmbeddings( refElement.type().id(), dim, codim, &(origins[ 0 ]), &(jacobianTransposeds[ 0 ]) );
\n+
\n+
805 std::get< codim >( geometries ).reserve( size );
\n+
806 for(
int i = 0; i <
size; ++i )
\n+
\n+
808 typename Codim< codim >::Geometry geometry( subRefElement( refElement, i, std::integral_constant< int, codim >() ), origins[ i ], jacobianTransposeds[ i ] );
\n+
809 std::get< codim >( geometries ).push_back( geometry );
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
An implementation of the Geometry interface for affine geometries.
\n
A unique label for each type of element that can occur in a grid.
\n-
An implementation of the Geometry interface for affine geometries.
\n+
\n
Definition affinegeometry.hh:21
\n-
Class providing access to the singletons of the reference elements.
Definition referenceelements.hh:170
\n+
@ size
Definition quadraturerules.hh:145
\n+
int binomial(int upper, int lower)
calculate
Definition simplex.cc:305
\n
typename Container::ReferenceElement ReferenceElement
The reference element type.
Definition referenceelements.hh:188
\n-
default traits class for MultiLinearGeometry
Definition multilineargeometry.hh:39
\n-
Impl::FieldMatrixHelper< ct > MatrixHelper
helper structure containing some matrix routines
Definition multilineargeometry.hh:58
\n-
static ct tolerance()
tolerance to numerical algorithms
Definition multilineargeometry.hh:61
\n-
template specifying the storage for the corners
Definition multilineargeometry.hh:129
\n-
std::vector< FieldVector< ct, cdim > > Type
Definition multilineargeometry.hh:130
\n-
will there be only one geometry type for a dimension?
Definition multilineargeometry.hh:148
\n-
static const unsigned int topologyId
Definition multilineargeometry.hh:150
\n-
static const bool v
Definition multilineargeometry.hh:149
\n-
generic geometry implementation based on corner coordinates
Definition multilineargeometry.hh:181
\n-
static void global(TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)
Definition multilineargeometry.hh:749
\n-
static const int mydimension
geometry dimension
Definition multilineargeometry.hh:189
\n-
Dune::GeometryType type() const
obtain the name of the reference element
Definition multilineargeometry.hh:269
\n-
Traits::MatrixHelper MatrixHelper
Definition multilineargeometry.hh:225
\n-
FieldVector< ctype, coorddimension > GlobalCoordinate
type of global coordinates
Definition multilineargeometry.hh:196
\n-
static void jacobianTransposed(TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt)
Definition multilineargeometry.hh:896
\n-
JacobianTransposed jacobianTransposed(const LocalCoordinate &local) const
obtain the transposed of the Jacobian
Definition multilineargeometry.hh:377
\n-
ReferenceElement refElement() const
Definition multilineargeometry.hh:425
\n-
GlobalCoordinate global(const LocalCoordinate &local) const
evaluate the mapping
Definition multilineargeometry.hh:290
\n-
GlobalCoordinate center() const
obtain the centroid of the mapping's image
Definition multilineargeometry.hh:282
\n-
GlobalCoordinate corner(int i) const
obtain coordinates of the i-th corner
Definition multilineargeometry.hh:275
\n-
Dune::ReferenceElements< ctype, mydimension > ReferenceElements
Definition multilineargeometry.hh:214
\n-
ct ctype
coordinate type
Definition multilineargeometry.hh:186
\n-
static void jacobianTransposed(TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt)
Definition multilineargeometry.hh:794
\n-
static const int coorddimension
coordinate dimension
Definition multilineargeometry.hh:191
\n-
int corners() const
obtain number of corners of the corresponding reference element
Definition multilineargeometry.hh:272
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TopologyId topologyId() const
Definition multilineargeometry.hh:430
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friend ReferenceElement referenceElement(const MultiLinearGeometry &geometry)
Definition multilineargeometry.hh:395
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LocalCoordinate local(const GlobalCoordinate &globalCoord) const
evaluate the inverse mapping
Definition multilineargeometry.hh:312
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static void global(TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)
Definition multilineargeometry.hh:780
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Volume volume() const
obtain the volume of the mapping's image
Definition multilineargeometry.hh:363
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FieldVector< ctype, mydimension > LocalCoordinate
type of local coordinates
Definition multilineargeometry.hh:194
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MultiLinearGeometry(const ReferenceElement &refElement, const Corners &corners)
constructor
Definition multilineargeometry.hh:239
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static bool affine(TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, JacobianTransposed &jt)
Definition multilineargeometry.hh:937
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std::conditional< hasSingleGeometryType, std::integral_constant< unsignedint, Traits::templatehasSingleGeometryType< mydimension >::topologyId >, unsignedint >::type TopologyId
Definition multilineargeometry.hh:226
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ctype Volume
type of volume
Definition multilineargeometry.hh:198
\n-
static bool affine(TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, JacobianTransposed &jt)
Definition multilineargeometry.hh:908
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JacobianInverse jacobianInverse(const LocalCoordinate &local) const
Obtain the Jacobian's inverse.
