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Nektar::MultiRegions::PreconditionerLowEnergy Class Reference

#include <PreconditionerLowEnergy.h>

Inheritance diagram for Nektar::MultiRegions::PreconditionerLowEnergy:
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Public Member Functions

 PreconditionerLowEnergy (const boost::shared_ptr< GlobalLinSys > &plinsys, const AssemblyMapSharedPtr &pLocToGloMap)
virtual ~PreconditionerLowEnergy ()
- Public Member Functions inherited from Nektar::MultiRegions::Preconditioner
 Preconditioner (const boost::shared_ptr< GlobalLinSys > &plinsys, const AssemblyMapSharedPtr &pLocToGloMap)
virtual ~Preconditioner ()
void DoPreconditioner (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
void DoPreconditionerWithNonVertOutput (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const Array< OneD, NekDouble > &pNonVertOutput, Array< OneD, NekDouble > &pVertForce=NullNekDouble1DArray)
void DoTransformToLowEnergy (Array< OneD, NekDouble > &pInOut, int offset)
void DoTransformToLowEnergy (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
void DoTransformFromLowEnergy (Array< OneD, NekDouble > &pInOut)
void DoMultiplybyInverseTransformationMatrix (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
void DoMultiplybyInverseTransposedTransformationMatrix (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
void BuildPreconditioner ()
void InitObject ()
Array< OneD, NekDouble > AssembleStaticCondGlobalDiagonals ()
 Performs global assembly of diagonal entries to global Schur complement matrix.
const DNekScalBlkMatSharedPtr & GetBlockTransformedSchurCompl () const
const DNekScalBlkMatSharedPtr & GetBlockCMatrix () const
const DNekScalBlkMatSharedPtr & GetBlockInvDMatrix () const
const DNekScalBlkMatSharedPtr & GetBlockSchurCompl () const
const DNekScalBlkMatSharedPtr & GetBlockTransformationMatrix () const
const DNekScalBlkMatSharedPtr & GetBlockTransposedTransformationMatrix () const
DNekScalMatSharedPtr TransformedSchurCompl (int offset, const boost::shared_ptr< DNekScalMat > &loc_mat)

Static Public Member Functions

static PreconditionerSharedPtr create (const boost::shared_ptr< GlobalLinSys > &plinsys, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
 Creates an instance of this class.

Static Public Attributes

static std::string className
 Name of class.

Protected Attributes

const boost::weak_ptr
< GlobalLinSys > 		m_linsys
boost::shared_ptr< AssemblyMap > m_locToGloMap
DNekBlkMatSharedPtr m_BlkMat
DNekScalMatSharedPtr m_bnd_mat
DNekScalBlkMatSharedPtr m_RBlk
DNekScalBlkMatSharedPtr m_RTBlk
DNekScalBlkMatSharedPtr m_InvRBlk
DNekScalBlkMatSharedPtr m_InvRTBlk
DNekScalMatSharedPtr m_Rtet
DNekScalMatSharedPtr m_RTtet
DNekScalMatSharedPtr m_Rinvtet
DNekScalMatSharedPtr m_RTinvtet
DNekScalMatSharedPtr m_Rhex
DNekScalMatSharedPtr m_RThex
DNekScalMatSharedPtr m_Rinvhex
DNekScalMatSharedPtr m_RTinvhex
DNekScalMatSharedPtr m_Rprism
DNekScalMatSharedPtr m_RTprism
DNekScalMatSharedPtr m_Rinvprism
DNekScalMatSharedPtr m_RTinvprism
Array< OneD, NekDouble > m_locToGloSignMult
Array< OneD, NekDouble > m_multiplicity
Array< OneD, int > m_map
- Protected Attributes inherited from Nektar::MultiRegions::Preconditioner
const boost::weak_ptr
< GlobalLinSys > 		m_linsys
PreconditionerType m_preconType
DNekMatSharedPtr m_preconditioner
boost::shared_ptr< AssemblyMap > m_locToGloMap
LibUtilities::CommSharedPtr m_comm

Private Member Functions

void SetUpReferenceElements (void)
 Sets up the reference elements needed by the preconditioner.
void CreateMultiplicityMap (void)
void SetupBlockTransformationMatrix (void)
void ModifyPrismTransformationMatrix (LocalRegions::TetExpSharedPtr TetExp, LocalRegions::PrismExpSharedPtr PrismExp, DNekMatSharedPtr Rmodprism, DNekMatSharedPtr RTmodprism)
 Modify the prism transformation matrix to align with the tetrahedral modes.
SpatialDomains::TetGeomSharedPtr CreateRefTetGeom (void)
 Sets up the reference tretrahedral element needed to construct *a low energy basis.
SpatialDomains::PrismGeomSharedPtr CreateRefPrismGeom (void)
 Sets up the reference prismatic element needed to construct *a low energy basis.
SpatialDomains::HexGeomSharedPtr CreateRefHexGeom (void)
 Sets up the reference hexahedral element needed to construct *a low energy basis.
virtual void v_InitObject ()
virtual void v_DoPreconditioner (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
virtual void v_DoTransformToLowEnergy (Array< OneD, NekDouble > &pInOut, int offset)
 Transform the solution vector vector to low energy.
virtual void v_DoTransformToLowEnergy (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
 Transform the solution vector vector to low energy.
virtual void v_DoTransformFromLowEnergy (Array< OneD, NekDouble > &pInOut)
 transform the solution vector from low energy back to the original basis.
virtual void v_DoMultiplybyInverseTransformationMatrix (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
 Multiply by the block inverse transformation matrix.
virtual void v_DoMultiplybyInverseTransposedTransformationMatrix (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
 Multiply by the block tranposed inverse transformation matrix.
virtual void v_BuildPreconditioner ()
 Construct the low energy preconditioner from $\mathbf{S}_{2}$.
virtual DNekScalMatSharedPtr v_TransformedSchurCompl (int offset, const boost::shared_ptr< DNekScalMat > &loc_mat)
 Set up the transformed block matrix system.

Additional Inherited Members

- Protected Member Functions inherited from Nektar::MultiRegions::Preconditioner
virtual DNekScalMatSharedPtr v_TransformedSchurCompl (int offset, const boost::shared_ptr< DNekScalMat > &loc_mat)
 Get block elemental transposed transformation matrix $\mathbf{R}^{T}$.

Detailed Description

This class implements low energy preconditioning for the conjugate

gradient matrix solver.

Definition at line 53 of file PreconditionerLowEnergy.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::PreconditionerLowEnergy::PreconditionerLowEnergy ( const boost::shared_ptr< GlobalLinSys > &  plinsys,
const AssemblyMapSharedPtr &  pLocToGloMap 
)

Definition at line 64 of file PreconditionerLowEnergy.cpp.

: Preconditioner(plinsys, pLocToGloMap),
m_linsys(plinsys),
m_locToGloMap(pLocToGloMap)
{
}
virtual Nektar::MultiRegions::PreconditionerLowEnergy::~PreconditionerLowEnergy ( )
inlinevirtual

Definition at line 75 of file PreconditionerLowEnergy.h.

{}

Member Function Documentation

static PreconditionerSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::create ( const boost::shared_ptr< GlobalLinSys > &  plinsys,
const boost::shared_ptr< AssemblyMap > &  pLocToGloMap 
)
inlinestatic

Creates an instance of this class.

Definition at line 57 of file PreconditionerLowEnergy.h.

{
PreconditionerSharedPtr p = MemoryManager<PreconditionerLowEnergy>::AllocateSharedPtr(plinsys,pLocToGloMap);
p->InitObject();
return p;
}
void Nektar::MultiRegions::PreconditionerLowEnergy::CreateMultiplicityMap ( void  )
private

Create the inverse multiplicity map.

Definition at line 1273 of file PreconditionerLowEnergy.cpp.

References m_locToGloMap, m_locToGloSignMult, m_multiplicity, Vmath::Sdiv(), and sign.

Referenced by v_InitObject().

{
unsigned int nGlobalBnd = m_locToGloMap->GetNumGlobalBndCoeffs();
unsigned int nEntries = m_locToGloMap->GetNumLocalBndCoeffs();
unsigned int i;
const Array<OneD, const int> &vMap
= m_locToGloMap->GetLocalToGlobalBndMap();
const Array< OneD, const NekDouble > &sign
= m_locToGloMap->GetLocalToGlobalBndSign();
bool m_signChange=m_locToGloMap->GetSignChange();
// Count the multiplicity of each global DOF on this process
Array<OneD, NekDouble> vCounts(nGlobalBnd, 0.0);
for (i = 0; i < nEntries; ++i)
{
vCounts[vMap[i]] += 1.0;
}
// Get universal multiplicity by globally assembling counts
m_locToGloMap->UniversalAssembleBnd(vCounts);
// Construct a map of 1/multiplicity
m_locToGloSignMult = Array<OneD, NekDouble>(nEntries);
for (i = 0; i < nEntries; ++i)
{
if(m_signChange)
{
m_locToGloSignMult[i] = sign[i]*1.0/vCounts[vMap[i]];
}
else
{
m_locToGloSignMult[i] = 1.0/vCounts[vMap[i]];
}
}
int nDirBnd = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBnd = nGlobalBnd - nDirBnd;
int nLocBnd = m_locToGloMap->GetNumLocalBndCoeffs();
//Set up multiplicity array for inverse transposed transformation matrix
Array<OneD,NekDouble> tmp(nGlobHomBnd,1.0);
m_multiplicity = Array<OneD,NekDouble>(nGlobHomBnd,1.0);
Array<OneD,NekDouble> loc(nLocBnd,1.0);
m_locToGloMap->GlobalToLocalBnd(tmp,loc, nDirBnd);
m_locToGloMap->AssembleBnd(loc,m_multiplicity, nDirBnd);
Vmath::Sdiv(nGlobHomBnd,1.0,m_multiplicity,1,m_multiplicity,1);
}
SpatialDomains::HexGeomSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::CreateRefHexGeom ( void  )
private

Sets up the reference hexahedral element needed to construct *a low energy basis.

