KratosMultiphysics
KRATOS Multiphysics (Kratos) is a framework for building parallel, multi-disciplinary simulation software, aiming at modularity, extensibility, and high performance. Kratos is written in C++, and counts with an extensive Python interface.
hexahedra_3d_27.h
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1 // | / |
2 // ' / __| _` | __| _ \ __|
3 // . \ | ( | | ( |\__ `
4 // _|\_\_| \__,_|\__|\___/ ____/
5 // Multi-Physics
6 //
7 // License: BSD License
8 // Kratos default license: kratos/license.txt
9 //
10 // Main authors: Riccardo Rossi
11 // Janosch Stascheit
12 // Felix Nagel
13 // contributors: Hoang Giang Bui
14 // Josep Maria Carbonell
15 //
16 
17 #pragma once
18 
19 // System includes
20 #include <numeric>
21 
22 // External includes
23 
24 // Project includes
25 #include "geometries/quadrilateral_3d_9.h"
26 #include "geometries/triangle_3d_3.h"
27 #include "utilities/integration_utilities.h"
28 #include "integration/hexahedron_gauss_legendre_integration_points.h"
29 
30 namespace Kratos
31 {
52 template<class TPointType> class Hexahedra3D27 : public Geometry<TPointType>
53 {
54 public:
62  typedef Geometry<TPointType> BaseType;
63 
67  typedef Line3D3<TPointType> EdgeType;
68  typedef Quadrilateral3D9<TPointType> FaceType;
69 
73  KRATOS_CLASS_POINTER_DEFINITION( Hexahedra3D27 );
74 
78  typedef GeometryData::IntegrationMethod IntegrationMethod;
79 
84  typedef typename BaseType::GeometriesArrayType GeometriesArrayType;
85 
89  typedef TPointType PointType;
90 
96  typedef typename BaseType::IndexType IndexType;
97 
98 
104  typedef typename BaseType::SizeType SizeType;
105 
110  typedef typename BaseType::PointsArrayType PointsArrayType;
111 
117  typedef typename BaseType::IntegrationPointType IntegrationPointType;
118 
125  typedef typename BaseType::IntegrationPointsArrayType IntegrationPointsArrayType;
126 
132  typedef typename BaseType::IntegrationPointsContainerType IntegrationPointsContainerType;
133 
138  typedef typename BaseType::ShapeFunctionsValuesContainerType
139  ShapeFunctionsValuesContainerType;
140 
145  typedef typename BaseType::ShapeFunctionsLocalGradientsContainerType
146  ShapeFunctionsLocalGradientsContainerType;
147 
153  typedef typename BaseType::JacobiansType JacobiansType;
154 
160  typedef typename BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType;
161 
167  typedef typename BaseType::ShapeFunctionsSecondDerivativesType
168  ShapeFunctionsSecondDerivativesType;
169 
173  typedef typename BaseType::NormalType NormalType;
174 
178  typedef typename BaseType::CoordinatesArrayType CoordinatesArrayType;
179 
183  typedef Matrix MatrixType;
184 
185 
190  Hexahedra3D27( const PointType& Point1, const PointType& Point2, const PointType& Point3,
191  const PointType& Point4, const PointType& Point5, const PointType& Point6,
192  const PointType& Point7, const PointType& Point8, const PointType& Point9,
193  const PointType& Point10, const PointType& Point11, const PointType& Point12,
194  const PointType& Point13, const PointType& Point14, const PointType& Point15,
195  const PointType& Point16, const PointType& Point17, const PointType& Point18,
196  const PointType& Point19, const PointType& Point20, const PointType& Point21,
197  const PointType& Point22, const PointType& Point23, const PointType& Point24,
198  const PointType& Point25, const PointType& Point26, const PointType& Point27
199  )
200  : BaseType( PointsArrayType(), &msGeometryData )
201  {
202  this->Points().push_back( typename PointType::Pointer( new PointType( Point1 ) ) );
203  this->Points().push_back( typename PointType::Pointer( new PointType( Point2 ) ) );
204  this->Points().push_back( typename PointType::Pointer( new PointType( Point3 ) ) );
205  this->Points().push_back( typename PointType::Pointer( new PointType( Point4 ) ) );
206  this->Points().push_back( typename PointType::Pointer( new PointType( Point5 ) ) );
207  this->Points().push_back( typename PointType::Pointer( new PointType( Point6 ) ) );
208  this->Points().push_back( typename PointType::Pointer( new PointType( Point7 ) ) );
209  this->Points().push_back( typename PointType::Pointer( new PointType( Point8 ) ) );
210  this->Points().push_back( typename PointType::Pointer( new PointType( Point9 ) ) );
211  this->Points().push_back( typename PointType::Pointer( new PointType( Point10 ) ) );
212  this->Points().push_back( typename PointType::Pointer( new PointType( Point11 ) ) );
213  this->Points().push_back( typename PointType::Pointer( new PointType( Point12 ) ) );
214  this->Points().push_back( typename PointType::Pointer( new PointType( Point13 ) ) );
215  this->Points().push_back( typename PointType::Pointer( new PointType( Point14 ) ) );
216  this->Points().push_back( typename PointType::Pointer( new PointType( Point15 ) ) );
217  this->Points().push_back( typename PointType::Pointer( new PointType( Point16 ) ) );
218  this->Points().push_back( typename PointType::Pointer( new PointType( Point17 ) ) );
219  this->Points().push_back( typename PointType::Pointer( new PointType( Point18 ) ) );
220  this->Points().push_back( typename PointType::Pointer( new PointType( Point19 ) ) );
221  this->Points().push_back( typename PointType::Pointer( new PointType( Point20 ) ) );
222  this->Points().push_back( typename PointType::Pointer( new PointType( Point21 ) ) );
223  this->Points().push_back( typename PointType::Pointer( new PointType( Point22 ) ) );
224  this->Points().push_back( typename PointType::Pointer( new PointType( Point23 ) ) );
225  this->Points().push_back( typename PointType::Pointer( new PointType( Point24 ) ) );
226  this->Points().push_back( typename PointType::Pointer( new PointType( Point25 ) ) );
227  this->Points().push_back( typename PointType::Pointer( new PointType( Point26 ) ) );
228  this->Points().push_back( typename PointType::Pointer( new PointType( Point27 ) ) );
229  }
230 
231  Hexahedra3D27( typename PointType::Pointer pPoint1,
232  typename PointType::Pointer pPoint2,
233  typename PointType::Pointer pPoint3,
234  typename PointType::Pointer pPoint4,
235  typename PointType::Pointer pPoint5,
236  typename PointType::Pointer pPoint6,
237  typename PointType::Pointer pPoint7,
238  typename PointType::Pointer pPoint8,
239  typename PointType::Pointer pPoint9,
240  typename PointType::Pointer pPoint10,
241  typename PointType::Pointer pPoint11,
242  typename PointType::Pointer pPoint12,
243  typename PointType::Pointer pPoint13,
244  typename PointType::Pointer pPoint14,
245  typename PointType::Pointer pPoint15,
246  typename PointType::Pointer pPoint16,
247  typename PointType::Pointer pPoint17,
248  typename PointType::Pointer pPoint18,
249  typename PointType::Pointer pPoint19,
250  typename PointType::Pointer pPoint20,
251  typename PointType::Pointer pPoint21,
252  typename PointType::Pointer pPoint22,
253  typename PointType::Pointer pPoint23,
254  typename PointType::Pointer pPoint24,
255  typename PointType::Pointer pPoint25,
256  typename PointType::Pointer pPoint26,
257  typename PointType::Pointer pPoint27 )
258  : BaseType( PointsArrayType(), &msGeometryData )
259  {
260  this->Points().push_back( pPoint1 );
261  this->Points().push_back( pPoint2 );
262  this->Points().push_back( pPoint3 );
263  this->Points().push_back( pPoint4 );
264  this->Points().push_back( pPoint5 );
265  this->Points().push_back( pPoint6 );
266  this->Points().push_back( pPoint7 );
267  this->Points().push_back( pPoint8 );
268  this->Points().push_back( pPoint9 );
269  this->Points().push_back( pPoint10 );
270  this->Points().push_back( pPoint11 );
271  this->Points().push_back( pPoint12 );
272  this->Points().push_back( pPoint13 );
273  this->Points().push_back( pPoint14 );
274  this->Points().push_back( pPoint15 );
275  this->Points().push_back( pPoint16 );
276  this->Points().push_back( pPoint17 );
277  this->Points().push_back( pPoint18 );
278  this->Points().push_back( pPoint19 );
279  this->Points().push_back( pPoint20 );
280  this->Points().push_back( pPoint21 );
281  this->Points().push_back( pPoint22 );
282  this->Points().push_back( pPoint23 );
283  this->Points().push_back( pPoint24 );