Definition multilineargeometry.hh:418
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MultiLinearGeometry(Dune::GeometryType gt, const Corners &corners)
constructor
Definition multilineargeometry.hh:255
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FieldMatrix< ctype, mydimension, coorddimension > JacobianTransposed
type of jacobian transposed
Definition multilineargeometry.hh:201
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ReferenceElements::ReferenceElement ReferenceElement
type of reference element
Definition multilineargeometry.hh:219
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JacobianInverseTransposed jacobianInverseTransposed(const LocalCoordinate &local) const
obtain the transposed of the Jacobian's inverse
Definition multilineargeometry.hh:738
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FieldMatrix< ctype, coorddimension, mydimension > Jacobian
Type for the Jacobian matrix.
Definition multilineargeometry.hh:207
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bool affine() const
is this mapping affine?
Definition multilineargeometry.hh:262
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FieldMatrix< ctype, mydimension, coorddimension > JacobianInverse
Type for the inverse Jacobian matrix.
Definition multilineargeometry.hh:210
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bool affine(JacobianTransposed &jacobianT) const
Definition multilineargeometry.hh:458
\n-
Volume integrationElement(const LocalCoordinate &local) const
obtain the integration element
Definition multilineargeometry.hh:350
\n-
Jacobian jacobian(const LocalCoordinate &local) const
Obtain the Jacobian.
Definition multilineargeometry.hh:407
\n-
Definition multilineargeometry.hh:488
\n-
void setup(const JacobianTransposed &jt)
Definition multilineargeometry.hh:492
\n-
ctype det() const
Definition multilineargeometry.hh:502
\n-
ctype detInv() const
Definition multilineargeometry.hh:503
\n-
void setupDeterminant(const JacobianTransposed &jt)
Definition multilineargeometry.hh:497
\n-
Implement a MultiLinearGeometry with additional caching.
Definition multilineargeometry.hh:526
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GlobalCoordinate global(const LocalCoordinate &local) const
evaluate the mapping
Definition multilineargeometry.hh:580
\n-
Base::ReferenceElement ReferenceElement
Definition multilineargeometry.hh:534
\n-
bool affine() const
is this mapping affine?
Definition multilineargeometry.hh:567
\n-
CachedMultiLinearGeometry(const ReferenceElement &referenceElement, const CornerStorage &cornerStorage)
Definition multilineargeometry.hh:551
\n-
ReferenceElement refElement() const
Definition multilineargeometry.hh:425
\n-
LocalCoordinate local(const GlobalCoordinate &global) const
evaluate the inverse mapping
Definition multilineargeometry.hh:604
\n-
Base::MatrixHelper MatrixHelper
Definition multilineargeometry.hh:531
\n-
Base::LocalCoordinate LocalCoordinate
Definition multilineargeometry.hh:541
\n-
JacobianInverse jacobianInverse(const LocalCoordinate &local) const
Obtain the Jacobian's inverse.
Definition multilineargeometry.hh:713
\n-
JacobianTransposed jacobianTransposed(const LocalCoordinate &local) const
obtain the transposed of the Jacobian
Definition multilineargeometry.hh:666
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GlobalCoordinate corner(int i) const
obtain coordinates of the i-th corner
Definition multilineargeometry.hh:275
\n-
Volume volume() const
obtain the volume of the mapping's image
Definition multilineargeometry.hh:649
\n-
CachedMultiLinearGeometry(Dune::GeometryType gt, const CornerStorage &cornerStorage)
Definition multilineargeometry.hh:559
\n-
ctype integrationElement(const LocalCoordinate &local) const
obtain the integration element
Definition multilineargeometry.hh:633
\n-
Base::ctype ctype
Definition multilineargeometry.hh:536
\n-
Jacobian jacobian(const LocalCoordinate &local) const
Obtain the Jacobian.
Definition multilineargeometry.hh:702
\n-
Base::JacobianInverseTransposed JacobianInverseTransposed
Definition multilineargeometry.hh:546
\n-
Base::JacobianTransposed JacobianTransposed
Definition multilineargeometry.hh:545
\n-
Base::JacobianInverse JacobianInverse
Definition multilineargeometry.hh:548
\n-
Base::Jacobian Jacobian
Definition multilineargeometry.hh:547
\n-
Base::Volume Volume
Definition multilineargeometry.hh:543
\n-
Base::GlobalCoordinate GlobalCoordinate
Definition multilineargeometry.hh:542
\n-
GlobalCoordinate center() const
obtain the centroid of the mapping's image
Definition multilineargeometry.hh:572
\n-
JacobianInverseTransposed jacobianInverseTransposed(const LocalCoordinate &local) const
obtain the transposed of the Jacobian's inverse
Definition multilineargeometry.hh:680
\n-
Unique label for each type of entities that can occur in DUNE grids.
Definition type.hh:126
\n+
static const ReferenceElement & general(const GeometryType &type)
get general reference elements
Definition referenceelements.hh:198
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