Definition at line 1512 of file PreconditionerLowEnergy.cpp.

References Nektar::StdRegions::eBackwards, and Nektar::StdRegions::eForwards.

Referenced by SetUpReferenceElements().

{
////////////////////////////////
// Set up Hexahedron vertices //
////////////////////////////////
const int three=3;
const int nVerts = 8;
const double point[][3] = {
{0,0,0}, {1,0,0}, {1,1,0}, {0,1,0},
{0,0,1}, {1,0,1}, {1,1,1}, {0,1,1}
};
// Populate the list of verts
SpatialDomains::PointGeomSharedPtr verts[8];
for( int i = 0; i < nVerts; ++i ) {
verts[i] = MemoryManager<SpatialDomains::PointGeom>
::AllocateSharedPtr(three, i, point[i][0],
point[i][1], point[i][2]);
}
/////////////////////////////
// Set up Hexahedron Edges //
/////////////////////////////
// SegGeom (int id, const int coordim), EdgeComponent(id, coordim)
const int nEdges = 12;
const int vertexConnectivity[][2] = {
{0,1}, {1,2}, {2,3}, {0,3}, {0,4}, {1,5},
{2,6}, {3,7}, {4,5}, {5,6}, {6,7}, {4,7}
};
// Populate the list of edges
SpatialDomains::SegGeomSharedPtr edges[nEdges];
for( int i = 0; i < nEdges; ++i ) {
SpatialDomains::PointGeomSharedPtr vertsArray[2];
for( int j = 0; j < 2; ++j ) {
vertsArray[j] = verts[vertexConnectivity[i][j]];
}
edges[i] = MemoryManager<SpatialDomains::SegGeom>::
AllocateSharedPtr( i, three, vertsArray);
}
/////////////////////////////
// Set up Hexahedron faces //
/////////////////////////////
const int nFaces = 6;
const int edgeConnectivity[][4] = {
{0,1,2,3}, {0,5,8,4}, {1,6,9,5},
{2,7,10,6}, {3,7,11,4}, {8,9,10,11}
};
const bool isEdgeFlipped[][4] = {
{0,0,0,1}, {0,0,1,1}, {0,0,1,1},
{0,0,1,1}, {0,0,1,1}, {0,0,0,1}
};
// Populate the list of faces
SpatialDomains::QuadGeomSharedPtr faces[nFaces];
for( int i = 0; i < nFaces; ++i ) {
SpatialDomains::SegGeomSharedPtr edgeArray[4];
StdRegions::Orientation eorientArray[4];
for( int j = 0; j < 4; ++j ) {
edgeArray[j] = edges[edgeConnectivity[i][j]];
eorientArray[j] = isEdgeFlipped[i][j] ?
StdRegions::eBackwards : StdRegions::eForwards;
}
faces[i] = MemoryManager<SpatialDomains::QuadGeom>::AllocateSharedPtr(i, edgeArray,
eorientArray);
}
SpatialDomains::HexGeomSharedPtr geom =
MemoryManager<SpatialDomains::HexGeom>::AllocateSharedPtr
(faces);
geom->SetOwnData();
return geom;
}
SpatialDomains::PrismGeomSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::CreateRefPrismGeom ( void  )
private

Sets up the reference prismatic element needed to construct *a low energy basis.

Definition at line 1330 of file PreconditionerLowEnergy.cpp.

References Nektar::StdRegions::eBackwards, and Nektar::StdRegions::eForwards.

Referenced by SetUpReferenceElements().

{
//////////////////////////
// Set up Prism element //
//////////////////////////
const int three=3;
const int nVerts = 6;
const double point[][3] = {
{-1,-1,0}, {1,-1,0}, {1,1,0},
{-1,1,0}, {0,-1,sqrt(double(3))}, {0,1,sqrt(double(3))},
};
//boost::shared_ptr<SpatialDomains::PointGeom> verts[6];
SpatialDomains::PointGeomSharedPtr verts[6];
for(int i=0; i < nVerts; ++i)
{
verts[i] = MemoryManager<SpatialDomains::PointGeom>::AllocateSharedPtr
( three, i, point[i][0], point[i][1], point[i][2] );
}
const int nEdges = 9;
const int vertexConnectivity[][2] = {
{0,1}, {1,2}, {3,2}, {0,3}, {0,4},
{1,4}, {2,5}, {3,5}, {4,5}
};
// Populate the list of edges
SpatialDomains::SegGeomSharedPtr edges[nEdges];
for(int i=0; i < nEdges; ++i){
SpatialDomains::PointGeomSharedPtr vertsArray[2];
for(int j=0; j<2; ++j)
{
vertsArray[j] = verts[vertexConnectivity[i][j]];
}
edges[i] = MemoryManager<SpatialDomains::SegGeom>::AllocateSharedPtr(i, three, vertsArray);
}
////////////////////////
// Set up Prism faces //
////////////////////////
const int nFaces = 5;
//quad-edge connectivity base-face0, vertical-quadface2, vertical-quadface4
const int quadEdgeConnectivity[][4] = { {0,1,2,3}, {1,6,8,5}, {3,7,8,4} };
const bool isQuadEdgeFlipped[][4] = { {0,0,1,1}, {0,0,1,1}, {0,0,1,1} };
// QuadId ordered as 0, 1, 2, otherwise return false
const int quadId[] = { 0,-1,1,-1,2 };
//triangle-edge connectivity side-triface-1, side triface-3
const int triEdgeConnectivity[][3] = { {0,5,4}, {2,6,7} };
const bool isTriEdgeFlipped[][3] = { {0,0,1}, {0,0,1} };
// TriId ordered as 0, 1, otherwise return false
const int triId[] = { -1,0,-1,1,-1 };
// Populate the list of faces
SpatialDomains::Geometry2DSharedPtr faces[nFaces];
for(int f = 0; f < nFaces; ++f){
if(f == 1 || f == 3) {
int i = triId[f];
SpatialDomains::SegGeomSharedPtr edgeArray[3];
StdRegions::Orientation eorientArray[3];
for(int j = 0; j < 3; ++j){
edgeArray[j] = edges[triEdgeConnectivity[i][j]];
eorientArray[j] = isTriEdgeFlipped[i][j] ? StdRegions::eBackwards : StdRegions::eForwards;
}
faces[f] = MemoryManager<SpatialDomains::TriGeom>::AllocateSharedPtr(f, edgeArray, eorientArray);
}
else {
int i = quadId[f];
SpatialDomains::SegGeomSharedPtr edgeArray[4];
StdRegions::Orientation eorientArray[4];
for(int j=0; j < 4; ++j){
edgeArray[j] = edges[quadEdgeConnectivity[i][j]];
eorientArray[j] = isQuadEdgeFlipped[i][j] ? StdRegions::eBackwards : StdRegions::eForwards;
}
faces[f] = MemoryManager<SpatialDomains::QuadGeom>::AllocateSharedPtr(f, edgeArray, eorientArray);
}
}
SpatialDomains::PrismGeomSharedPtr geom = MemoryManager<SpatialDomains::PrismGeom>::AllocateSharedPtr(faces);
geom->SetOwnData();
return geom;
}
SpatialDomains::TetGeomSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::CreateRefTetGeom ( void  )
private

Sets up the reference tretrahedral element needed to construct *a low energy basis.

Definition at line 1420 of file PreconditionerLowEnergy.cpp.

References Nektar::StdRegions::eBackwards, and Nektar::StdRegions::eForwards.

Referenced by SetUpReferenceElements().