284  this->Points().push_back( pPoint25 );
285  this->Points().push_back( pPoint26 );
286  this->Points().push_back( pPoint27 );
287  }
288 
289  Hexahedra3D27( const PointsArrayType& ThisPoints )
290  : BaseType( ThisPoints, &msGeometryData )
291  {
292  if ( this->PointsNumber() != 27 )
293  KRATOS_ERROR << "Invalid points number. Expected 27, given " << this->PointsNumber() << std::endl;
294  }
295 
297  explicit Hexahedra3D27(
298  const IndexType GeometryId,
299  const PointsArrayType& rThisPoints
300  ) : BaseType( GeometryId, rThisPoints, &msGeometryData)
301  {
302  KRATOS_ERROR_IF( this->PointsNumber() != 27 ) << "Invalid points number. Expected 27, given " << this->PointsNumber() << std::endl;
303  }
304 
306  explicit Hexahedra3D27(
307  const std::string& rGeometryName,
308  const PointsArrayType& rThisPoints
309  ) : BaseType( rGeometryName, rThisPoints, &msGeometryData)
310  {
311  KRATOS_ERROR_IF(this->PointsNumber() != 27) << "Invalid points number. Expected 27, given " << this->PointsNumber() << std::endl;
312  }
313 
323  Hexahedra3D27( Hexahedra3D27 const& rOther )
324  : BaseType( rOther )
325  {
326  }
327 
340  template<class TOtherPointType> Hexahedra3D27( Hexahedra3D27<TOtherPointType> const& rOther )
341  : BaseType( rOther )
342  {
343  }
344 
346  ~Hexahedra3D27() override {}
347 
348  GeometryData::KratosGeometryFamily GetGeometryFamily() const override
349  {
350  return GeometryData::KratosGeometryFamily::Kratos_Hexahedra;
351  }
352 
353  GeometryData::KratosGeometryType GetGeometryType() const override
354  {
355  return GeometryData::KratosGeometryType::Kratos_Hexahedra3D27;
356  }
357 
373  Hexahedra3D27& operator=( const Hexahedra3D27& rOther )
374  {
375  BaseType::operator=( rOther );
376  return *this;
377  }
378 
390  template<class TOtherPointType>
391  Hexahedra3D27& operator=( Hexahedra3D27<TOtherPointType> const & rOther )
392  {
393  BaseType::operator=( rOther );
394 
395  return *this;
396  }
397 
398 
409  typename BaseType::Pointer Create(
410  IndexType NewId,
411  PointsArrayType const& rThisPoints
412  ) const override
413  {
414  return typename BaseType::Pointer( new Hexahedra3D27( NewId, rThisPoints ) );
415  }
416 
423  typename BaseType::Pointer Create(
424  const IndexType NewGeometryId,
425  const BaseType& rGeometry
426  ) const override
427  {
428  auto p_geometry = typename BaseType::Pointer( new Hexahedra3D27( NewGeometryId, rGeometry.Points() ) );
429  p_geometry->SetData(rGeometry.GetData());
430  return p_geometry;
431  }
432 
453  double Length() const override
454  {
455  return sqrt( fabs( this->DeterminantOfJacobian( PointType() ) ) );
456  }
457 
473  double Area() const override
474  {
475  return Volume();
476  }
477 
486  double Volume() const override
487  {
488  return IntegrationUtilities::ComputeVolume3DGeometry(*this);
489  }
490 
505  double DomainSize() const override
506  {
507  return Volume();
508  }
509 
518  bool IsInside(
519  const CoordinatesArrayType& rPoint,
520  CoordinatesArrayType& rResult,
521  const double Tolerance = std::numeric_limits<double>::epsilon()
522  ) const override
523  {
524  this->PointLocalCoordinates( rResult, rPoint );
525 
526  if ( std::abs( rResult[0] ) <= (1.0 + Tolerance) )
527  {
528  if ( std::abs( rResult[1] ) <= (1.0 + Tolerance) )
529  {
530  if ( std::abs( rResult[2] ) <= (1.0 + Tolerance) )
531  {
532  return true;
533  }
534  }
535  }
536 
537  return false;
538  }
539 
543 
555  SizeType EdgesNumber() const override
556  {
557  return 12;
558  }
559 
568  GeometriesArrayType GenerateEdges() const override
569  {
570  GeometriesArrayType edges = GeometriesArrayType();
571  typedef typename Geometry<TPointType>::Pointer EdgePointerType;
572  //0
573  edges.push_back( EdgePointerType( new EdgeType(
574  this->pGetPoint( 0 ),
575  this->pGetPoint( 1 ),
576  this->pGetPoint( 8 ) ) ) );
577  edges.push_back( EdgePointerType( new EdgeType(
578  this->pGetPoint( 1 ),
579  this->pGetPoint( 2 ),
580  this->pGetPoint( 9 ) ) ) );
581  edges.push_back( EdgePointerType( new EdgeType(
582  this->pGetPoint( 2 ),
583  this->pGetPoint( 3 ),
584  this->pGetPoint( 10 ) ) ) );
585  edges.push_back( EdgePointerType( new EdgeType(
586  this->pGetPoint( 3 ),
587  this->pGetPoint( 0 ),
588  this->pGetPoint( 11 ) ) ) );
589 
590  //4
591  edges.push_back( EdgePointerType( new EdgeType(
592  this->pGetPoint( 4 ),
593  this->pGetPoint( 5 ),
594  this->pGetPoint( 16 ) ) ) );
595  edges.push_back( EdgePointerType( new EdgeType(
596  this->pGetPoint( 5 ),
597  this->pGetPoint( 6 ),
598  this->pGetPoint( 17 ) ) ) );
599  edges.push_back( EdgePointerType( new EdgeType(
600  this->pGetPoint( 6 ),
601  this->pGetPoint( 7 ),
602  this->pGetPoint( 18 ) ) ) );
603  edges.push_back( EdgePointerType( new EdgeType(
604  this->pGetPoint( 7 ),
605  this->pGetPoint( 4 ),
606  this->pGetPoint( 19 ) ) ) );
607 
608  //8
609  edges.push_back( EdgePointerType( new EdgeType(
610  this->pGetPoint( 0 ),
611  this->pGetPoint( 4 ),
612  this->pGetPoint( 12 ) ) ) );
613  edges.push_back( EdgePointerType( new EdgeType(
614  this->pGetPoint( 1 ),
615  this->pGetPoint( 5 ),
616  this->pGetPoint( 13 ) ) ) );
617  edges.push_back( EdgePointerType( new EdgeType(
618  this->pGetPoint( 2 ),
619  this->pGetPoint( 6 ),
620  this->pGetPoint( 14 ) ) ) );
621  edges.push_back( EdgePointerType( new EdgeType(
622  this->pGetPoint( 3 ),
623  this->pGetPoint( 7 ),
624  this->pGetPoint( 15 ) ) ) );
625  return edges;
626  }
627 
633  double AverageEdgeLength() const override
634  {
635  constexpr double w = 1.0/12.0;
636  const GeometriesArrayType edges = this->GenerateEdges();
637  return std::accumulate(
638  edges.begin(),
639  edges.end(),
640  0.0,
641  [](double sum, const auto& rEdge) {return sum + rEdge.Length();}
642  ) * w;
643  }
644 
648 
656  SizeType FacesNumber() const override
657  {
658  return 6;
659  }
660 
669  GeometriesArrayType GenerateFaces() const override
670  {
671  GeometriesArrayType faces = GeometriesArrayType();
672  typedef typename Geometry<TPointType>::Pointer FacePointerType;
673 
674  faces.push_back( FacePointerType( new FaceType(
675  this->pGetPoint( 3 ),
676  this->pGetPoint( 2 ),
677  this->pGetPoint( 1 ),
678  this->pGetPoint( 0 ),
679  this->pGetPoint( 10 ),
680  this->pGetPoint( 9 ),
681  this->pGetPoint( 8 ),
682  this->pGetPoint( 11 ),
683  this->pGetPoint( 20 ) ) ) );
684  faces.push_back( FacePointerType( new FaceType(
685  this->pGetPoint( 0 ),
686  this->pGetPoint( 1 ),
687  this->pGetPoint( 5 ),
688  this->pGetPoint( 4 ),
689  this->pGetPoint( 8 ),
690  this->pGetPoint( 13 ),
691  this->pGetPoint( 16 ),
692  this->pGetPoint( 12 ),
693  this->pGetPoint( 21 ) ) ) );
694  faces.push_back( FacePointerType( new FaceType(
695  this->pGetPoint( 2 ),
696  this->pGetPoint( 6 ),
697  this->pGetPoint( 5 ),
698  this->pGetPoint( 1 ),
699  this->pGetPoint( 14 ),
700  this->pGetPoint( 17 ),
701  this->pGetPoint( 13 ),
702  this->pGetPoint( 9 ),
703  this->pGetPoint( 22 ) ) ) );
704  faces.push_back( FacePointerType( new FaceType(
705  this->pGetPoint( 7 ),
706  this->pGetPoint( 6 ),
707  this->pGetPoint( 2 ),
708  this->pGetPoint( 3 ),
709  this->pGetPoint( 18 ),
710  this->pGetPoint( 14 ),
711  this->pGetPoint( 10 ),
712  this->pGetPoint( 15 ),
713  this->pGetPoint( 23 ) ) ) );
714  faces.push_back( FacePointerType( new FaceType(
715  this->pGetPoint( 7 ),
716  this->pGetPoint( 3 ),
717  this->pGetPoint( 0 ),
718  this->pGetPoint( 4 ),
719  this->pGetPoint( 15 ),
720  this->pGetPoint( 11 ),
721  this->pGetPoint( 12 ),
722  this->pGetPoint( 19 ),
723  this->pGetPoint( 24 ) ) ) );
724  faces.push_back( FacePointerType( new FaceType(
725  this->pGetPoint( 4 ),
726  this->pGetPoint( 5 ),
727  this->pGetPoint( 6 ),
728  this->pGetPoint( 7 ),
729  this->pGetPoint( 16 ),
730  this->pGetPoint( 17 ),
731  this->pGetPoint( 18 ),
732  this->pGetPoint( 19 ),
733  this->pGetPoint( 25 ) ) ) );
734  return faces;
735  }
736 
737 
752  double ShapeFunctionValue( IndexType ShapeFunctionIndex,
753  const CoordinatesArrayType& rPoint ) const override
754  {
755  double fx1 = 0.5 * ( rPoint[0] - 1.0 ) * ( rPoint[0] );
756  double fx2 = 0.5 * ( rPoint[0] + 1.0 ) * ( rPoint[0] );