{
/////////////////////////////////
// Set up Tetrahedron vertices //
/////////////////////////////////
int i,j;
const int three=3;
const int nVerts = 4;
const double point[][3] = {
{-1,-1/sqrt(double(3)),-1/sqrt(double(6))},
{1,-1/sqrt(double(3)),-1/sqrt(double(6))},
{0,2/sqrt(double(3)),-1/sqrt(double(6))},
{0,0,3/sqrt(double(6))}};
boost::shared_ptr<SpatialDomains::PointGeom> verts[4];
for(i=0; i < nVerts; ++i)
{
verts[i] =
MemoryManager<SpatialDomains::PointGeom>::
AllocateSharedPtr
( three, i, point[i][0], point[i][1], point[i][2] );
}
//////////////////////////////
// Set up Tetrahedron Edges //
//////////////////////////////
// SegGeom (int id, const int coordim), EdgeComponent(id, coordim)
const int nEdges = 6;
const int vertexConnectivity[][2] = {
{0,1},{1,2},{0,2},{0,3},{1,3},{2,3}
};
// Populate the list of edges
SpatialDomains::SegGeomSharedPtr edges[nEdges];
for(i=0; i < nEdges; ++i)
{
boost::shared_ptr<SpatialDomains::PointGeom>
vertsArray[2];
for(j=0; j<2; ++j)
{
vertsArray[j] = verts[vertexConnectivity[i][j]];
}
edges[i] = MemoryManager<SpatialDomains::SegGeom>
::AllocateSharedPtr(i, three, vertsArray);
}
//////////////////////////////
// Set up Tetrahedron faces //
//////////////////////////////
const int nFaces = 4;
const int edgeConnectivity[][3] = {
{0,1,2}, {0,4,3}, {1,5,4}, {2,5,3}
};
const bool isEdgeFlipped[][3] = {
{0,0,1}, {0,0,1}, {0,0,1}, {0,0,1}
};
// Populate the list of faces
SpatialDomains::TriGeomSharedPtr faces[nFaces];
for(i=0; i < nFaces; ++i)
{
SpatialDomains::SegGeomSharedPtr edgeArray[3];
StdRegions::Orientation eorientArray[3];
for(j=0; j < 3; ++j)
{
edgeArray[j] = edges[edgeConnectivity[i][j]];
eorientArray[j] = isEdgeFlipped[i][j] ?
StdRegions::eBackwards : StdRegions::eForwards;
}
faces[i] = MemoryManager<SpatialDomains::TriGeom>
::AllocateSharedPtr(i, edgeArray, eorientArray);
}
SpatialDomains::TetGeomSharedPtr geom =
MemoryManager<SpatialDomains::TetGeom>::AllocateSharedPtr
(faces);
geom->SetOwnData();
return geom;
}
void Nektar::MultiRegions::PreconditionerLowEnergy::ModifyPrismTransformationMatrix ( LocalRegions::TetExpSharedPtr  TetExp,
LocalRegions::PrismExpSharedPtr  PrismExp,
DNekMatSharedPtr  Rmodprism,
DNekMatSharedPtr  RTmodprism 
)
private

Modify the prism transformation matrix to align with the tetrahedral modes.

This routine replaces the edge and triangular face components of the prismatic vertex transformation matrices $\mathbf{R}_{ve}$ and $\mathbf{R}_{vf}$ with the corresponding components from the tetrahedral transformation matrices. Additionally, triangular face components in the prismatic edge transformation matrix $\mathbf{R}_{ef}$ with the corresponding component from the tetrahedral transformation matrix.

Definition at line 1869 of file PreconditionerLowEnergy.cpp.

Referenced by SetUpReferenceElements().

{
NekDouble Rvalue, RTvalue;
int i, j;
//For a tet element the bottom face is made up of the following:
//vertices: 0, 1 and 2 edges: 0, 1 and 2 face: 0. We first need to
//determine the mode locations of these vertices, edges and face so
//we can extract the correct values from the tetrahedral R matrix.
//These are the vertex mode locations of R which need to be replaced
//in the prism element
int TetVertex0=TetExp->GetVertexMap(0);
int TetVertex1=TetExp->GetVertexMap(1);
int TetVertex2=TetExp->GetVertexMap(2);
int TetVertex3=TetExp->GetVertexMap(3);
//These are the edge mode locations of R which need to be replaced
//in the prism element
Array<OneD, unsigned int> TetEdge0=TetExp->GetEdgeInverseBoundaryMap(0);
Array<OneD, unsigned int> TetEdge1=TetExp->GetEdgeInverseBoundaryMap(1);
Array<OneD, unsigned int> TetEdge2=TetExp->GetEdgeInverseBoundaryMap(2);
Array<OneD, unsigned int> TetEdge3=TetExp->GetEdgeInverseBoundaryMap(3);
Array<OneD, unsigned int> TetEdge4=TetExp->GetEdgeInverseBoundaryMap(4);
Array<OneD, unsigned int> TetEdge5=TetExp->GetEdgeInverseBoundaryMap(5);
//These are the face mode locations of R which need to be replaced
//in the prism element
Array<OneD, unsigned int> TetFace=TetExp->GetFaceInverseBoundaryMap(1);
//Prism vertex modes
int PrismVertex0=PrismExp->GetVertexMap(0);
int PrismVertex1=PrismExp->GetVertexMap(1);
int PrismVertex2=PrismExp->GetVertexMap(2);
int PrismVertex3=PrismExp->GetVertexMap(3);
int PrismVertex4=PrismExp->GetVertexMap(4);
int PrismVertex5=PrismExp->GetVertexMap(5);
//Prism edge modes
Array<OneD, unsigned int> PrismEdge0=
PrismExp->GetEdgeInverseBoundaryMap(0);
Array<OneD, unsigned int> PrismEdge1=
PrismExp->GetEdgeInverseBoundaryMap(1);
Array<OneD, unsigned int> PrismEdge2=
PrismExp->GetEdgeInverseBoundaryMap(2);
Array<OneD, unsigned int> PrismEdge3=
PrismExp->GetEdgeInverseBoundaryMap(3);
Array<OneD, unsigned int> PrismEdge4=
PrismExp->GetEdgeInverseBoundaryMap(4);
Array<OneD, unsigned int> PrismEdge5=
PrismExp->GetEdgeInverseBoundaryMap(5);
Array<OneD, unsigned int> PrismEdge6=
PrismExp->GetEdgeInverseBoundaryMap(6);
Array<OneD, unsigned int> PrismEdge7=
PrismExp->GetEdgeInverseBoundaryMap(7);
Array<OneD, unsigned int> PrismEdge8=
PrismExp->GetEdgeInverseBoundaryMap(8);
//Prism face 1 & 3 face modes
Array<OneD, unsigned int> PrismFace1=
PrismExp->GetFaceInverseBoundaryMap(1);
Array<OneD, unsigned int> PrismFace3=
PrismExp->GetFaceInverseBoundaryMap(3);
Array<OneD, unsigned int> PrismFace0=
PrismExp->GetFaceInverseBoundaryMap(0);
Array<OneD, unsigned int> PrismFace2=
PrismExp->GetFaceInverseBoundaryMap(2);
Array<OneD, unsigned int> PrismFace4=
PrismExp->GetFaceInverseBoundaryMap(4);
//vertex 0 edge 0 3 & 4
for(i=0; i< PrismEdge0.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex0,TetEdge0[i]);
Rmodprism->SetValue(PrismVertex0,PrismEdge0[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex0,TetEdge2[i]);
Rmodprism->SetValue(PrismVertex0,PrismEdge3[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex0,TetEdge3[i]);
Rmodprism->SetValue(PrismVertex0,PrismEdge4[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge0[i],TetVertex0);
RTmodprism->SetValue(PrismEdge0[i],PrismVertex0,RTvalue);
RTvalue=(*m_RTtet)(TetEdge2[i],TetVertex0);
RTmodprism->SetValue(PrismEdge3[i],PrismVertex0,RTvalue);
RTvalue=(*m_RTtet)(TetEdge3[i],TetVertex0);
RTmodprism->SetValue(PrismEdge4[i],PrismVertex0,RTvalue);
}
//vertex 1 edge 0 1 & 5
for(i=0; i< PrismEdge1.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex1,TetEdge0[i]);
Rmodprism->SetValue(PrismVertex1,PrismEdge0[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex1,TetEdge1[i]);
Rmodprism->SetValue(PrismVertex1,PrismEdge1[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex1,TetEdge4[i]);
Rmodprism->SetValue(PrismVertex1,PrismEdge5[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge0[i],TetVertex1);
RTmodprism->SetValue(PrismEdge0[i],PrismVertex1,RTvalue);
RTvalue=(*m_RTtet)(TetEdge1[i],TetVertex1);
RTmodprism->SetValue(PrismEdge1[i],PrismVertex1,RTvalue);
RTvalue=(*m_RTtet)(TetEdge4[i],TetVertex1);
RTmodprism->SetValue(PrismEdge5[i],PrismVertex1,RTvalue);
}
//vertex 2 edge 1 2 & 6
for(i=0; i< PrismEdge2.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex2,TetEdge1[i]);
Rmodprism->SetValue(PrismVertex2,PrismEdge1[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex1,TetEdge0[i]);
Rmodprism->SetValue(PrismVertex2,PrismEdge2[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex2,TetEdge5[i]);
Rmodprism->SetValue(PrismVertex2,PrismEdge6[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge1[i],TetVertex2);
RTmodprism->SetValue(PrismEdge1[i],PrismVertex2,RTvalue);
RTvalue=(*m_RTtet)(TetEdge0[i],TetVertex1);
RTmodprism->SetValue(PrismEdge2[i],PrismVertex2,RTvalue);
RTvalue=(*m_RTtet)(TetEdge5[i],TetVertex2);
RTmodprism->SetValue(PrismEdge6[i],PrismVertex2,RTvalue);
}
//vertex 3 edge 3 2 & 7
for(i=0; i< PrismEdge3.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex2,TetEdge2[i]);
Rmodprism->SetValue(PrismVertex3,PrismEdge3[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex0,TetEdge0[i]);
Rmodprism->SetValue(PrismVertex3,PrismEdge2[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex2,TetEdge5[i]);
Rmodprism->SetValue(PrismVertex3,PrismEdge7[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge2[i],TetVertex2);
RTmodprism->SetValue(PrismEdge3[i],PrismVertex3,RTvalue);
RTvalue=(*m_RTtet)(TetEdge0[i],TetVertex0);
RTmodprism->SetValue(PrismEdge2[i],PrismVertex3,RTvalue);
RTvalue=(*m_RTtet)(TetEdge5[i],TetVertex2);
RTmodprism->SetValue(PrismEdge7[i],PrismVertex3,RTvalue);
}
//vertex 4 edge 4 5 & 8
for(i=0; i< PrismEdge4.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex3,TetEdge3[i]);
Rmodprism->SetValue(PrismVertex4,PrismEdge4[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex3,TetEdge4[i]);
Rmodprism->SetValue(PrismVertex4,PrismEdge5[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex0,TetEdge2[i]);
Rmodprism->SetValue(PrismVertex4,PrismEdge8[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge3[i],TetVertex3);
RTmodprism->SetValue(PrismEdge4[i],PrismVertex4,RTvalue);
RTvalue=(*m_RTtet)(TetEdge4[i],TetVertex3);
RTmodprism->SetValue(PrismEdge5[i],PrismVertex4,RTvalue);
RTvalue=(*m_RTtet)(TetEdge2[i],TetVertex0);
RTmodprism->SetValue(PrismEdge8[i],PrismVertex4,RTvalue);
}
//vertex 5 edge 6 7 & 8
for(i=0; i< PrismEdge5.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex3,TetEdge3[i]);
Rmodprism->SetValue(PrismVertex5,PrismEdge6[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex3,TetEdge4[i]);
Rmodprism->SetValue(PrismVertex5,PrismEdge7[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex2,TetEdge2[i]);
Rmodprism->SetValue(PrismVertex5,PrismEdge8[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetEdge3[i],TetVertex3);
RTmodprism->SetValue(PrismEdge6[i],PrismVertex5,RTvalue);
RTvalue=(*m_RTtet)(TetEdge4[i],TetVertex3);
RTmodprism->SetValue(PrismEdge7[i],PrismVertex5,RTvalue);
RTvalue=(*m_RTtet)(TetEdge2[i],TetVertex2);
RTmodprism->SetValue(PrismEdge8[i],PrismVertex5,RTvalue);
}
// face 1 vertices 0 1 4
for(i=0; i< PrismFace1.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex0,TetFace[i]);
Rmodprism->SetValue(PrismVertex0,PrismFace1[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex1,TetFace[i]);
Rmodprism->SetValue(PrismVertex1,PrismFace1[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex3,TetFace[i]);
Rmodprism->SetValue(PrismVertex4,PrismFace1[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetFace[i],TetVertex0);
RTmodprism->SetValue(PrismFace1[i],PrismVertex0,RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetVertex1);
RTmodprism->SetValue(PrismFace1[i],PrismVertex1,RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetVertex3);
RTmodprism->SetValue(PrismFace1[i],PrismVertex4,RTvalue);
}
// face 3 vertices 2, 3 & 5
for(i=0; i< PrismFace3.num_elements(); ++i)
{
Rvalue=(*m_Rtet)(TetVertex1,TetFace[i]);
Rmodprism->SetValue(PrismVertex2,PrismFace3[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex0,TetFace[i]);
Rmodprism->SetValue(PrismVertex3,PrismFace3[i],Rvalue);
Rvalue=(*m_Rtet)(TetVertex3,TetFace[i]);
Rmodprism->SetValue(PrismVertex5,PrismFace3[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetFace[i],TetVertex1);
RTmodprism->SetValue(PrismFace3[i],PrismVertex2,RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetVertex0);
RTmodprism->SetValue(PrismFace3[i],PrismVertex3,RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetVertex3);
RTmodprism->SetValue(PrismFace3[i],PrismVertex5,RTvalue);
}
// Face 1 edge 0 4 5
for(i=0; i< PrismFace1.num_elements(); ++i)
{
for(j=0; j<PrismEdge0.num_elements(); ++j)
{
Rvalue=(*m_Rtet)(TetEdge0[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge0[j],PrismFace1[i],Rvalue);
Rvalue=(*m_Rtet)(TetEdge3[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge4[j],PrismFace1[i],Rvalue);
Rvalue=(*m_Rtet)(TetEdge4[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge5[j],PrismFace1[i],Rvalue);
//transposed values
RTvalue=(*m_RTtet)(TetFace[i],TetEdge0[j]);
RTmodprism->SetValue(PrismFace1[i],PrismEdge0[j],RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetEdge3[j]);
RTmodprism->SetValue(PrismFace1[i],PrismEdge4[j],RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetEdge4[j]);
RTmodprism->SetValue(PrismFace1[i],PrismEdge5[j],RTvalue);
}
}
// Face 3 edge 2 6 7
for(i=0; i< PrismFace3.num_elements(); ++i)
{
for(j=0; j<PrismEdge2.num_elements(); ++j)
{
Rvalue=(*m_Rtet)(TetEdge0[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge2[j],PrismFace3[i],Rvalue);
Rvalue=(*m_Rtet)(TetEdge4[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge6[j],PrismFace3[i],Rvalue);
Rvalue=(*m_Rtet)(TetEdge3[j],TetFace[i]);
Rmodprism->SetValue(PrismEdge7[j],PrismFace3[i],Rvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetEdge0[j]);
RTmodprism->SetValue(PrismFace3[i],PrismEdge2[j],RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetEdge4[j]);
RTmodprism->SetValue(PrismFace3[i],PrismEdge6[j],RTvalue);
RTvalue=(*m_RTtet)(TetFace[i],TetEdge3[j]);
RTmodprism->SetValue(PrismFace3[i],PrismEdge7[j],RTvalue);
}
}
}
void Nektar::MultiRegions::PreconditionerLowEnergy::SetupBlockTransformationMatrix ( void  )
private

Set a block transformation matrices for each element type. These are needed in routines that transform the schur complement matrix to and from the low energy basis.

Definition at line 912 of file PreconditionerLowEnergy.cpp.

References Nektar::eDIAGONAL, Nektar::LibUtilities::eHexahedron, Nektar::LibUtilities::ePrism, Nektar::LibUtilities::eTetrahedron, m_InvRBlk, m_InvRTBlk, m_linsys, m_locToGloMap, m_RBlk, m_Rhex, m_Rinvhex, m_Rinvprism, m_Rinvtet, m_Rprism, m_RTBlk, m_Rtet, m_RThex, m_RTinvhex, m_RTinvprism, m_RTinvtet, m_RTprism, and m_RTtet.

Referenced by v_InitObject().

{
boost::shared_ptr<MultiRegions::ExpList>
expList=((m_linsys.lock())->GetLocMat()).lock();
StdRegions::StdExpansionSharedPtr locExpansion;
int n, nel;
const Array<OneD,const unsigned int>& nbdry_size
= m_locToGloMap->GetNumLocalBndCoeffsPerPatch();
int n_exp=expList->GetNumElmts();
//maps for different element types
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transmatrixmap;
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transposedtransmatrixmap;
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> invtransmatrixmap;
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> invtransposedtransmatrixmap;
//Transformation matrix map
transmatrixmap[LibUtilities::eTetrahedron]=m_Rtet;
transmatrixmap[LibUtilities::ePrism]=m_Rprism;
transmatrixmap[LibUtilities::eHexahedron]=m_Rhex;
//Transposed transformation matrix map
transposedtransmatrixmap[LibUtilities::eTetrahedron]=m_RTtet;
transposedtransmatrixmap[LibUtilities::ePrism]=m_RTprism;
transposedtransmatrixmap[LibUtilities::eHexahedron]=m_RThex;
//Inverse transfomation map
invtransmatrixmap[LibUtilities::eTetrahedron]=m_Rinvtet;
invtransmatrixmap[LibUtilities::ePrism]=m_Rinvprism;
invtransmatrixmap[LibUtilities::eHexahedron]=m_Rinvhex;
//Inverse transposed transformation map
invtransposedtransmatrixmap[LibUtilities::eTetrahedron]=m_RTinvtet;
invtransposedtransmatrixmap[LibUtilities::ePrism]=m_RTinvprism;
invtransposedtransmatrixmap[LibUtilities::eHexahedron]=m_RTinvhex;
MatrixStorage blkmatStorage = eDIAGONAL;
//Variants of R matrices required for low energy preconditioning
m_RBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
m_RTBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
m_InvRBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
m_InvRTBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
for(n=0; n < n_exp; ++n)
{
nel = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(nel);
LibUtilities::ShapeType eType=locExpansion->DetShapeType();
//Block R matrix
m_RBlk->SetBlock(n,n, transmatrixmap[eType]);
//Block RT matrix
m_RTBlk->SetBlock(n,n, transposedtransmatrixmap[eType]);
//Block inverse R matrix
m_InvRBlk->SetBlock(n,n, invtransmatrixmap[eType]);
//Block inverse RT matrix
m_InvRTBlk->SetBlock(n,n, invtransposedtransmatrixmap[eType]);
}
}
void Nektar::MultiRegions::PreconditionerLowEnergy::SetUpReferenceElements ( void  )
private

Sets up the reference elements needed by the preconditioner.

Sets up reference elements which are used to preconditioning the corresponding matrices. Currently we support tetrahedral, prismatic and hexahedral elements

Definition at line 1601 of file PreconditionerLowEnergy.cpp.