757  double fx3 = 1.0 - ( rPoint[0] * rPoint[0] );
758  double fy1 = 0.5 * ( rPoint[1] - 1.0 ) * ( rPoint[1] );
759  double fy2 = 0.5 * ( rPoint[1] + 1.0 ) * ( rPoint[1] );
760  double fy3 = 1.0 - ( rPoint[1] * rPoint[1] );
761  double fz1 = 0.5 * ( rPoint[2] - 1.0 ) * ( rPoint[2] );
762  double fz2 = 0.5 * ( rPoint[2] + 1.0 ) * ( rPoint[2] );
763  double fz3 = 1.0 - ( rPoint[2] * rPoint[2] );
764 
765  switch ( ShapeFunctionIndex )
766  {
767  case 0:
768  return( fx1*fy1*fz1 );
769  case 1:
770  return( fx2*fy1*fz1 );
771  case 2:
772  return( fx2*fy2*fz1 );
773  case 3:
774  return( fx1*fy2*fz1 );
775  case 4:
776  return( fx1*fy1*fz2 );
777  case 5:
778  return( fx2*fy1*fz2 );
779  case 6:
780  return( fx2*fy2*fz2 );
781  case 7:
782  return( fx1*fy2*fz2 );
783  case 8:
784  return( fx3*fy1*fz1 );
785  case 9:
786  return( fx2*fy3*fz1 );
787  case 10:
788  return( fx3*fy2*fz1 );
789  case 11:
790  return( fx1*fy3*fz1 );
791  case 12:
792  return( fx1*fy1*fz3 );
793  case 13:
794  return( fx2*fy1*fz3 );
795  case 14:
796  return( fx2*fy2*fz3 );
797  case 15:
798  return( fx1*fy2*fz3 );
799  case 16:
800  return( fx3*fy1*fz2 );
801  case 17:
802  return( fx2*fy3*fz2 );
803  case 18:
804  return( fx3*fy2*fz2 );
805  case 19:
806  return( fx1*fy3*fz2 );
807  case 20:
808  return( fx3*fy3*fz1 );
809  case 21:
810  return( fx3*fy1*fz3 );
811  case 22:
812  return( fx2*fy3*fz3 );
813  case 23:
814  return( fx3*fy2*fz3 );
815  case 24:
816  return( fx1*fy3*fz3 );
817  case 25:
818  return( fx3*fy3*fz2 );
819  case 26:
820  return( fx3*fy3*fz3 );
821 
822  default:
823  KRATOS_ERROR << "Wrong index of shape function!" << *this << std::endl;
824  }
825 
826  return 0;
827  }
828 
840  Vector& ShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType& rCoordinates) const override
841  {
842  if(rResult.size() != 27) rResult.resize(27,false);
843 
844  double fx1 = 0.5 * ( rCoordinates[0] - 1.0 ) * ( rCoordinates[0] );
845  double fx2 = 0.5 * ( rCoordinates[0] + 1.0 ) * ( rCoordinates[0] );
846  double fx3 = 1.0 - ( rCoordinates[0] * rCoordinates[0] );
847  double fy1 = 0.5 * ( rCoordinates[1] - 1.0 ) * ( rCoordinates[1] );
848  double fy2 = 0.5 * ( rCoordinates[1] + 1.0 ) * ( rCoordinates[1] );
849  double fy3 = 1.0 - ( rCoordinates[1] * rCoordinates[1] );
850  double fz1 = 0.5 * ( rCoordinates[2] - 1.0 ) * ( rCoordinates[2] );
851  double fz2 = 0.5 * ( rCoordinates[2] + 1.0 ) * ( rCoordinates[2] );
852  double fz3 = 1.0 - ( rCoordinates[2] * rCoordinates[2] );
853 
854  rResult[0] = ( fx1*fy1*fz1 );
855  rResult[1] = ( fx2*fy1*fz1 );
856  rResult[2] = ( fx2*fy2*fz1 );
857  rResult[3] = ( fx1*fy2*fz1 );
858  rResult[4] = ( fx1*fy1*fz2 );
859  rResult[5] = ( fx2*fy1*fz2 );
860  rResult[6] = ( fx2*fy2*fz2 );
861  rResult[7] = ( fx1*fy2*fz2 );
862  rResult[8] = ( fx3*fy1*fz1 );
863  rResult[9] = ( fx2*fy3*fz1 );
864  rResult[10] = ( fx3*fy2*fz1 );
865  rResult[11] = ( fx1*fy3*fz1 );
866  rResult[12] = ( fx1*fy1*fz3 );
867  rResult[13] = ( fx2*fy1*fz3 );
868  rResult[14] = ( fx2*fy2*fz3 );
869  rResult[15] = ( fx1*fy2*fz3 );
870  rResult[16] = ( fx3*fy1*fz2 );
871  rResult[17] = ( fx2*fy3*fz2 );
872  rResult[18] = ( fx3*fy2*fz2 );
873  rResult[19] = ( fx1*fy3*fz2 );
874  rResult[20] = ( fx3*fy3*fz1 );
875  rResult[21] = ( fx3*fy1*fz3 );
876  rResult[22] = ( fx2*fy3*fz3 );
877  rResult[23] = ( fx3*fy2*fz3 );
878  rResult[24] = ( fx1*fy3*fz3 );
879  rResult[25] = ( fx3*fy3*fz2 );
880  rResult[26] = ( fx3*fy3*fz3 );
881 
882  return rResult;
883  }
884 
885  bool HasIntersection(const Point& rLowPoint, const Point& rHighPoint) const override
886  {
887  constexpr std::array<std::array<std::size_t, 3>, 48> triangle_faces{{
888  { 0, 11, 8}, {11, 20, 8}, { 8, 20, 1}, {20, 9, 1}, {11, 3, 20}, { 3, 10, 20}, {20, 10, 9}, {10, 2, 9},
889  { 0, 12, 24}, {24, 11, 0}, {11, 24, 15}, {15, 3, 11}, {12, 4, 19}, {19, 24, 12}, {24, 19, 7}, { 7, 15, 24},
890  { 3, 15, 23}, {23, 10, 3}, {10, 23, 14}, {14, 2, 10}, {15, 7, 18}, {18, 23, 15}, {23, 18, 6}, { 6, 14, 23},
891  { 2, 14, 22}, {22, 9, 2}, { 9, 22, 13}, {13, 1, 9}, {14, 6, 17}, {17, 22, 14}, {22, 17, 5}, { 5, 13, 22},
892  {12, 0, 8}, {21, 12, 8}, {21, 8, 1}, {13, 21, 1}, { 4, 12, 21}, {21, 16, 4}, {16, 21, 13}, {13, 5, 16},
893  { 4, 16, 19}, {16, 25, 19}, {16, 5, 25}, { 5, 17, 25}, {19, 25, 7}, {25, 18, 7}, {25, 17, 18}, {17, 6, 18}
894  }};
895 
896  for (const auto& r_nodes: triangle_faces) {
897  // TODO: Replace the construction of a heavy object defining the HasIntersection method externally as a static method
898  auto face = Triangle3D3<TPointType>(this->pGetPoint(r_nodes[0]), this->pGetPoint(r_nodes[1]), this->pGetPoint(r_nodes[2]));
899  if (face.HasIntersection(rLowPoint, rHighPoint)) return true;
900  }
901 
902  // if there are no faces intersecting the box then or the box is inside the tetrahedron or it does not have intersection
903  CoordinatesArrayType local_coordinates;
904  return IsInside(rLowPoint,local_coordinates);
905  }
906 
918  std::string Info() const override
919  {
920  return "3 dimensional hexahedra with 27 nodes and quadratic shape functions in 3D space";
921  }
922 
930  void PrintInfo( std::ostream& rOStream ) const override
931  {
932  rOStream << "3 dimensional hexahedra with 27 nodes and quadratic shape functions in 3D space";
933  }
934 
944  void PrintData( std::ostream& rOStream ) const override
945  {
946  // Base Geometry class PrintData call
947  BaseType::PrintData( rOStream );
948  std::cout << std::endl;
949 
950  // If the geometry has valid points, calculate and output its data
951  if (this->AllPointsAreValid()) {
952  Matrix jacobian;
953  this->Jacobian( jacobian, PointType() );
954  rOStream << " Jacobian in the origin\t : " << jacobian;
955  }
956  }
957 
969  Matrix& ShapeFunctionsLocalGradients( Matrix& result,
970  const CoordinatesArrayType& rPoint ) const override
971  {
972  double fx1 = 0.5 * ( rPoint[0] - 1.0 ) * ( rPoint[0] );
973  double fx2 = 0.5 * ( rPoint[0] + 1.0 ) * ( rPoint[0] );
974  double fx3 = 1.0 - ( rPoint[0] * rPoint[0] );
975  double fy1 = 0.5 * ( rPoint[1] - 1.0 ) * ( rPoint[1] );
976  double fy2 = 0.5 * ( rPoint[1] + 1.0 ) * ( rPoint[1] );
977  double fy3 = 1.0 - ( rPoint[1] * rPoint[1] );
978  double fz1 = 0.5 * ( rPoint[2] - 1.0 ) * ( rPoint[2] );
979  double fz2 = 0.5 * ( rPoint[2] + 1.0 ) * ( rPoint[2] );
980  double fz3 = 1.0 - ( rPoint[2] * rPoint[2] );
981 
982  double gx1 = 0.5 * ( 2.0 * rPoint[0] - 1.0 );
983  double gx2 = 0.5 * ( 2.0 * rPoint[0] + 1.0 );
984  double gx3 = -2 * rPoint[0];
985  double gy1 = 0.5 * ( 2.0 * rPoint[1] - 1.0 );
986  double gy2 = 0.5 * ( 2.0 * rPoint[1] + 1.0 );
987  double gy3 = -2 * rPoint[1];
988  double gz1 = 0.5 * ( 2.0 * rPoint[2] - 1.0 );
989  double gz2 = 0.5 * ( 2.0 * rPoint[2] + 1.0 );
990  double gz3 = -2 * rPoint[2];
991  //setting up result matrix
992 
993  if ( result.size1() != 27 || result.size2() != 3 )
994  result.resize( 27, 3, false );
995 
996  result( 0, 0 ) = gx1 * fy1 * fz1;
997 
998  result( 0, 1 ) = fx1 * gy1 * fz1;
999 
1000  result( 0, 2 ) = fx1 * fy1 * gz1;
1001 
1002  result( 1, 0 ) = gx2 * fy1 * fz1;
1003 
1004  result( 1, 1 ) = fx2 * gy1 * fz1;
1005 
1006  result( 1, 2 ) = fx2 * fy1 * gz1;
1007 
1008  result( 2, 0 ) = gx2 * fy2 * fz1;
1009 
1010  result( 2, 1 ) = fx2 * gy2 * fz1;
1011 
1012  result( 2, 2 ) = fx2 * fy2 * gz1;
1013 
1014  result( 3, 0 ) = gx1 * fy2 * fz1;
1015 
1016  result( 3, 1 ) = fx1 * gy2 * fz1;
1017 
1018  result( 3, 2 ) = fx1 * fy2 * gz1;
1019 
1020  result( 4, 0 ) = gx1 * fy1 * fz2;
1021 
1022  result( 4, 1 ) = fx1 * gy1 * fz2;
1023 
1024  result( 4, 2 ) = fx1 * fy1 * gz2;
1025 
1026  result( 5, 0 ) = gx2 * fy1 * fz2;
1027 
1028  result( 5, 1 ) = fx2 * gy1 * fz2;
1029 
1030  result( 5, 2 ) = fx2 * fy1 * gz2;
1031 
1032  result( 6, 0 ) = gx2 * fy2 * fz2;
1033 
1034  result( 6, 1 ) = fx2 * gy2 * fz2;
1035 
1036  result( 6, 2 ) = fx2 * fy2 * gz2;
1037 
1038  result( 7, 0 ) = gx1 * fy2 * fz2;
1039 
1040  result( 7, 1 ) = fx1 * gy2 * fz2;
1041 
1042  result( 7, 2 ) = fx1 * fy2 * gz2;
1043 
1044  result( 8, 0 ) = gx3 * fy1 * fz1;
1045 
1046  result( 8, 1 ) = fx3 * gy1 * fz1;
1047 
1048  result( 8, 2 ) = fx3 * fy1 * gz1;