References CreateRefHexGeom(), CreateRefPrismGeom(), CreateRefTetGeom(), Nektar::eFULL, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::eGaussRadauMAlpha2Beta0, Nektar::LibUtilities::eHexahedron, Nektar::StdRegions::eMass, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::ePreconR, Nektar::StdRegions::ePreconRMass, Nektar::StdRegions::ePreconRT, Nektar::StdRegions::ePreconRTMass, Nektar::LibUtilities::ePrism, Nektar::LibUtilities::eTetrahedron, Nektar::MultiRegions::GlobalMatrixKey::GetConstFactors(), Nektar::MultiRegions::GlobalMatrixKey::GetMatrixType(), Nektar::MultiRegions::GlobalMatrixKey::GetNVarCoeffs(), Nektar::MultiRegions::GlobalMatrixKey::GetVarCoeffs(), m_linsys, m_Rhex, m_Rinvhex, m_Rinvprism, m_Rinvtet, m_Rprism, m_Rtet, m_RThex, m_RTinvhex, m_RTinvprism, m_RTinvtet, m_RTprism, m_RTtet, and ModifyPrismTransformationMatrix().

Referenced by v_InitObject().

{
int cnt,i,j;
boost::shared_ptr<MultiRegions::ExpList>
expList=((m_linsys.lock())->GetLocMat()).lock();
GlobalLinSysKey m_linSysKey=(m_linsys.lock())->GetKey();
StdRegions::VarCoeffMap vVarCoeffMap;
StdRegions::StdExpansionSharedPtr locExpansion;
locExpansion = expList->GetExp(0);
DNekScalBlkMatSharedPtr RtetBlk, RprismBlk;
DNekScalBlkMatSharedPtr RTtetBlk, RTprismBlk;
DNekScalMatSharedPtr Rprismoriginal;
DNekScalMatSharedPtr RTprismoriginal;
DNekMatSharedPtr Rtettmp, RTtettmp, Rhextmp, RThextmp, Rprismtmp, RTprismtmp ;
/*
* Set up a Tetrahral & prismatic element which comprises
* equilateral triangles as all faces for the tet and the end faces
* for the prism. Using these elements a new expansion is created
* (which is the same as the expansion specified in the input
* file).
*/
SpatialDomains::TetGeomSharedPtr tetgeom=CreateRefTetGeom();
SpatialDomains::PrismGeomSharedPtr prismgeom=CreateRefPrismGeom();
SpatialDomains::HexGeomSharedPtr hexgeom=CreateRefHexGeom();
//Expansion as specified in the input file - here we need to alter
//this so we can read in different exapansions for different element
//types
int nummodes=locExpansion->GetBasisNumModes(0);
//Bases for Tetrahedral element
const LibUtilities::BasisKey TetBa(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
const LibUtilities::BasisKey TetBb(
LibUtilities::eModified_B, nummodes,
LibUtilities::PointsKey(nummodes,LibUtilities::eGaussRadauMAlpha1Beta0));
const LibUtilities::BasisKey TetBc(
LibUtilities::eModified_C, nummodes,
LibUtilities::PointsKey(nummodes,LibUtilities::eGaussRadauMAlpha2Beta0));
//Create reference tetrahedral expansion
LocalRegions::TetExpSharedPtr TetExp;
TetExp = MemoryManager<LocalRegions::TetExp>
::AllocateSharedPtr(TetBa,TetBb,TetBc,
tetgeom);
//Bases for prismatic element
const LibUtilities::BasisKey PrismBa(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
const LibUtilities::BasisKey PrismBb(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
const LibUtilities::BasisKey PrismBc(
LibUtilities::eModified_B, nummodes,
LibUtilities::PointsKey(nummodes,LibUtilities::eGaussRadauMAlpha1Beta0));
//Create reference prismatic expansion
LocalRegions::PrismExpSharedPtr PrismExp;
PrismExp = MemoryManager<LocalRegions::PrismExp>
::AllocateSharedPtr(PrismBa,PrismBb,PrismBc,
prismgeom);
//Bases for prismatic element
const LibUtilities::BasisKey HexBa(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
const LibUtilities::BasisKey HexBb(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
const LibUtilities::BasisKey HexBc(
LibUtilities::eModified_A, nummodes,
LibUtilities::PointsKey(nummodes+1,LibUtilities::eGaussLobattoLegendre));
//Create reference prismatic expansion
LocalRegions::HexExpSharedPtr HexExp;
HexExp = MemoryManager<LocalRegions::HexExp>
::AllocateSharedPtr(HexBa,HexBb,HexBc,
hexgeom);
// retrieve variable coefficient
if(m_linSysKey.GetNVarCoeffs() > 0)
{
StdRegions::VarCoeffMap::const_iterator x;
cnt = expList->GetPhys_Offset(0);
for (x = m_linSysKey.GetVarCoeffs().begin();
x != m_linSysKey.GetVarCoeffs().end(); ++x)
{
vVarCoeffMap[x->first] = x->second + cnt;
}
}
StdRegions::MatrixType PreconR,PreconRT;
if(m_linSysKey.GetMatrixType() == StdRegions::eMass)
{
PreconR = StdRegions::ePreconRMass;
PreconRT = StdRegions::ePreconRTMass;
}
else
{
PreconR = StdRegions::ePreconR;
PreconRT = StdRegions::ePreconRT;
}
/*
* Matrix keys - for each element type there are two matrix keys
* corresponding to the transformation matrix R and its transpose
*/
//Matrix keys for tetrahedral element transformation matrix
LocalRegions::MatrixKey TetR
(PreconR, LibUtilities::eTetrahedron,
*TetExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
//Matrix keys for tetrahedral transposed transformation matrix
LocalRegions::MatrixKey TetRT
(PreconRT, LibUtilities::eTetrahedron,
*TetExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
//Matrix keys for prismatic element transformation matrix
LocalRegions::MatrixKey PrismR
(PreconR, LibUtilities::ePrism,
*PrismExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
//Matrix keys for prismatic element transposed transformation matrix
LocalRegions::MatrixKey PrismRT
(PreconRT, LibUtilities::ePrism,
*PrismExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
//Matrix keys for hexahedral element transformation matrix
LocalRegions::MatrixKey HexR
(PreconR, LibUtilities::eHexahedron,
*HexExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
//Matrix keys for hexahedral element transposed transformation
//matrix
LocalRegions::MatrixKey HexRT
(PreconRT, LibUtilities::eHexahedron,
*HexExp, m_linSysKey.GetConstFactors(),
vVarCoeffMap);
/*
* Create transformation matrices for the tetrahedral element
*/
//Get tetrahedral transformation matrix
m_Rtet = TetExp->GetLocMatrix(TetR);
//Get tetrahedral transposed transformation matrix
m_RTtet = TetExp->GetLocMatrix(TetRT);
// Using the transformation matrix and the inverse transformation
// matrix create the inverse matrices
Rtettmp=TetExp->BuildInverseTransformationMatrix(m_Rtet);
//Inverse transposed transformation matrix
RTtettmp=TetExp->BuildInverseTransformationMatrix(m_Rtet);
RTtettmp->Transpose();
m_Rinvtet = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,Rtettmp);
m_RTinvtet = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,RTtettmp);
/*
* Create transformation matrices for the hexahedral element
*/
//Get hexahedral transformation matrix
m_Rhex = HexExp->GetLocMatrix(HexR);
//Get hexahedral transposed transformation matrix
m_RThex = HexExp->GetLocMatrix(HexRT);
// Using the transformation matrix and the inverse transformation
// matrix create the inverse matrices
Rhextmp=HexExp->BuildInverseTransformationMatrix(m_Rhex);
//Inverse transposed transformation matrix
RThextmp=HexExp->BuildInverseTransformationMatrix(m_Rhex);
RThextmp->Transpose();
m_Rinvhex = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,Rhextmp);
m_RTinvhex = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,RThextmp);
/*
* Create transformation matrices for the prismatic element
*/
//Get prism transformation matrix
Rprismoriginal = PrismExp->GetLocMatrix(PrismR);
//Get prism transposed transformation matrix
RTprismoriginal = PrismExp->GetLocMatrix(PrismRT);
unsigned int nRows=Rprismoriginal->GetRows();
NekDouble zero=0.0;
DNekMatSharedPtr Rtmpprism = MemoryManager<DNekMat>::
AllocateSharedPtr(nRows,nRows,zero,eFULL);
DNekMatSharedPtr RTtmpprism = MemoryManager<DNekMat>::
AllocateSharedPtr(nRows,nRows,zero,eFULL);
NekDouble Rvalue, RTvalue;
//Copy values from the prism transformation matrix
for(i=0; i<nRows; ++i)
{
for(j=0; j<nRows; ++j)
{
Rvalue=(*Rprismoriginal)(i,j);
RTvalue=(*RTprismoriginal)(i,j);
Rtmpprism->SetValue(i,j,Rvalue);
RTtmpprism->SetValue(i,j,RTvalue);
}
}
//Replace triangular faces and edges of the prims transformation
//matrix with the corresponding values of the tetrahedral
//transformation matrix.
ModifyPrismTransformationMatrix(TetExp,PrismExp,Rtmpprism,RTtmpprism);
m_Rprism = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,Rtmpprism);
m_RTprism = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,RTtmpprism);
//Inverse transformation matrix
Rprismtmp=PrismExp->BuildInverseTransformationMatrix(m_Rprism);
//Inverse transposed transformation matrix
RTprismtmp=PrismExp->BuildInverseTransformationMatrix(m_Rprism);
RTprismtmp->Transpose();
m_Rinvprism = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,Rprismtmp);
m_RTinvprism = MemoryManager<DNekScalMat>
::AllocateSharedPtr(1.0,RTprismtmp);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_BuildPreconditioner ( )
privatevirtual

Construct the low energy preconditioner from $\mathbf{S}_{2}$.

\[\mathbf{M}^{-1}=\left[\begin{array}{ccc} Diag[(\mathbf{S_{2}})_{vv}] & & \\ & (\mathbf{S}_{2})_{eb} & \\ & & (\mathbf{S}_{2})_{fb} \end{array}\right] \]

where $\mathbf{R}$ is the transformation matrix and $\mathbf{S}_{2}$ the Schur complement of the modified basis, given by

\[\mathbf{S}_{2}=\mathbf{R}\mathbf{S}_{1}\mathbf{R}^{T}\]

where $\mathbf{S}_{1}$ is the local schur complement matrix for each element.

  • Count edges, face and add up edges and face sizes

Definition at line 118 of file PreconditionerLowEnergy.cpp.

References Nektar::StdRegions::StdExpansion::as(), Vmath::Assmb(), Nektar::MultiRegions::DeterminePeriodicFaceOrient(), Nektar::eDIAGONAL, Nektar::SpatialDomains::eDirichlet, Nektar::eFULL, Nektar::LibUtilities::eHexahedron, Nektar::LibUtilities::ePrism, Nektar::LibUtilities::eTetrahedron, Gs::Gather(), Nektar::StdRegions::StdExpansion::GetEdgeInverseBoundaryMap(), Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), Nektar::StdRegions::StdExpansion::GetFaceIntNcoeffs(), Nektar::StdRegions::StdExpansion::GetFaceOrient(), Gs::gs_add, Gs::Init(), m_BlkMat, Nektar::MultiRegions::Preconditioner::m_comm, m_linsys, m_locToGloMap, m_RBlk, m_Rhex, m_Rprism, m_RTBlk, m_Rtet, m_RThex, m_RTprism, m_RTtet, and Nektar::LibUtilities::ReduceMax.

{
boost::shared_ptr<MultiRegions::ExpList>
expList=((m_linsys.lock())->GetLocMat()).lock();
LocalRegions::ExpansionSharedPtr locExpansion;
GlobalLinSysKey m_linSysKey=(m_linsys.lock())->GetKey();
StdRegions::VarCoeffMap vVarCoeffMap;
int i, j, k;
int nVerts, nEdges,nFaces;
int eid, fid, n, cnt, nedgemodes, nfacemodes;
NekDouble zero = 0.0;
int vMap1, vMap2, sign1, sign2;
int m, v, eMap1, eMap2, fMap1, fMap2;
int offset, globalrow, globalcol, nCoeffs;
// Periodic information
PeriodicMap periodicVerts;
PeriodicMap periodicEdges;
PeriodicMap periodicFaces;
expList->GetPeriodicEntities(periodicVerts,periodicEdges,periodicFaces);
//matrix storage
MatrixStorage storage = eFULL;
MatrixStorage vertstorage = eDIAGONAL;
MatrixStorage blkmatStorage = eDIAGONAL;
//local element static condensed matrices
DNekScalBlkMatSharedPtr loc_mat;
DNekScalMatSharedPtr bnd_mat;
DNekMatSharedPtr pRS;
DNekMatSharedPtr pRSRT;
//Transformation matrices
DNekMat R;
DNekMat RT;
DNekMat RS;
DNekMat RSRT;
int nDirBnd = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nNonDirVerts = m_locToGloMap->GetNumNonDirVertexModes();
//Vertex, edge and face preconditioner matrices
DNekMatSharedPtr VertBlk = MemoryManager<DNekMat>::
AllocateSharedPtr(nNonDirVerts,nNonDirVerts,zero,vertstorage);
Array<OneD, NekDouble> vertArray(nNonDirVerts,0.0);
Array<OneD, long> VertBlockToUniversalMap(nNonDirVerts,-1);
//maps for different element types
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transmatrixmap;
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transposedtransmatrixmap;
//Transformation matrix
transmatrixmap[LibUtilities::eTetrahedron]= m_Rtet;
transmatrixmap[LibUtilities::ePrism] = m_Rprism;
transmatrixmap[LibUtilities::eHexahedron] = m_Rhex;
//Transposed transformation matrix
transposedtransmatrixmap[LibUtilities::eTetrahedron]= m_RTtet;
transposedtransmatrixmap[LibUtilities::ePrism] = m_RTprism;
transposedtransmatrixmap[LibUtilities::eHexahedron] = m_RThex;
int n_exp = expList->GetNumElmts();
int nNonDirEdgeIDs=m_locToGloMap->GetNumNonDirEdges();
int nNonDirFaceIDs=m_locToGloMap->GetNumNonDirFaces();
//set the number of blocks in the matrix
int numBlks = 1+nNonDirEdgeIDs+nNonDirFaceIDs;
Array<OneD,unsigned int> n_blks(numBlks);
for(i = 0; i < numBlks; ++i)
{
n_blks[i] = 0;
}
n_blks[0]=nNonDirVerts;
set<int> edgeDirMap;
set<int> faceDirMap;
map<int,int> uniqueEdgeMap;
map<int,int> uniqueFaceMap;
//this should be of size total number of local edges
Array<OneD, int> edgemodeoffset(nNonDirEdgeIDs,0);
Array<OneD, int> facemodeoffset(nNonDirFaceIDs,0);
Array<OneD, int> edgeglobaloffset(nNonDirEdgeIDs,0);
Array<OneD, int> faceglobaloffset(nNonDirFaceIDs,0);
const Array<OneD, const ExpListSharedPtr>& bndCondExp = expList->GetBndCondExpansions();
StdRegions::StdExpansion2DSharedPtr bndCondFaceExp;
const Array<OneD, const SpatialDomains::BoundaryConditionShPtr>& bndConditions = expList->GetBndConditions();
int meshVertId;
int meshEdgeId;
int meshFaceId;
const Array<OneD, const int> &extradiredges
= m_locToGloMap->GetExtraDirEdges();
for(i=0; i<extradiredges.num_elements(); ++i)
{
meshEdgeId=extradiredges[i];
edgeDirMap.insert(meshEdgeId);
}
//Determine which boundary edges and faces have dirichlet values
for(i = 0; i < bndCondExp.num_elements(); i++)
{
cnt = 0;
for(j = 0; j < bndCondExp[i]->GetNumElmts(); j++)
{
bndCondFaceExp = boost::dynamic_pointer_cast<
StdRegions::StdExpansion2D>(bndCondExp[i]->GetExp(j));
if (bndConditions[i]->GetBoundaryConditionType() ==
SpatialDomains::eDirichlet)
{
for(k = 0; k < bndCondFaceExp->GetNedges(); k++)
{
meshEdgeId = bndCondFaceExp->as<LocalRegions::Expansion2D>()->GetGeom2D()->GetEid(k);
if(edgeDirMap.count(meshEdgeId) == 0)
{
edgeDirMap.insert(meshEdgeId);
}
}
meshFaceId = bndCondFaceExp->as<LocalRegions::Expansion2D>()->GetGeom2D()->GetFid();
faceDirMap.insert(meshFaceId);
}
}
}
int dof=0;
int maxFaceDof=0;
int maxEdgeDof=0;
int nlocalNonDirEdges=0;
int nlocalNonDirFaces=0;
int edgematrixlocation=0;
int ntotaledgeentries=0;
map<int,int> EdgeSize;
map<int,int> FaceSize;
/// - Count edges, face and add up edges and face sizes
for(n = 0; n < n_exp; ++n)
{
eid = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(eid);
nEdges = locExpansion->GetNedges();
for(j = 0; j < nEdges; ++j)
{
int nEdgeInteriorCoeffs = locExpansion->GetEdgeNcoeffs(j) - 2;
meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetEid(j);
EdgeSize[meshEdgeId] = nEdgeInteriorCoeffs;
}
nFaces = locExpansion->GetNfaces();
for(j = 0; j < nFaces; ++j)
{
int nFaceInteriorCoeffs = locExpansion->GetFaceIntNcoeffs(j);
meshFaceId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetFid(j);
FaceSize[meshFaceId] = nFaceInteriorCoeffs;
}
}
m_comm = expList->GetComm();
// Loop over all the elements in the domain and compute max edge
// DOF and set up unique ordering.
// First do periodic edges
PeriodicMap::const_iterator pIt;
for (pIt = periodicEdges.begin(); pIt != periodicEdges.end(); ++pIt)
{
meshEdgeId = pIt->first;
if(edgeDirMap.count(meshEdgeId)==0)
{
dof = EdgeSize[meshEdgeId];
if(uniqueEdgeMap.count(meshEdgeId)==0 && dof > 0)
{
bool SetUpNewEdge = true;
for (i = 0; i < pIt->second.size(); ++i)
{
if (!pIt->second[i].isLocal)
{
continue;
}
int meshEdgeId2 = pIt->second[i].id;
if(edgeDirMap.count(meshEdgeId2)==0)
{
if(uniqueEdgeMap.count(meshEdgeId2)!=0)
{
// set unique map to same location
uniqueEdgeMap[meshEdgeId] =
uniqueEdgeMap[meshEdgeId2];
SetUpNewEdge = false;
}
}
else
{
edgeDirMap.insert(meshEdgeId);
SetUpNewEdge = false;
}
}
if(SetUpNewEdge)
{
uniqueEdgeMap[meshEdgeId]=edgematrixlocation;
edgeglobaloffset[edgematrixlocation]+=ntotaledgeentries;
edgemodeoffset[edgematrixlocation]=dof*dof;
ntotaledgeentries+=dof*dof;
n_blks[1+edgematrixlocation++]=dof;
}
}
}
}
for(cnt=n=0; n < n_exp; ++n)
{
eid = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(eid);
for (j = 0; j < locExpansion->GetNedges(); ++j)
{
meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetEid(j);
dof = EdgeSize[meshEdgeId];
maxEdgeDof = (dof > maxEdgeDof ? dof : maxEdgeDof);
if(edgeDirMap.count(meshEdgeId)==0)
{
if(uniqueEdgeMap.count(meshEdgeId)==0 && dof > 0)
{
uniqueEdgeMap[meshEdgeId]=edgematrixlocation;
edgeglobaloffset[edgematrixlocation]+=ntotaledgeentries;
edgemodeoffset[edgematrixlocation]=dof*dof;
ntotaledgeentries+=dof*dof;
n_blks[1+edgematrixlocation++]=dof;
}
nlocalNonDirEdges+=dof*dof;
}
}
}
int facematrixlocation=0;
int ntotalfaceentries=0;
// Loop over all the elements in the domain and compute max face
// DOF. Reduce across all processes to get universal maximum.
// - Periodic faces
for (pIt = periodicFaces.begin(); pIt != periodicFaces.end(); ++pIt)
{
meshFaceId = pIt->first;
if(faceDirMap.count(meshFaceId)==0)
{
dof = FaceSize[meshFaceId];
if(uniqueFaceMap.count(meshFaceId) == 0 && dof > 0)
{
bool SetUpNewFace = true;
if(pIt->second[0].isLocal)
{
int meshFaceId2 = pIt->second[0].id;
if(faceDirMap.count(meshFaceId2)==0)
{
if(uniqueFaceMap.count(meshFaceId2)!=0)
{
// set unique map to same location
uniqueFaceMap[meshFaceId] =
uniqueFaceMap[meshFaceId2];
SetUpNewFace = false;
}
}
else // set face to be a Dirichlet face
{
faceDirMap.insert(meshFaceId);
SetUpNewFace = false;
}
}
if(SetUpNewFace)
{
uniqueFaceMap[meshFaceId]=facematrixlocation;
facemodeoffset[facematrixlocation]=dof*dof;
faceglobaloffset[facematrixlocation]+=ntotalfaceentries;
ntotalfaceentries+=dof*dof;
n_blks[1+nNonDirEdgeIDs+facematrixlocation++]=dof;
}
}
}
}
for(cnt=n=0; n < n_exp; ++n)
{
eid = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(eid);
for (j = 0; j < locExpansion->GetNfaces(); ++j)
{
meshFaceId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetFid(j);
dof = FaceSize[meshFaceId];
maxFaceDof = (dof > maxFaceDof ? dof : maxFaceDof);
if(faceDirMap.count(meshFaceId)==0)
{
if(uniqueFaceMap.count(meshFaceId)==0 && dof > 0)
{
uniqueFaceMap[meshFaceId]=facematrixlocation;
facemodeoffset[facematrixlocation]=dof*dof;
faceglobaloffset[facematrixlocation]+=ntotalfaceentries;
ntotalfaceentries+=dof*dof;
n_blks[1+nNonDirEdgeIDs+facematrixlocation++]=dof;
}
nlocalNonDirFaces+=dof*dof;
}
}
}
m_comm->AllReduce(maxEdgeDof, LibUtilities::ReduceMax);
m_comm->AllReduce(maxFaceDof, LibUtilities::ReduceMax);
//Allocate arrays for block to universal map (number of expansions * p^2)
Array<OneD, long> EdgeBlockToUniversalMap(ntotaledgeentries,-1);
Array<OneD, long> FaceBlockToUniversalMap(ntotalfaceentries,-1);
Array<OneD, int> localEdgeToGlobalMatrixMap(nlocalNonDirEdges,-1);
Array<OneD, int> localFaceToGlobalMatrixMap(nlocalNonDirFaces,-1);
//Allocate arrays to store matrices (number of expansions * p^2)
Array<OneD, NekDouble> EdgeBlockArray(nlocalNonDirEdges,-1);
Array<OneD, NekDouble> FaceBlockArray(nlocalNonDirFaces,-1);
int edgematrixoffset=0;
int facematrixoffset=0;
int vGlobal;
for(n=0; n < n_exp; ++n)
{
eid = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(eid);