1049 
1050  result( 9, 0 ) = gx2 * fy3 * fz1;
1051 
1052  result( 9, 1 ) = fx2 * gy3 * fz1;
1053 
1054  result( 9, 2 ) = fx2 * fy3 * gz1;
1055 
1056  result( 10, 0 ) = gx3 * fy2 * fz1;
1057 
1058  result( 10, 1 ) = fx3 * gy2 * fz1;
1059 
1060  result( 10, 2 ) = fx3 * fy2 * gz1;
1061 
1062  result( 11, 0 ) = gx1 * fy3 * fz1;
1063 
1064  result( 11, 1 ) = fx1 * gy3 * fz1;
1065 
1066  result( 11, 2 ) = fx1 * fy3 * gz1;
1067 
1068  result( 12, 0 ) = gx1 * fy1 * fz3;
1069 
1070  result( 12, 1 ) = fx1 * gy1 * fz3;
1071 
1072  result( 12, 2 ) = fx1 * fy1 * gz3;
1073 
1074  result( 13, 0 ) = gx2 * fy1 * fz3;
1075 
1076  result( 13, 1 ) = fx2 * gy1 * fz3;
1077 
1078  result( 13, 2 ) = fx2 * fy1 * gz3;
1079 
1080  result( 14, 0 ) = gx2 * fy2 * fz3;
1081 
1082  result( 14, 1 ) = fx2 * gy2 * fz3;
1083 
1084  result( 14, 2 ) = fx2 * fy2 * gz3;
1085 
1086  result( 15, 0 ) = gx1 * fy2 * fz3;
1087 
1088  result( 15, 1 ) = fx1 * gy2 * fz3;
1089 
1090  result( 15, 2 ) = fx1 * fy2 * gz3;
1091 
1092  result( 16, 0 ) = gx3 * fy1 * fz2;
1093 
1094  result( 16, 1 ) = fx3 * gy1 * fz2;
1095 
1096  result( 16, 2 ) = fx3 * fy1 * gz2;
1097 
1098  result( 17, 0 ) = gx2 * fy3 * fz2;
1099 
1100  result( 17, 1 ) = fx2 * gy3 * fz2;
1101 
1102  result( 17, 2 ) = fx2 * fy3 * gz2;
1103 
1104  result( 18, 0 ) = gx3 * fy2 * fz2;
1105 
1106  result( 18, 1 ) = fx3 * gy2 * fz2;
1107 
1108  result( 18, 2 ) = fx3 * fy2 * gz2;
1109 
1110  result( 19, 0 ) = gx1 * fy3 * fz2;
1111 
1112  result( 19, 1 ) = fx1 * gy3 * fz2;
1113 
1114  result( 19, 2 ) = fx1 * fy3 * gz2;
1115 
1116  result( 20, 0 ) = gx3 * fy3 * fz1;
1117 
1118  result( 20, 1 ) = fx3 * gy3 * fz1;
1119 
1120  result( 20, 2 ) = fx3 * fy3 * gz1;
1121 
1122  result( 21, 0 ) = gx3 * fy1 * fz3;
1123 
1124  result( 21, 1 ) = fx3 * gy1 * fz3;
1125 
1126  result( 21, 2 ) = fx3 * fy1 * gz3;
1127 
1128  result( 22, 0 ) = gx2 * fy3 * fz3;
1129 
1130  result( 22, 1 ) = fx2 * gy3 * fz3;
1131 
1132  result( 22, 2 ) = fx2 * fy3 * gz3;
1133 
1134  result( 23, 0 ) = gx3 * fy2 * fz3;
1135 
1136  result( 23, 1 ) = fx3 * gy2 * fz3;
1137 
1138  result( 23, 2 ) = fx3 * fy2 * gz3;
1139 
1140  result( 24, 0 ) = gx1 * fy3 * fz3;
1141 
1142  result( 24, 1 ) = fx1 * gy3 * fz3;
1143 
1144  result( 24, 2 ) = fx1 * fy3 * gz3;
1145 
1146  result( 25, 0 ) = gx3 * fy3 * fz2;
1147 
1148  result( 25, 1 ) = fx3 * gy3 * fz2;
1149 
1150  result( 25, 2 ) = fx3 * fy3 * gz2;
1151 
1152  result( 26, 0 ) = gx3 * fy3 * fz3;
1153 
1154  result( 26, 1 ) = fx3 * gy3 * fz3;
1155 
1156  result( 26, 2 ) = fx3 * fy3 * gz3;
1157 
1158  return( result );
1159  }
1160 
1161 private:
1164 
1165  static const GeometryData msGeometryData;
1166 
1167  static const GeometryDimension msGeometryDimension;
1168 
1172 
1173  friend class Serializer;
1174 
1175  void save( Serializer& rSerializer ) const override
1176  {
1177  KRATOS_SERIALIZE_SAVE_BASE_CLASS( rSerializer, BaseType );
1178  }
1179 
1180  void load( Serializer& rSerializer ) override
1181  {
1182  KRATOS_SERIALIZE_LOAD_BASE_CLASS( rSerializer, BaseType );
1183  }
1184 
1185  Hexahedra3D27(): BaseType( PointsArrayType(), &msGeometryData ) {}
1186 
1205  static Matrix CalculateShapeFunctionsIntegrationPointsValues(
1206  typename BaseType::IntegrationMethod ThisMethod )
1207  {
1208  IntegrationPointsContainerType all_integration_points =
1209  AllIntegrationPoints();
1210  IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
1211  //number of integration points
1212  const int integration_points_number = integration_points.size();
1213  //number of nodes in current geometry
1214  const int points_number = 27;
1215  //setting up return matrix
1216  Matrix shape_function_values( integration_points_number, points_number );
1217  //loop over all integration points
1218 
1219  for ( int pnt = 0; pnt < integration_points_number; pnt++ )
1220  {
1221  double fx1 = 0.5 * ( integration_points[pnt].X() - 1.0 ) * ( integration_points[pnt].X() );
1222  double fx2 = 0.5 * ( integration_points[pnt].X() + 1.0 ) * ( integration_points[pnt].X() );
1223  double fx3 = 1.0 - ( integration_points[pnt].X() * integration_points[pnt].X() );
1224  double fy1 = 0.5 * ( integration_points[pnt].Y() - 1.0 ) * ( integration_points[pnt].Y() );
1225  double fy2 = 0.5 * ( integration_points[pnt].Y() + 1.0 ) * ( integration_points[pnt].Y() );
1226  double fy3 = 1.0 - ( integration_points[pnt].Y() * integration_points[pnt].Y() );
1227  double fz1 = 0.5 * ( integration_points[pnt].Z() - 1.0 ) * ( integration_points[pnt].Z() );
1228  double fz2 = 0.5 * ( integration_points[pnt].Z() + 1.0 ) * ( integration_points[pnt].Z() );
1229  double fz3 = 1.0 - ( integration_points[pnt].Z() * integration_points[pnt].Z() );
1230 
1231  shape_function_values( pnt, 0 ) = ( fx1 * fy1 * fz1 );
1232  shape_function_values( pnt, 1 ) = ( fx2 * fy1 * fz1 );
1233  shape_function_values( pnt, 2 ) = ( fx2 * fy2 * fz1 );
1234  shape_function_values( pnt, 3 ) = ( fx1 * fy2 * fz1 );
1235  shape_function_values( pnt, 4 ) = ( fx1 * fy1 * fz2 );
1236  shape_function_values( pnt, 5 ) = ( fx2 * fy1 * fz2 );
1237  shape_function_values( pnt, 6 ) = ( fx2 * fy2 * fz2 );
1238  shape_function_values( pnt, 7 ) = ( fx1 * fy2 * fz2 );
1239  shape_function_values( pnt, 8 ) = ( fx3 * fy1 * fz1 );
1240  shape_function_values( pnt, 9 ) = ( fx2 * fy3 * fz1 );
1241  shape_function_values( pnt, 10 ) = ( fx3 * fy2 * fz1 );
1242  shape_function_values( pnt, 11 ) = ( fx1 * fy3 * fz1 );
1243  shape_function_values( pnt, 12 ) = ( fx1 * fy1 * fz3 );
1244  shape_function_values( pnt, 13 ) = ( fx2 * fy1 * fz3 );
1245  shape_function_values( pnt, 14 ) = ( fx2 * fy2 * fz3 );
1246  shape_function_values( pnt, 15 ) = ( fx1 * fy2 * fz3 );
1247  shape_function_values( pnt, 16 ) = ( fx3 * fy1 * fz2 );
1248  shape_function_values( pnt, 17 ) = ( fx2 * fy3 * fz2 );
1249  shape_function_values( pnt, 18 ) = ( fx3 * fy2 * fz2 );
1250  shape_function_values( pnt, 19 ) = ( fx1 * fy3 * fz2 );
1251  shape_function_values( pnt, 20 ) = ( fx3 * fy3 * fz1 );
1252  shape_function_values( pnt, 21 ) = ( fx3 * fy1 * fz3 );
1253  shape_function_values( pnt, 22 ) = ( fx2 * fy3 * fz3 );
1254  shape_function_values( pnt, 23 ) = ( fx3 * fy2 * fz3 );
1255  shape_function_values( pnt, 24 ) = ( fx1 * fy3 * fz3 );
1256  shape_function_values( pnt, 25 ) = ( fx3 * fy3 * fz2 );
1257  shape_function_values( pnt, 26 ) = ( fx3 * fy3 * fz3 );
1258  }
1259 
1260  return shape_function_values;
1261  }
1262 
1274  static ShapeFunctionsGradientsType
1275  CalculateShapeFunctionsIntegrationPointsLocalGradients(
1276  typename BaseType::IntegrationMethod ThisMethod )
1277  {
1278  const IntegrationPointsContainerType all_integration_points =
1279  AllIntegrationPoints();
1280  const IntegrationPointsArrayType integration_points = all_integration_points[static_cast<int>(ThisMethod)];
1281  //number of integration points
1282  const int integration_points_number = integration_points.size();
1283  ShapeFunctionsGradientsType d_shape_f_values( integration_points_number );
1284  //initialising container //loop over all integration points
1285 
1286  for ( int pnt = 0; pnt < integration_points_number; pnt++ )
1287  {
1288  double fx1 = 0.5 * ( integration_points[pnt].X() - 1.0 ) * ( integration_points[pnt].X() );
1289  double fx2 = 0.5 * ( integration_points[pnt].X() + 1.0 ) * ( integration_points[pnt].X() );
1290  double fx3 = 1.0 - ( integration_points[pnt].X() * integration_points[pnt].X() );
1291  double fy1 = 0.5 * ( integration_points[pnt].Y() - 1.0 ) * ( integration_points[pnt].Y() );
1292  double fy2 = 0.5 * ( integration_points[pnt].Y() + 1.0 ) * ( integration_points[pnt].Y() );
1293  double fy3 = 1.0 - ( integration_points[pnt].Y() * integration_points[pnt].Y() );
1294  double fz1 = 0.5 * ( integration_points[pnt].Z() - 1.0 ) * ( integration_points[pnt].Z() );
1295  double fz2 = 0.5 * ( integration_points[pnt].Z() + 1.0 ) * ( integration_points[pnt].Z() );
1296  double fz3 = 1.0 - ( integration_points[pnt].Z() * integration_points[pnt].Z() );
1297 
1298  double gx1 = 0.5 * ( 2.0 * integration_points[pnt].X() - 1.0 );
1299  double gx2 = 0.5 * ( 2.0 * integration_points[pnt].X() + 1.0 );
1300  double gx3 = -2 * integration_points[pnt].X();