//loop over the edges of the expansion
for(j = 0; j < locExpansion->GetNedges(); ++j)
{
//get mesh edge id
meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetEid(j);
nedgemodes=locExpansion->GetEdgeNcoeffs(j)-2;
if(edgeDirMap.count(meshEdgeId)==0)
{
// Determine the Global edge offset
int edgeOffset = edgeglobaloffset[uniqueEdgeMap[meshEdgeId]];
// Determine a universal map offset
int uniOffset = meshEdgeId;
pIt = periodicEdges.find(meshEdgeId);
if (pIt != periodicEdges.end())
{
for (int l = 0; l < pIt->second.size(); ++l)
{
uniOffset = min(uniOffset, pIt->second[l].id);
}
}
uniOffset = uniOffset *maxEdgeDof*maxEdgeDof;
for(k=0; k<nedgemodes*nedgemodes; ++k)
{
vGlobal=edgeOffset+k;
localEdgeToGlobalMatrixMap[edgematrixoffset+k]=vGlobal;
EdgeBlockToUniversalMap[vGlobal] = uniOffset + k + 1;
}
edgematrixoffset+=nedgemodes*nedgemodes;
}
}
Array<OneD, unsigned int> faceInteriorMap;
Array<OneD, int> faceInteriorSign;
//loop over the faces of the expansion
for(j = 0; j < locExpansion->GetNfaces(); ++j)
{
//get mesh face id
meshFaceId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetFid(j);
nfacemodes = locExpansion->GetFaceIntNcoeffs(j);
//Check if face has dirichlet values
if(faceDirMap.count(meshFaceId)==0)
{
// Determine the Global edge offset
int faceOffset = faceglobaloffset[uniqueFaceMap[meshFaceId]];
// Determine a universal map offset
int uniOffset = meshFaceId;
// use minimum face edge when periodic
pIt = periodicFaces.find(meshFaceId);
if (pIt != periodicFaces.end())
{
uniOffset = min(uniOffset, pIt->second[0].id);
}
uniOffset = uniOffset * maxFaceDof * maxFaceDof;
for(k=0; k<nfacemodes*nfacemodes; ++k)
{
vGlobal=faceOffset+k;
localFaceToGlobalMatrixMap[facematrixoffset+k]
= vGlobal;
FaceBlockToUniversalMap[vGlobal] = uniOffset + k + 1;
}
facematrixoffset+=nfacemodes*nfacemodes;
}
}
}
edgematrixoffset=0;
facematrixoffset=0;
m_BlkMat = MemoryManager<DNekBlkMat>
::AllocateSharedPtr(n_blks, n_blks, blkmatStorage);
const Array<OneD,const unsigned int>& nbdry_size
= m_locToGloMap->GetNumLocalBndCoeffsPerPatch();
//Variants of R matrices required for low energy preconditioning
m_RBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
m_RTBlk = MemoryManager<DNekScalBlkMat>
::AllocateSharedPtr(nbdry_size, nbdry_size , blkmatStorage);
//Here we loop over the expansion and build the block low energy
//preconditioner as well as the block versions of the transformation
//matrices.
for(cnt=n=0; n < n_exp; ++n)
{
eid = expList->GetOffset_Elmt_Id(n);
locExpansion = expList->GetExp(eid);
nCoeffs=locExpansion->NumBndryCoeffs();
LibUtilities::ShapeType eType=locExpansion->DetShapeType();
//Get correct transformation matrix for element type
R=(*(transmatrixmap[eType]));
RT=(*(transposedtransmatrixmap[eType]));
pRS = MemoryManager<DNekMat>::AllocateSharedPtr
(nCoeffs, nCoeffs, zero, storage);
RS = (*pRS);
pRSRT = MemoryManager<DNekMat>::AllocateSharedPtr
(nCoeffs, nCoeffs, zero, storage);
RSRT = (*pRSRT);
nVerts=locExpansion->GetGeom()->GetNumVerts();
nEdges=locExpansion->GetGeom()->GetNumEdges();
nFaces=locExpansion->GetGeom()->GetNumFaces();
//Get statically condensed matrix
loc_mat = (m_linsys.lock())->GetStaticCondBlock(n);
//Extract boundary block (elemental S1)
bnd_mat=loc_mat->GetBlock(0,0);
//offset by number of rows
offset = bnd_mat->GetRows();
DNekScalMat &S=(*bnd_mat);
//Calculate S*trans(R) (note R is already transposed)
RS=R*S;
//Calculate R*S*trans(R)
RSRT=RS*RT;
//loop over vertices of the element and return the vertex map
//for each vertex
for (v=0; v<nVerts; ++v)
{
vMap1=locExpansion->GetVertexMap(v);
//Get vertex map
globalrow = m_locToGloMap->
GetLocalToGlobalBndMap(cnt+vMap1)-nDirBnd;
if(globalrow >= 0)
{
for (m=0; m<nVerts; ++m)
{
vMap2=locExpansion->GetVertexMap(m);
//global matrix location (without offset due to
//dirichlet values)
globalcol = m_locToGloMap->
GetLocalToGlobalBndMap(cnt+vMap2)-nDirBnd;
//offset for dirichlet conditions
if (globalcol == globalrow)
{
//modal connectivity between elements
sign1 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + vMap1);
sign2 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + vMap2);
vertArray[globalrow]
+= sign1*sign2*RSRT(vMap1,vMap2);
meshVertId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetVid(v);
pIt = periodicVerts.find(meshVertId);
if (pIt != periodicVerts.end())
{
for (k = 0; k < pIt->second.size(); ++k)
{
meshVertId = min(meshVertId, pIt->second[k].id);
}
}
VertBlockToUniversalMap[globalrow]
= meshVertId + 1;
}
}
}
}
//loop over edges of the element and return the edge map
for (eid=0; eid<nEdges; ++eid)
{
nedgemodes=locExpansion->GetEdgeNcoeffs(eid)-2;
DNekMatSharedPtr m_locMat =
MemoryManager<DNekMat>::AllocateSharedPtr
(nedgemodes,nedgemodes,zero,storage);
meshEdgeId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetEid(eid);
Array<OneD, unsigned int> edgemodearray = locExpansion->GetEdgeInverseBoundaryMap(eid);
if(edgeDirMap.count(meshEdgeId)==0)
{
for (v=0; v<nedgemodes; ++v)
{
eMap1=edgemodearray[v];
for (m=0; m<nedgemodes; ++m)
{
eMap2=edgemodearray[m];
//modal connectivity between elements
sign1 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + eMap1);
sign2 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + eMap2);
NekDouble globalEdgeValue = sign1*sign2*RSRT(eMap1,eMap2);
EdgeBlockArray[edgematrixoffset+v*nedgemodes+m]=globalEdgeValue;
}
}
edgematrixoffset+=nedgemodes*nedgemodes;
}
}
//loop over faces of the element and return the face map
for (fid=0; fid<nFaces; ++fid)
{
nfacemodes = locExpansion->GetFaceIntNcoeffs(fid);
DNekMatSharedPtr m_locMat =
MemoryManager<DNekMat>::AllocateSharedPtr
(nfacemodes,nfacemodes,zero,storage);
meshFaceId = locExpansion->as<LocalRegions::Expansion3D>()->GetGeom3D()->GetFid(fid);
if(faceDirMap.count(meshFaceId)==0)
{
Array<OneD, unsigned int> facemodearray;
StdRegions::Orientation faceOrient = locExpansion->GetFaceOrient(fid);
pIt = periodicFaces.find(meshFaceId);
if (pIt != periodicFaces.end())
{
if(meshFaceId == min(meshFaceId, pIt->second[0].id))
{
facemodearray = locExpansion->GetFaceInverseBoundaryMap(fid,faceOrient);
faceOrient = DeterminePeriodicFaceOrient(faceOrient,pIt->second[0].orient);
}
}
facemodearray = locExpansion->GetFaceInverseBoundaryMap(fid,faceOrient);
for (v=0; v<nfacemodes; ++v)
{
fMap1=facemodearray[v];
for (m=0; m<nfacemodes; ++m)
{
fMap2=facemodearray[m];
//modal connectivity between elements
sign1 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + fMap1);
sign2 = m_locToGloMap->
GetLocalToGlobalBndSign(cnt + fMap2);
// Get the face-face value from the low energy matrix (S2)
NekDouble globalFaceValue = sign1*sign2*RSRT(fMap1,fMap2);
//local face value to global face value
FaceBlockArray[facematrixoffset+v*nfacemodes+m]=globalFaceValue;
}
}
facematrixoffset+=nfacemodes*nfacemodes;
}
}
//offset for the expansion
cnt+=offset;
//Here we build the block matrices for R and RT
m_RBlk->SetBlock(n,n, transmatrixmap[eType]);
m_RTBlk->SetBlock(n,n, transposedtransmatrixmap[eType]);
}
if(nNonDirVerts!=0)
{
//Exchange vertex data over different processes
Gs::gs_data *tmp = Gs::Init(VertBlockToUniversalMap, m_comm);
Gs::Gather(vertArray, Gs::gs_add, tmp);
}
Array<OneD, NekDouble> GlobalEdgeBlock(ntotaledgeentries,0.0);
if(ntotaledgeentries)
{
//Assemble edge matrices of each process
Vmath::Assmb(EdgeBlockArray.num_elements(),
EdgeBlockArray,
localEdgeToGlobalMatrixMap,
GlobalEdgeBlock);
}
//Exchange edge data over different processes
Gs::gs_data *tmp1 = Gs::Init(EdgeBlockToUniversalMap, m_comm);
Gs::Gather(GlobalEdgeBlock, Gs::gs_add, tmp1);
Array<OneD, NekDouble> GlobalFaceBlock(ntotalfaceentries,0.0);
if(ntotalfaceentries)
{
//Assemble face matrices of each process
Vmath::Assmb(FaceBlockArray.num_elements(),
FaceBlockArray,
localFaceToGlobalMatrixMap,
GlobalFaceBlock);
}
//Exchange face data over different processes
Gs::gs_data *tmp2 = Gs::Init(FaceBlockToUniversalMap, m_comm);
Gs::Gather(GlobalFaceBlock, Gs::gs_add, tmp2);
// Populate vertex block
for (int i = 0; i < nNonDirVerts; ++i)
{
VertBlk->SetValue(i,i,1.0/vertArray[i]);
}
//Set the first block to be the diagonal of the vertex space
m_BlkMat->SetBlock(0,0, VertBlk);
offset=0;
//Build the edge matrices from the vector
DNekMatSharedPtr gmat;
for(int loc=0; loc<nNonDirEdgeIDs; ++loc)
{
nedgemodes = n_blks[1+loc];
gmat = MemoryManager<DNekMat>::AllocateSharedPtr
(nedgemodes,nedgemodes,zero,storage);
for (v=0; v<nedgemodes; ++v)
{
for (m=0; m<nedgemodes; ++m)
{
NekDouble EdgeValue = GlobalEdgeBlock[offset+v*nedgemodes+m];
gmat->SetValue(v,m,EdgeValue);
}
}
m_BlkMat->SetBlock(1+loc,1+loc, gmat);
offset+=edgemodeoffset[loc];
}
offset=0;
Array<OneD, int> globalToUniversalMap = m_locToGloMap->GetGlobalToUniversalBndMap();
//Build the face matrices from the vector
for(int loc=0; loc<nNonDirFaceIDs; ++loc)
{
nfacemodes=n_blks[1+nNonDirEdgeIDs+loc];
gmat = MemoryManager<DNekMat>::AllocateSharedPtr
(nfacemodes,nfacemodes,zero,storage);
for (v=0; v<nfacemodes; ++v)
{
for (m=0; m<nfacemodes; ++m)
{
NekDouble FaceValue = GlobalFaceBlock[offset+v*nfacemodes+m];
gmat->SetValue(v,m,FaceValue);
}
}
m_BlkMat->SetBlock(1+nNonDirEdgeIDs+loc,1+nNonDirEdgeIDs+loc, gmat);
offset+=facemodeoffset[loc];
}
int totblks=m_BlkMat->GetNumberOfBlockRows();
for (i=1; i< totblks; ++i)
{
unsigned int nmodes=m_BlkMat->GetNumberOfRowsInBlockRow(i);
if(nmodes)
{
DNekMatSharedPtr tmp_mat =
MemoryManager<DNekMat>::AllocateSharedPtr
(nmodes,nmodes,zero,storage);
tmp_mat=m_BlkMat->GetBlock(i,i);
tmp_mat->Invert();
m_BlkMat->SetBlock(i,i,tmp_mat);
}
}
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoMultiplybyInverseTransformationMatrix ( const Array< OneD, NekDouble > &  pInput,
Array< OneD, NekDouble > &  pOutput 
)
privatevirtual