1301  double gy1 = 0.5 * ( 2.0 * integration_points[pnt].Y() - 1.0 );
1302  double gy2 = 0.5 * ( 2.0 * integration_points[pnt].Y() + 1.0 );
1303  double gy3 = -2 * integration_points[pnt].Y();
1304  double gz1 = 0.5 * ( 2.0 * integration_points[pnt].Z() - 1.0 );
1305  double gz2 = 0.5 * ( 2.0 * integration_points[pnt].Z() + 1.0 );
1306  double gz3 = -2 * integration_points[pnt].Z();
1307  //setting up result matrix
1308  Matrix result = ZeroMatrix( 27, 3 );
1309 
1310  result( 0, 0 ) = gx1 * fy1 * fz1;
1311  result( 0, 1 ) = fx1 * gy1 * fz1;
1312  result( 0, 2 ) = fx1 * fy1 * gz1;
1313 
1314  result( 1, 0 ) = gx2 * fy1 * fz1;
1315  result( 1, 1 ) = fx2 * gy1 * fz1;
1316  result( 1, 2 ) = fx2 * fy1 * gz1;
1317 
1318  result( 2, 0 ) = gx2 * fy2 * fz1;
1319  result( 2, 1 ) = fx2 * gy2 * fz1;
1320  result( 2, 2 ) = fx2 * fy2 * gz1;
1321 
1322  result( 3, 0 ) = gx1 * fy2 * fz1;
1323  result( 3, 1 ) = fx1 * gy2 * fz1;
1324  result( 3, 2 ) = fx1 * fy2 * gz1;
1325 
1326  result( 4, 0 ) = gx1 * fy1 * fz2;
1327  result( 4, 1 ) = fx1 * gy1 * fz2;
1328  result( 4, 2 ) = fx1 * fy1 * gz2;
1329 
1330  result( 5, 0 ) = gx2 * fy1 * fz2;
1331  result( 5, 1 ) = fx2 * gy1 * fz2;
1332  result( 5, 2 ) = fx2 * fy1 * gz2;
1333 
1334  result( 6, 0 ) = gx2 * fy2 * fz2;
1335  result( 6, 1 ) = fx2 * gy2 * fz2;
1336  result( 6, 2 ) = fx2 * fy2 * gz2;
1337 
1338  result( 7, 0 ) = gx1 * fy2 * fz2;
1339  result( 7, 1 ) = fx1 * gy2 * fz2;
1340  result( 7, 2 ) = fx1 * fy2 * gz2;
1341 
1342  result( 8, 0 ) = gx3 * fy1 * fz1;
1343  result( 8, 1 ) = fx3 * gy1 * fz1;
1344  result( 8, 2 ) = fx3 * fy1 * gz1;
1345 
1346  result( 9, 0 ) = gx2 * fy3 * fz1;
1347  result( 9, 1 ) = fx2 * gy3 * fz1;
1348  result( 9, 2 ) = fx2 * fy3 * gz1;
1349 
1350  result( 10, 0 ) = gx3 * fy2 * fz1;
1351  result( 10, 1 ) = fx3 * gy2 * fz1;
1352  result( 10, 2 ) = fx3 * fy2 * gz1;
1353 
1354  result( 11, 0 ) = gx1 * fy3 * fz1;
1355  result( 11, 1 ) = fx1 * gy3 * fz1;
1356  result( 11, 2 ) = fx1 * fy3 * gz1;
1357 
1358  result( 12, 0 ) = gx1 * fy1 * fz3;
1359  result( 12, 1 ) = fx1 * gy1 * fz3;
1360  result( 12, 2 ) = fx1 * fy1 * gz3;
1361 
1362  result( 13, 0 ) = gx2 * fy1 * fz3;
1363  result( 13, 1 ) = fx2 * gy1 * fz3;
1364  result( 13, 2 ) = fx2 * fy1 * gz3;
1365 
1366  result( 14, 0 ) = gx2 * fy2 * fz3;
1367  result( 14, 1 ) = fx2 * gy2 * fz3;
1368  result( 14, 2 ) = fx2 * fy2 * gz3;
1369 
1370  result( 15, 0 ) = gx1 * fy2 * fz3;
1371  result( 15, 1 ) = fx1 * gy2 * fz3;
1372  result( 15, 2 ) = fx1 * fy2 * gz3;
1373 
1374  result( 16, 0 ) = gx3 * fy1 * fz2;
1375  result( 16, 1 ) = fx3 * gy1 * fz2;
1376  result( 16, 2 ) = fx3 * fy1 * gz2;
1377 
1378  result( 17, 0 ) = gx2 * fy3 * fz2;
1379  result( 17, 1 ) = fx2 * gy3 * fz2;
1380  result( 17, 2 ) = fx2 * fy3 * gz2;
1381 
1382  result( 18, 0 ) = gx3 * fy2 * fz2;
1383  result( 18, 1 ) = fx3 * gy2 * fz2;
1384  result( 18, 2 ) = fx3 * fy2 * gz2;
1385 
1386  result( 19, 0 ) = gx1 * fy3 * fz2;
1387  result( 19, 1 ) = fx1 * gy3 * fz2;
1388  result( 19, 2 ) = fx1 * fy3 * gz2;
1389 
1390  result( 20, 0 ) = gx3 * fy3 * fz1;
1391  result( 20, 1 ) = fx3 * gy3 * fz1;
1392  result( 20, 2 ) = fx3 * fy3 * gz1;
1393 
1394  result( 21, 0 ) = gx3 * fy1 * fz3;
1395  result( 21, 1 ) = fx3 * gy1 * fz3;
1396  result( 21, 2 ) = fx3 * fy1 * gz3;
1397 
1398  result( 22, 0 ) = gx2 * fy3 * fz3;
1399  result( 22, 1 ) = fx2 * gy3 * fz3;
1400  result( 22, 2 ) = fx2 * fy3 * gz3;
1401 
1402  result( 23, 0 ) = gx3 * fy2 * fz3;
1403  result( 23, 1 ) = fx3 * gy2 * fz3;
1404  result( 23, 2 ) = fx3 * fy2 * gz3;
1405 
1406  result( 24, 0 ) = gx1 * fy3 * fz3;
1407  result( 24, 1 ) = fx1 * gy3 * fz3;
1408  result( 24, 2 ) = fx1 * fy3 * gz3;
1409 
1410  result( 25, 0 ) = gx3 * fy3 * fz2;
1411  result( 25, 1 ) = fx3 * gy3 * fz2;
1412  result( 25, 2 ) = fx3 * fy3 * gz2;
1413 
1414  result( 26, 0 ) = gx3 * fy3 * fz3;
1415  result( 26, 1 ) = fx3 * gy3 * fz3;
1416  result( 26, 2 ) = fx3 * fy3 * gz3;
1417 
1418  d_shape_f_values[pnt] = result;
1419  }
1420 
1421  return d_shape_f_values;
1422  }
1423 
1430  ShapeFunctionsSecondDerivativesType& ShapeFunctionsSecondDerivatives( ShapeFunctionsSecondDerivativesType& rResult, const CoordinatesArrayType& rPoint ) const override
1431  {
1432  if ( rResult.size() != this->PointsNumber() ) {
1433  rResult.resize(this->PointsNumber());
1434  }
1435 
1436  for ( unsigned int i = 0; i < this->PointsNumber(); i++ )
1437  {
1438  rResult[i].resize( 3, 3, false );
1439  }
1440 
1441  const double fx1 = 0.5 * ( rPoint[0] - 1 ) * rPoint[0];
1442  const double fx2 = 0.5 * ( rPoint[0] + 1 ) * rPoint[0];
1443  const double fx3 = 1 - rPoint[0] * rPoint[0];
1444  const double fy1 = 0.5 * ( rPoint[1] - 1 ) * rPoint[1];
1445  const double fy2 = 0.5 * ( rPoint[1] + 1 ) * rPoint[1];
1446  const double fy3 = 1 - rPoint[1] * rPoint[1];
1447  const double fz1 = 0.5 * ( rPoint[2] - 1 ) * rPoint[2];
1448  const double fz2 = 0.5 * ( rPoint[2] + 1 ) * rPoint[2];
1449  const double fz3 = 1 - rPoint[2] * rPoint[2];
1450 
1451  const double gx1 = 0.5 * ( 2 * rPoint[0] - 1 );
1452  const double gx2 = 0.5 * ( 2 * rPoint[0] + 1 );
1453  const double gx3 = -2.0 * rPoint[0];
1454  const double gy1 = 0.5 * ( 2 * rPoint[1] - 1 );
1455  const double gy2 = 0.5 * ( 2 * rPoint[1] + 1 );
1456  const double gy3 = -2.0 * rPoint[1];
1457  const double gz1 = 0.5 * ( 2 * rPoint[2] - 1 );
1458  const double gz2 = 0.5 * ( 2 * rPoint[2] + 1 );
1459  const double gz3 = -2.0 * rPoint[2];
1460 
1461  const double hx1 = 1.0;
1462  const double hx2 = 1.0;
1463  const double hx3 = -2.0;
1464  const double hy1 = 1.0;
1465  const double hy2 = 1.0;
1466  const double hy3 = -2.0;
1467  const double hz1 = 1.0;
1468  const double hz2 = 1.0;
1469  const double hz3 = -2.0;
1470 
1471  rResult[0]( 0, 0 ) = hx1 * fy1 * fz1;
1472  rResult[0]( 0, 1 ) = gx1 * gy1 * fz1;
1473  rResult[0]( 0, 2 ) = gx1 * fy1 * gz1;
1474  rResult[0]( 1, 0 ) = gx1 * gy1 * fz1;
1475  rResult[0]( 1, 1 ) = fx1 * hy1 * fz1;
1476  rResult[0]( 1, 2 ) = fx1 * gy1 * gz1;
1477  rResult[0]( 2, 0 ) = gx1 * fy1 * gz1;
1478  rResult[0]( 2, 1 ) = fx1 * gy1 * gz1;
1479  rResult[0]( 2, 2 ) = fx1 * fy1 * hz1;
1480 
1481  rResult[1]( 0, 0 ) = hx2 * fy1 * fz1;
1482  rResult[1]( 0, 1 ) = gx2 * gy1 * fz1;
1483  rResult[1]( 0, 2 ) = gx2 * fy1 * gz1;
1484  rResult[1]( 1, 0 ) = gx2 * gy1 * fz1;
1485  rResult[1]( 1, 1 ) = fx2 * hy1 * fz1;
1486  rResult[1]( 1, 2 ) = fx2 * gy1 * gz1;
1487  rResult[1]( 2, 0 ) = gx2 * fy1 * gz1;
1488  rResult[1]( 2, 1 ) = fx2 * gy1 * gz1;
1489  rResult[1]( 2, 2 ) = fx2 * fy1 * hz1;
1490 
1491  rResult[2]( 0, 0 ) = hx2 * fy2 * fz1;
1492  rResult[2]( 0, 1 ) = gx2 * gy2 * fz1;
1493  rResult[2]( 0, 2 ) = gx2 * fy2 * gz1;
1494  rResult[2]( 1, 0 ) = gx2 * gy2 * fz1;
1495  rResult[2]( 1, 1 ) = fx2 * hy2 * fz1;
1496  rResult[2]( 1, 2 ) = fx2 * gy2 * gz1;
1497  rResult[2]( 2, 0 ) = gx2 * fy2 * gz1;
1498  rResult[2]( 2, 1 ) = fx2 * gy2 * gz1;
1499  rResult[2]( 2, 2 ) = fx2 * fy2 * hz1;
1500 
1501  rResult[3]( 0, 0 ) = hx1 * fy2 * fz1;
1502  rResult[3]( 0, 1 ) = gx1 * gy2 * fz1;
1503  rResult[3]( 0, 2 ) = gx1 * fy2 * gz1;
1504  rResult[3]( 1, 0 ) = gx1 * gy2 * fz1;
1505  rResult[3]( 1, 1 ) = fx1 * hy2 * fz1;
1506  rResult[3]( 1, 2 ) = fx1 * gy2 * gz1;
1507  rResult[3]( 2, 0 ) = gx1 * fy2 * gz1;
1508  rResult[3]( 2, 1 ) = fx1 * gy2 * gz1;
1509  rResult[3]( 2, 2 ) = fx1 * fy2 * hz1;
1510 
1511  rResult[4]( 0, 0 ) = hx1 * fy1 * fz2;
1512  rResult[4]( 0, 1 ) = gx1 * gy1 * fz2;
1513  rResult[4]( 0, 2 ) = gx1 * fy1 * gz2;
1514  rResult[4]( 1, 0 ) = gx1 * gy1 * fz2;
1515  rResult[4]( 1, 1 ) = fx1 * hy1 * fz2;
1516  rResult[4]( 1, 2 ) = fx1 * gy1 * gz2;
1517  rResult[4]( 2, 0 ) = gx1 * fy1 * gz2;
1518  rResult[4]( 2, 1 ) = fx1 * gy1 * gz2;
1519  rResult[4]( 2, 2 ) = fx1 * fy1 * hz2;
1520 
1521  rResult[5]( 0, 0 ) = hx2 * fy1 * fz2;
1522  rResult[5]( 0, 1 ) = gx2 * gy1 * fz2;
1523  rResult[5]( 0, 2 ) = gx2 * fy1 * gz2;
1524  rResult[5]( 1, 0 ) = gx2 * gy1 * fz2;
1525  rResult[5]( 1, 1 ) = fx2 * hy1 * fz2;
1526  rResult[5]( 1, 2 ) = fx2 * gy1 * gz2;
1527  rResult[5]( 2, 0 ) = gx2 * fy1 * gz2;
1528  rResult[5]( 2, 1 ) = fx2 * gy1 * gz2;
1529  rResult[5]( 2, 2 ) = fx2 * fy1 * hz2;
1530 
1531  rResult[6]( 0, 0 ) = hx2 * fy2 * fz2;
1532  rResult[6]( 0, 1 ) = gx2 * gy2 * fz2;
1533  rResult[6]( 0, 2 ) = gx2 * fy2 * gz2;
1534  rResult[6]( 1, 0 ) = gx2 * gy2 * fz2;
1535  rResult[6]( 1, 1 ) = fx2 * hy2 * fz2;
1536  rResult[6]( 1, 2 ) = fx2 * gy2 * gz2;
1537  rResult[6]( 2, 0 ) = gx2 * fy2 * gz2;
1538  rResult[6]( 2, 1 ) = fx2 * gy2 * gz2;
1539  rResult[6]( 2, 2 ) = fx2 * fy2 * hz2;
1540 
1541  rResult[7]( 0, 0 ) = hx1 * fy2 * fz2;
1542  rResult[7]( 0, 1 ) = gx1 * gy2 * fz2;
1543  rResult[7]( 0, 2 ) = gx1 * fy2 * gz2;
1544  rResult[7]( 1, 0 ) = gx1 * gy2 * fz2;
1545  rResult[7]( 1, 1 ) = fx1 * hy2 * fz2;
1546  rResult[7]( 1, 2 ) = fx1 * gy2 * gz2;
1547  rResult[7]( 2, 0 ) = gx1 * fy2 * gz2;
1548  rResult[7]( 2, 1 ) = fx1 * gy2 * gz2;
1549  rResult[7]( 2, 2 ) = fx1 * fy2 * hz2;
1550 
1551  rResult[8]( 0, 0 ) = hx3 * fy1 * fz1;
1552  rResult[8]( 0, 1 ) = gx3 * gy1 * fz1;
1553  rResult[8]( 0, 2 ) = gx3 * fy1 * gz1;
1554  rResult[8]( 1, 0 ) = gx3 * gy1 * fz1;
1555  rResult[8]( 1, 1 ) = fx3 * hy1 * fz1;
1556  rResult[8]( 1, 2 ) = fx3 * gy1 * gz1;
1557  rResult[8]( 2, 0 ) = gx3 * fy1 * gz1;
1558  rResult[8]( 2, 1 ) = fx3 * gy1 * gz1;
1559  rResult[8]( 2, 2 ) = fx3 * fy1 * hz1;
1560 
1561  rResult[9]( 0, 0 ) = hx2 * fy3 * fz1;
1562  rResult[9]( 0, 1 ) = gx2 * gy3 * fz1;
1563  rResult[9]( 0, 2 ) = gx2 * fy3 * gz1;
1564  rResult[9]( 1, 0 ) = gx2 * gy3 * fz1;
1565  rResult[9]( 1, 1 ) = fx2 * hy3 * fz1;
1566  rResult[9]( 1, 2 ) = fx2 * gy3 * gz1;
1567  rResult[9]( 2, 0 ) = gx2 * fy3 * gz1;
1568  rResult[9]( 2, 1 ) = fx2 * gy3 * gz1;
1569  rResult[9]( 2, 2 ) = fx2 * fy3 * hz1;
1570 
1571  rResult[10]( 0, 0 ) = hx3 * fy2 * fz1;
1572  rResult[10]( 0, 1 ) = gx3 * gy2 * fz1;
1573  rResult[10]( 0, 2 ) = gx3 * fy2 * gz1;
1574  rResult[10]( 1, 0 ) = gx3 * gy2 * fz1;
1575  rResult[10]( 1, 1 ) = fx3 * hy2 * fz1;
1576  rResult[10]( 1, 2 ) = fx3 * gy2 * gz1;
1577  rResult[10]( 2, 0 ) = gx3 * fy2 * gz1;
1578  rResult[10]( 2, 1 ) = fx3 * gy2 * gz1;
1579  rResult[10]( 2, 2 ) = fx3 * fy2 * hz1;
1580 
1581  rResult[11]( 0, 0 ) = hx1 * fy3 * fz1;
1582  rResult[11]( 0, 1 ) = gx1 * gy3 * fz1;
1583  rResult[11]( 0, 2 ) = gx1 * fy3 * gz1;
1584  rResult[11]( 1, 0 ) = gx1 * gy3 * fz1;
1585  rResult[11]( 1, 1 ) = fx1 * hy3 * fz1;
1586  rResult[11]( 1, 2 ) = fx1 * gy3 * gz1;
1587  rResult[11]( 2, 0 ) = gx1 * fy3 * gz1;
1588  rResult[11]( 2, 1 ) = fx1 * gy3 * gz1;
1589  rResult[11]( 2, 2 ) = fx1 * fy3 * hz1;
1590 
1591  rResult[12]( 0, 0 ) = hx1 * fy1 * fz3;
1592  rResult[12]( 0, 1 ) = gx1 * gy1 * fz3;
1593  rResult[12]( 0, 2 ) = gx1 * fy1 * gz3;
1594  rResult[12]( 1, 0 ) = gx1 * gy1 * fz3;
1595  rResult[12]( 1, 1 ) = fx1 * hy1 * fz3;
1596  rResult[12]( 1, 2 ) = fx1 * gy1 * gz3;
1597  rResult[12]( 2, 0 ) = gx1 * fy1 * gz3;
1598  rResult[12]( 2, 1 ) = fx1 * gy1 * gz3;
1599  rResult[12]( 2, 2 ) = fx1 * fy1 * hz3;
1600 
1601  rResult[13]( 0, 0 ) = hx2 * fy1 * fz3;
1602  rResult[13]( 0, 1 ) = gx2 * gy1 * fz3;
1603  rResult[13]( 0, 2 ) = gx2 * fy1 * gz3;
1604  rResult[13]( 1, 0 ) = gx2 * gy1 * fz3;
1605  rResult[13]( 1, 1 ) = fx2 * hy1 * fz3;
1606  rResult[13]( 1, 2 ) = fx2 * gy1 * gz3;
1607  rResult[13]( 2, 0 ) = gx2 * fy1 * gz3;
1608  rResult[13]( 2, 1 ) = fx2 * gy1 * gz3;
1609  rResult[13]( 2, 2 ) = fx2 * fy1 * hz3;
1610 
1611  rResult[14]( 0, 0 ) = hx2 * fy2 * fz3;
1612  rResult[14]( 0, 1 ) = gx2 * gy2 * fz3;
1613  rResult[14]( 0, 2 ) = gx2 * fy2 * gz3;
1614  rResult[14]( 1, 0 ) = gx2 * gy2 * fz3;
1615  rResult[14]( 1, 1 ) = fx2 * hy2 * fz3;
1616  rResult[14]( 1, 2 ) = fx2 * gy2 * gz3;
1617  rResult[14]( 2, 0 ) = gx2 * fy2 * gz3;
1618  rResult[14]( 2, 1 ) = fx2 * gy2 * gz3;
1619  rResult[14]( 2, 2 ) = fx2 * fy2 * hz3;
1620 
1621  rResult[15]( 0, 0 ) = hx1 * fy2 * fz3;
1622  rResult[15]( 0, 1 ) = gx1 * gy2 * fz3;
1623  rResult[15]( 0, 2 ) = gx1 * fy2 * gz3;
1624  rResult[15]( 1, 0 ) = gx1 * gy2 * fz3;
1625  rResult[15]( 1, 1 ) = fx1 * hy2 * fz3;
1626  rResult[15]( 1, 2 ) = fx1 * gy2 * gz3;
1627  rResult[15]( 2, 0 ) = gx1 * fy2 * gz3;
1628  rResult[15]( 2, 1 ) = fx1 * gy2 * gz3;
1629  rResult[15]( 2, 2 ) = fx1 * fy2 * hz3;
1630 
1631  rResult[16]( 0, 0 ) = hx3 * fy1 * fz2;
1632  rResult[16]( 0, 1 ) = gx3 * gy1 * fz2;
1633  rResult[16]( 0, 2 ) = gx3 * fy1 * gz2;
1634  rResult[16]( 1, 0 ) = gx3 * gy1 * fz2;
1635  rResult[16]( 1, 1 ) = fx3 * hy1 * fz2;
1636  rResult[16]( 1, 2 ) = fx3 * gy1 * gz2;
1637  rResult[16]( 2, 0 ) = gx3 * fy1 * gz2;
1638  rResult[16]( 2, 1 ) = fx3 * gy1 * gz2;
1639  rResult[16]( 2, 2 ) = fx3 * fy1 * hz2;
1640 
1641  rResult[17]( 0, 0 ) = hx2 * fy3 * fz2;
1642  rResult[17]( 0, 1 ) = gx2 * gy3 * fz2;
1643  rResult[17]( 0, 2 ) = gx2 * fy3 * gz2;
1644  rResult[17]( 1, 0 ) = gx2 * gy3 * fz2;
1645  rResult[17]( 1, 1 ) = fx2 * hy3 * fz2;
1646  rResult[17]( 1, 2 ) = fx2 * gy3 * gz2;
1647  rResult[17]( 2, 0 ) = gx2 * fy3 * gz2;
1648  rResult[17]( 2, 1 ) = fx2 * gy3 * gz2;
1649  rResult[17]( 2, 2 ) = fx2 * fy3 * hz2;
1650 
1651  rResult[18]( 0, 0 ) = hx3 * fy2 * fz2;
1652  rResult[18]( 0, 1 ) = gx3 * gy2 * fz2;
1653  rResult[18]( 0, 2 ) = gx3 * fy2 * gz2;
1654  rResult[18]( 1, 0 ) = gx3 * gy2 * fz2;
1655  rResult[18]( 1, 1 ) = fx3 * hy2 * fz2;
1656  rResult[18]( 1, 2 ) = fx3 * gy2 * gz2;
1657  rResult[18]( 2, 0 ) = gx3 * fy2 * gz2;
1658  rResult[18]( 2, 1 ) = fx3 * gy2 * gz2;
1659  rResult[18]( 2, 2 ) = fx3 * fy2 * hz2;
1660 
1661  rResult[19]( 0, 0 ) = hx1 * fy3 * fz2;
1662  rResult[19]( 0, 1 ) = gx1 * gy3 * fz2;
1663  rResult[19]( 0, 2 ) = gx1 * fy3 * gz2;
1664  rResult[19]( 1, 0 ) = gx1 * gy3 * fz2;
1665  rResult[19]( 1, 1 ) = fx1 * hy3 * fz2;
1666  rResult[19]( 1, 2 ) = fx1 * gy3 * gz2;
1667  rResult[19]( 2, 0 ) = gx1 * fy3 * gz2;
1668  rResult[19]( 2, 1 ) = fx1 * gy3 * gz2;
1669  rResult[19]( 2, 2 ) = fx1 * fy3 * hz2;
1670 
1671  rResult[20]( 0, 0 ) = hx3 * fy3 * fz1;
1672  rResult[20]( 0, 1 ) = gx3 * gy3 * fz1;
1673  rResult[20]( 0, 2 ) = gx3 * fy3 * gz1;
1674  rResult[20]( 1, 0 ) = gx3 * gy3 * fz1;
1675  rResult[20]( 1, 1 ) = fx3 * hy3 * fz1;
1676  rResult[20]( 1, 2 ) = fx3 * gy3 * gz1;
1677  rResult[20]( 2, 0 ) = gx3 * fy3 * gz1;
1678  rResult[20]( 2, 1 ) = fx3 * gy3 * gz1;
1679  rResult[20]( 2, 2 ) = fx3 * fy3 * hz1;
1680 
1681  rResult[21]( 0, 0 ) = hx3 * fy1 * fz3;
1682  rResult[21]( 0, 1 ) = gx3 * gy1 * fz3;
1683  rResult[21]( 0, 2 ) = gx3 * fy1 * gz3;
1684  rResult[21]( 1, 0 ) = gx3 * gy1 * fz3;
1685  rResult[21]( 1, 1 ) = fx3 * hy1 * fz3;
1686  rResult[21]( 1, 2 ) = fx3 * gy1 * gz3;
1687  rResult[21]( 2, 0 ) = gx3 * fy1 * gz3;
1688  rResult[21]( 2, 1 ) = fx3 * gy1 * gz3;
1689  rResult[21]( 2, 2 ) = fx3 * fy1 * hz3;
1690 
1691  rResult[22]( 0, 0 ) = hx2 * fy3 * fz3;
1692  rResult[22]( 0, 1 ) = gx2 * gy3 * fz3;
1693  rResult[22]( 0, 2 ) = gx2 * fy3 * gz3;
1694  rResult[22]( 1, 0 ) = gx2 * gy3 * fz3;
1695  rResult[22]( 1, 1 ) = fx2 * hy3 * fz3;
1696  rResult[22]( 1, 2 ) = fx2 * gy3 * gz3;
1697  rResult[22]( 2, 0 ) = gx2 * fy3 * gz3;
1698  rResult[22]( 2, 1 ) = fx2 * gy3 * gz3;
1699  rResult[22]( 2, 2 ) = fx2 * fy3 * hz3;
1700 
1701  rResult[23]( 0, 0 ) = hx3 * fy2 * fz3;
1702  rResult[23]( 0, 1 ) = gx3 * gy2 * fz3;
1703  rResult[23]( 0, 2 ) = gx3 * fy2 * gz3;
1704  rResult[23]( 1, 0 ) = gx3 * gy2 * fz3;
1705  rResult[23]( 1, 1 ) = fx3 * hy2 * fz3;
1706  rResult[23]( 1, 2 ) = fx3 * gy2 * gz3;
1707  rResult[23]( 2, 0 ) = gx3 * fy2 * gz3;
1708  rResult[23]( 2, 1 ) = fx3 * gy2 * gz3;
1709  rResult[23]( 2, 2 ) = fx3 * fy2 * hz3;
1710 
1711  rResult[24]( 0, 0 ) = hx1 * fy3 * fz3;
1712  rResult[24]( 0, 1 ) = gx1 * gy3 * fz3;
1713  rResult[24]( 0, 2 ) = gx1 * fy3 * gz3;
1714  rResult[24]( 1, 0 ) = gx1 * gy3 * fz3;
1715  rResult[24]( 1, 1 ) = fx1 * hy3 * fz3;
1716  rResult[24]( 1, 2 ) = fx1 * gy3 * gz3;
1717  rResult[24]( 2, 0 ) = gx1 * fy3 * gz3;
1718  rResult[24]( 2, 1 ) = fx1 * gy3 * gz3;
1719  rResult[24]( 2, 2 ) = fx1 * fy3 * hz3;
1720 
1721  rResult[25]( 0, 0 ) = hx3 * fy3 * fz2;
1722  rResult[25]( 0, 1 ) = gx3 * gy3 * fz2;
1723  rResult[25]( 0, 2 ) = gx3 * fy3 * gz2;
1724  rResult[25]( 1, 0 ) = gx3 * gy3 * fz2;
1725  rResult[25]( 1, 1 ) = fx3 * hy3 * fz2;
1726  rResult[25]( 1, 2 ) = fx3 * gy3 * gz2;
1727  rResult[25]( 2, 0 ) = gx3 * fy3 * gz2;
1728  rResult[25]( 2, 1 ) = fx3 * gy3 * gz2;
1729  rResult[25]( 2, 2 ) = fx3 * fy3 * hz2;
1730 
1731  rResult[26]( 0, 0 ) = hx3 * fy3 * fz3;
1732  rResult[26]( 0, 1 ) = gx3 * gy3 * fz3;
1733  rResult[26]( 0, 2 ) = gx3 * fy3 * gz3;
1734  rResult[26]( 1, 0 ) = gx3 * gy3 * fz3;
1735  rResult[26]( 1, 1 ) = fx3 * hy3 * fz3;
1736  rResult[26]( 1, 2 ) = fx3 * gy3 * gz3;
1737  rResult[26]( 2, 0 ) = gx3 * fy3 * gz3;
1738  rResult[26]( 2, 1 ) = fx3 * gy3 * gz3;
1739  rResult[26]( 2, 2 ) = fx3 * fy3 * hz3;
1740 
1741  return rResult;
1742  }
1743 
1744 
1748  static const IntegrationPointsContainerType AllIntegrationPoints()
1749  {
1750  IntegrationPointsContainerType integration_points =
1751  {
1752  {
1753  Quadrature < HexahedronGaussLegendreIntegrationPoints1,
1754  3, IntegrationPoint<3> >::GenerateIntegrationPoints(),
1755  Quadrature < HexahedronGaussLegendreIntegrationPoints2,
1756  3, IntegrationPoint<3> >::GenerateIntegrationPoints(),
1757  Quadrature < HexahedronGaussLegendreIntegrationPoints3,
1758  3, IntegrationPoint<3> >::GenerateIntegrationPoints(),
1759  Quadrature < HexahedronGaussLegendreIntegrationPoints4,
1760  3, IntegrationPoint<3> >::GenerateIntegrationPoints(),
1761  Quadrature < HexahedronGaussLegendreIntegrationPoints5,
1762  3, IntegrationPoint<3> >::GenerateIntegrationPoints()
1763  }
1764  };
1765  return integration_points;
1766  }
1767 
1768  static const ShapeFunctionsValuesContainerType AllShapeFunctionsValues()
1769  {
1770  ShapeFunctionsValuesContainerType shape_functions_values =
1771  {
1772  {
1773  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
1774  GeometryData::IntegrationMethod::GI_GAUSS_1 ),
1775  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
1776  GeometryData::IntegrationMethod::GI_GAUSS_2 ),
1777  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
1778  GeometryData::IntegrationMethod::GI_GAUSS_3 ),
1779  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
1780  GeometryData::IntegrationMethod::GI_GAUSS_4 ),
1781  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsValues(
1782  GeometryData::IntegrationMethod::GI_GAUSS_5 )
1783  }
1784  };
1785  return shape_functions_values;
1786  }
1787 
1788  static const ShapeFunctionsLocalGradientsContainerType
1789  AllShapeFunctionsLocalGradients()
1790  {
1791  ShapeFunctionsLocalGradientsContainerType shape_functions_local_gradients =
1792  {
1793  {
1794  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
1795  GeometryData::IntegrationMethod::GI_GAUSS_1 ),
1796  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
1797  GeometryData::IntegrationMethod::GI_GAUSS_2 ),
1798  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
1799  GeometryData::IntegrationMethod::GI_GAUSS_3 ),
1800  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
1801  GeometryData::IntegrationMethod::GI_GAUSS_4 ),
1802  Hexahedra3D27<TPointType>::CalculateShapeFunctionsIntegrationPointsLocalGradients(
1803  GeometryData::IntegrationMethod::GI_GAUSS_5 )
1804  }
1805  };
1806  return shape_functions_local_gradients;
1807  }
1808 
1809 
1814  template<class TOtherPointType> friend class Hexahedra3D27;
1815 
1816 
1821 };// Class Geometry
1822 
1823 
1831 template<class TPointType> inline std::istream& operator >> (
1832  std::istream& rIStream, Hexahedra3D27<TPointType>& rThis );
1833 
1837 template<class TPointType> inline std::ostream& operator << (
1838  std::ostream& rOStream, const Hexahedra3D27<TPointType>& rThis )
1839 {
1840  rThis.PrintInfo( rOStream );
1841  rOStream << std::endl;
1842  rThis.PrintData( rOStream );
1843 
1844  return rOStream;
1845 }
1846 
1847 template<class TPointType> const
1848 GeometryData Hexahedra3D27<TPointType>::msGeometryData(
1849  &msGeometryDimension,
1850  GeometryData::IntegrationMethod::GI_GAUSS_3,
1851  Hexahedra3D27<TPointType>::AllIntegrationPoints(),
1852  Hexahedra3D27<TPointType>::AllShapeFunctionsValues(),
1853  AllShapeFunctionsLocalGradients()
1854 );
1855 
1856 template<class TPointType>
1857 const GeometryDimension Hexahedra3D27<TPointType>::msGeometryDimension(3, 3);
1858 
1859 }// namespace Kratos.
Kratos::GeometryData
Definition: geometry_data.h:60
Kratos::GeometryData::KratosGeometryType
KratosGeometryType
Definition: geometry_data.h:110
Kratos::GeometryData::IntegrationMethod
IntegrationMethod
Definition: geometry_data.h:76
Kratos::GeometryData::KratosGeometryFamily
KratosGeometryFamily
Definition: geometry_data.h:91
Kratos::GeometryDimension
Definition: geometry_dimension.h:42
Kratos::Geometry
Geometry base class.
Definition: geometry.h:71
Kratos::Geometry::PointsNumber
SizeType PointsNumber() const
Definition: geometry.h:528
Kratos::Geometry::PrintData
virtual void PrintData(std::ostream &rOStream) const
Print object's data.
Definition: geometry.h:3834
Kratos::Geometry::operator=
Geometry & operator=(const Geometry &rOther)
Definition: geometry.h:400
Kratos::Geometry::IntegrationPointsArrayType
std::vector< IntegrationPointType > IntegrationPointsArrayType
Definition: geometry.h:161
Kratos::Geometry::GetData
DataValueContainer & GetData()
Definition: geometry.h:591
Kratos::Geometry::SizeType
std::size_t SizeType
Definition: geometry.h:144
Kratos::Geometry::pGetPoint
const TPointType::Pointer pGetPoint(const int Index) const
Definition: geometry.h:1790
Kratos::Geometry::IndexType
std::size_t IndexType
Definition: geometry.h:137
Kratos::Geometry::ShapeFunctionsValuesContainerType
std::array< Matrix, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)> ShapeFunctionsValuesContainerType
Definition: geometry.h:172
Kratos::Geometry::DeterminantOfJacobian
Vector & DeterminantOfJacobian(Vector &rResult) const
Definition: geometry.h:3154
Kratos::Geometry::PointLocalCoordinates
virtual CoordinatesArrayType & PointLocalCoordinates(CoordinatesArrayType &rResult, const CoordinatesArrayType &rPoint) const
Returns the local coordinates of a given arbitrary point.
Definition: geometry.h:1854
Kratos::Geometry::Points
const PointsArrayType & Points() const
Definition: geometry.h:1768
Kratos::Geometry::AllPointsAreValid
bool AllPointsAreValid() const
Checks if the geometry points are valid Checks if the geometry points are valid from the pointer valu...
Definition: geometry.h:4093
Kratos::Geometry::IntegrationPointsContainerType
std::array< IntegrationPointsArrayType, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)> IntegrationPointsContainerType
Definition: geometry.h:167
Kratos::Geometry::Jacobian
JacobiansType & Jacobian(JacobiansType &rResult) const
Definition: geometry.h:2901
Kratos::Geometry::ShapeFunctionsLocalGradientsContainerType
GeometryData::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType
Definition: geometry.h:177
Kratos::Geometry::IntegrationMethod
GeometryData::IntegrationMethod IntegrationMethod
Definition: geometry.h:122
Kratos::Hexahedra3D27
A twenty-seven node hexahedra geometry with second order shape functions.
Definition: hexahedra_3d_27.h:53
Kratos::Hexahedra3D27::Volume
double Volume() const override
This method calculate and return volume of this geometry.
Definition: hexahedra_3d_27.h:486
Kratos::Hexahedra3D27::IndexType
BaseType::IndexType IndexType
Definition: hexahedra_3d_27.h:96
Kratos::Hexahedra3D27::PointType
TPointType PointType
Definition: hexahedra_3d_27.h:89
Kratos::Hexahedra3D27::GetGeometryFamily
GeometryData::KratosGeometryFamily GetGeometryFamily() const override
Definition: hexahedra_3d_27.h:348
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(const std::string &rGeometryName, const PointsArrayType &rThisPoints)
Constructor with Geometry Name.
Definition: hexahedra_3d_27.h:306
Kratos::Hexahedra3D27::ShapeFunctionsValuesContainerType
BaseType::ShapeFunctionsValuesContainerType ShapeFunctionsValuesContainerType
Definition: hexahedra_3d_27.h:139
Kratos::Hexahedra3D27::EdgesNumber
SizeType EdgesNumber() const override
This method gives you number of all edges of this geometry.
Definition: hexahedra_3d_27.h:555
Kratos::Hexahedra3D27::Create
BaseType::Pointer Create(IndexType NewId, PointsArrayType const &rThisPoints) const override
Creates a new geometry pointer.
Definition: hexahedra_3d_27.h:409
Kratos::Hexahedra3D27::Create
BaseType::Pointer Create(const IndexType NewGeometryId, const BaseType &rGeometry) const override
Creates a new geometry pointer.
Definition: hexahedra_3d_27.h:423
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(Hexahedra3D27< TOtherPointType > const &rOther)
Definition: hexahedra_3d_27.h:340
Kratos::Hexahedra3D27::IntegrationMethod
GeometryData::IntegrationMethod IntegrationMethod
Definition: hexahedra_3d_27.h:78
Kratos::Hexahedra3D27::PrintData
void PrintData(std::ostream &rOStream) const override
Definition: hexahedra_3d_27.h:944
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(typename PointType::Pointer pPoint1, typename PointType::Pointer pPoint2, typename PointType::Pointer pPoint3, typename PointType::Pointer pPoint4, typename PointType::Pointer pPoint5, typename PointType::Pointer pPoint6, typename PointType::Pointer pPoint7, typename PointType::Pointer pPoint8, typename PointType::Pointer pPoint9, typename PointType::Pointer pPoint10, typename PointType::Pointer pPoint11, typename PointType::Pointer pPoint12, typename PointType::Pointer pPoint13, typename PointType::Pointer pPoint14, typename PointType::Pointer pPoint15, typename PointType::Pointer pPoint16, typename PointType::Pointer pPoint17, typename PointType::Pointer pPoint18, typename PointType::Pointer pPoint19, typename PointType::Pointer pPoint20, typename PointType::Pointer pPoint21, typename PointType::Pointer pPoint22, typename PointType::Pointer pPoint23, typename PointType::Pointer pPoint24, typename PointType::Pointer pPoint25, typename PointType::Pointer pPoint26, typename PointType::Pointer pPoint27)
Definition: hexahedra_3d_27.h:231
Kratos::Hexahedra3D27::ShapeFunctionsLocalGradients
Matrix & ShapeFunctionsLocalGradients(Matrix &result, const CoordinatesArrayType &rPoint) const override
Definition: hexahedra_3d_27.h:969
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(const PointType &Point1, const PointType &Point2, const PointType &Point3, const PointType &Point4, const PointType &Point5, const PointType &Point6, const PointType &Point7, const PointType &Point8, const PointType &Point9, const PointType &Point10, const PointType &Point11, const PointType &Point12, const PointType &Point13, const PointType &Point14, const PointType &Point15, const PointType &Point16, const PointType &Point17, const PointType &Point18, const PointType &Point19, const PointType &Point20, const PointType &Point21, const PointType &Point22, const PointType &Point23, const PointType &Point24, const PointType &Point25, const PointType &Point26, const PointType &Point27)
Definition: hexahedra_3d_27.h:190
Kratos::Hexahedra3D27::CoordinatesArrayType
BaseType::CoordinatesArrayType CoordinatesArrayType
Definition: hexahedra_3d_27.h:178
Kratos::Hexahedra3D27::DomainSize
double DomainSize() const override
Definition: hexahedra_3d_27.h:505
Kratos::Hexahedra3D27::GenerateEdges
GeometriesArrayType GenerateEdges() const override
This method gives you all edges of this geometry.
Definition: hexahedra_3d_27.h:568
Kratos::Hexahedra3D27::ShapeFunctionValue
double ShapeFunctionValue(IndexType ShapeFunctionIndex, const CoordinatesArrayType &rPoint) const override
Definition: hexahedra_3d_27.h:752
Kratos::Hexahedra3D27::FaceType
Quadrilateral3D9< TPointType > FaceType
Definition: hexahedra_3d_27.h:68
Kratos::Hexahedra3D27::KRATOS_CLASS_POINTER_DEFINITION
KRATOS_CLASS_POINTER_DEFINITION(Hexahedra3D27)
Kratos::Hexahedra3D27::PrintInfo
void PrintInfo(std::ostream &rOStream) const override
Definition: hexahedra_3d_27.h:930
Kratos::Hexahedra3D27::PointsArrayType
BaseType::PointsArrayType PointsArrayType
Definition: hexahedra_3d_27.h:110
Kratos::Hexahedra3D27::JacobiansType
BaseType::JacobiansType JacobiansType
Definition: hexahedra_3d_27.h:153
Kratos::Hexahedra3D27::GenerateFaces
GeometriesArrayType GenerateFaces() const override
Returns all faces of the current geometry.
Definition: hexahedra_3d_27.h:669
Kratos::Hexahedra3D27::~Hexahedra3D27
~Hexahedra3D27() override
Destructor. Does nothing!!!
Definition: hexahedra_3d_27.h:346
Kratos::Hexahedra3D27::IntegrationPointsContainerType
BaseType::IntegrationPointsContainerType IntegrationPointsContainerType
Definition: hexahedra_3d_27.h:132
Kratos::Hexahedra3D27::ShapeFunctionsGradientsType
BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType
Definition: hexahedra_3d_27.h:160
Kratos::Hexahedra3D27::EdgeType
Line3D3< TPointType > EdgeType
Definition: hexahedra_3d_27.h:67
Kratos::Hexahedra3D27::IsInside
bool IsInside(const CoordinatesArrayType &rPoint, CoordinatesArrayType &rResult, const double Tolerance=std::numeric_limits< double >::epsilon()) const override
Returns whether given arbitrary point is inside the Geometry and the respective local point for the g...
Definition: hexahedra_3d_27.h:518
Kratos::Hexahedra3D27::NormalType
BaseType::NormalType NormalType
Definition: hexahedra_3d_27.h:173
Kratos::Hexahedra3D27::IntegrationPointType
BaseType::IntegrationPointType IntegrationPointType
Definition: hexahedra_3d_27.h:117
Kratos::Hexahedra3D27::BaseType
Geometry< TPointType > BaseType
Definition: hexahedra_3d_27.h:62
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(Hexahedra3D27 const &rOther)
Definition: hexahedra_3d_27.h:323
Kratos::Hexahedra3D27::FacesNumber
SizeType FacesNumber() const override
Returns the number of faces of the current geometry.
Definition: hexahedra_3d_27.h:656
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(const IndexType GeometryId, const PointsArrayType &rThisPoints)
Constructor with Geometry Id.
Definition: hexahedra_3d_27.h:297
Kratos::Hexahedra3D27::operator=
Hexahedra3D27 & operator=(const Hexahedra3D27 &rOther)
Definition: hexahedra_3d_27.h:373
Kratos::Hexahedra3D27::Area
double Area() const override
Definition: hexahedra_3d_27.h:473
Kratos::Hexahedra3D27::AverageEdgeLength
double AverageEdgeLength() const override
Definition: hexahedra_3d_27.h:633
Kratos::Hexahedra3D27::GetGeometryType
GeometryData::KratosGeometryType GetGeometryType() const override
Definition: hexahedra_3d_27.h:353
Kratos::Hexahedra3D27::Hexahedra3D27
Hexahedra3D27(const PointsArrayType &ThisPoints)
Definition: hexahedra_3d_27.h:289
Kratos::Hexahedra3D27::operator=
Hexahedra3D27 & operator=(Hexahedra3D27< TOtherPointType > const &rOther)
Definition: hexahedra_3d_27.h:391
Kratos::Hexahedra3D27::MatrixType
Matrix MatrixType
Definition: hexahedra_3d_27.h:183
Kratos::Hexahedra3D27::IntegrationPointsArrayType
BaseType::IntegrationPointsArrayType IntegrationPointsArrayType
Definition: hexahedra_3d_27.h:125
Kratos::Hexahedra3D27::ShapeFunctionsSecondDerivativesType
BaseType::ShapeFunctionsSecondDerivativesType ShapeFunctionsSecondDerivativesType
Definition: hexahedra_3d_27.h:168
Kratos::Hexahedra3D27::Info
std::string Info() const override
Definition: hexahedra_3d_27.h:918
Kratos::Hexahedra3D27::Hexahedra3D27
friend class Hexahedra3D27
Definition: hexahedra_3d_27.h:1814
Kratos::Hexahedra3D27::GeometriesArrayType
BaseType::GeometriesArrayType GeometriesArrayType
Definition: hexahedra_3d_27.h:84
Kratos::Hexahedra3D27::HasIntersection
bool HasIntersection(const Point &rLowPoint, const Point &rHighPoint) const override
Definition: hexahedra_3d_27.h:885
Kratos::Hexahedra3D27::Length
double Length() const override
Definition: hexahedra_3d_27.h:453
Kratos::Hexahedra3D27::ShapeFunctionsLocalGradientsContainerType
BaseType::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType
Definition: hexahedra_3d_27.h:146
Kratos::Hexahedra3D27::SizeType
BaseType::SizeType SizeType
Definition: hexahedra_3d_27.h:104
Kratos::Hexahedra3D27::ShapeFunctionsValues
Vector & ShapeFunctionsValues(Vector &rResult, const CoordinatesArrayType &rCoordinates) const override
Definition: hexahedra_3d_27.h:840
Kratos::IntegrationPoint
Short class definition.
Definition: integration_point.h:52
Kratos::IntegrationUtilities::ComputeVolume3DGeometry
static double ComputeVolume3DGeometry(const Geometry< TPointType > &rGeometry)
This method calculates and returns the volume of the geometry from a 3D geometry.
Definition: integration_utilities.h:168
Kratos::Internals::Matrix
Definition: amatrix_interface.h:41
Kratos::Internals::Matrix::resize
void resize(std::size_t NewSize1, std::size_t NewSize2, bool preserve=0)
Definition: amatrix_interface.h:224
Kratos::Line3D3
An three node 3D line geometry with quadratic shape functions.
Definition: line_3d_3.h:66
Kratos::Node
This class defines the node.
Definition: node.h:65
Kratos::Point
Point class.
Definition: point.h:59
Kratos::PointerVector
PointerVector is a container like stl vector but using a vector to store pointers to its data.
Definition: pointer_vector.h:72
Kratos::PointerVector::end
iterator end()
Definition: pointer_vector.h:177
Kratos::PointerVector::begin
iterator begin()
Definition: pointer_vector.h:169
Kratos::PointerVector::push_back
void push_back(const TPointerType &x)
Definition: pointer_vector.h:270
Kratos::Quadrilateral3D9
A nine node 3D quadrilateral geometry with quadratic shape functions.
Definition: quadrilateral_3d_9.h:48
Kratos::Serializer
The serialization consists in storing the state of an object into a storage format like data file or ...
Definition: serializer.h:123
Kratos::Triangle3D3
A three node 3D triangle geometry with linear shape functions.
Definition: triangle_3d_3.h:77
Kratos::array_1d
Short class definition.
Definition: array_1d.h:61
KRATOS_SERIALIZE_SAVE_BASE_CLASS
#define KRATOS_SERIALIZE_SAVE_BASE_CLASS(Serializer, BaseType)
Definition: define.h:812
KRATOS_SERIALIZE_LOAD_BASE_CLASS
#define KRATOS_SERIALIZE_LOAD_BASE_CLASS(Serializer, BaseType)
Definition: define.h:815
KRATOS_ERROR
#define KRATOS_ERROR
Definition: exception.h:161
KRATOS_ERROR_IF
#define KRATOS_ERROR_IF(conditional)
Definition: exception.h:162
hexahedron_gauss_legendre_integration_points.h
integration_utilities.h
Kratos
REF: G. R. Cowper, GAUSSIAN QUADRATURE FORMULAS FOR TRIANGLES.
Definition: mesh_condition.cpp:21
Kratos::ZeroMatrix
KratosZeroMatrix< double > ZeroMatrix
Definition: amatrix_interface.h:559
Kratos::Matrix
Internals::Matrix< double, AMatrix::dynamic, AMatrix::dynamic > Matrix
Definition: amatrix_interface.h:470
Kratos::sum
TExpressionType::data_type sum(AMatrix::MatrixExpression< TExpressionType, TCategory > const &TheExpression)
Definition: amatrix_interface.h:675
Kratos::msGeometryDimension
const GeometryData Hexahedra3D27< TPointType >::msGeometryData & msGeometryDimension(), Hexahedra3D27< TPointType >::AllShapeFunctionsValues(), AllShapeFunctionsLocalGradients()
Definition: brep_curve.h:483
Kratos::operator>>
std::istream & operator>>(std::istream &rIStream, LinearMasterSlaveConstraint &rThis)
input stream function
Kratos::msGeometryDimension
const GeometryData BrepCurve< TContainerPointType, TContainerPointEmbeddedType >::msGeometryData & msGeometryDimension
Definition: brep_curve.h:483
Kratos::operator<<
std::ostream & operator<<(std::ostream &rOStream, const LinearMasterSlaveConstraint &rThis)
output stream function
Definition: linear_master_slave_constraint.h:432
generate_convection_diffusion_explicit_element.w
w
Definition: generate_convection_diffusion_explicit_element.py:108
ode_solve.load
def load(f)
Definition: ode_solve.py:307
tensors::i
integer i
Definition: TensorModule.f:17
quadrilateral_3d_9.h
triangle_3d_3.h
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