Multiply by the block inverse transformation matrix.

Definition at line 1127 of file PreconditionerLowEnergy.cpp.

References ASSERTL1, Nektar::eWrapper, Vmath::Gathr(), m_InvRBlk, m_locToGloMap, m_locToGloSignMult, m_map, and Vmath::Vcopy().

{
int nGlobBndDofs = m_locToGloMap->GetNumGlobalBndCoeffs();
int nDirBndDofs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBndDofs = nGlobBndDofs - nDirBndDofs;
int nLocBndDofs = m_locToGloMap->GetNumLocalBndCoeffs();
ASSERTL1(pInput.num_elements() >= nGlobHomBndDofs,
"Input array is greater than the nGlobHomBndDofs");
ASSERTL1(pOutput.num_elements() >= nGlobHomBndDofs,
"Output array is greater than the nGlobHomBndDofs");
//vectors of length number of non-dirichlet boundary dofs
NekVector<NekDouble> F_GlobBnd(nGlobHomBndDofs,pInput,eWrapper);
NekVector<NekDouble> F_HomBnd(nGlobHomBndDofs,pOutput,
eWrapper);
//Block inverse transformation matrix
DNekScalBlkMat &invR = *m_InvRBlk;
Array<OneD, NekDouble> pLocal(nLocBndDofs, 0.0);
NekVector<NekDouble> F_LocBnd(nLocBndDofs,pLocal,eWrapper);
m_map = m_locToGloMap->GetLocalToGlobalBndMap();
// Allocated array of size number of global boundary dofs and copy
// the input array to the tmp array offset by Dirichlet boundary
// conditions.
Array<OneD,NekDouble> tmp(nGlobBndDofs,0.0);
Vmath::Vcopy(nGlobHomBndDofs, pInput.get(), 1, tmp.get() + nDirBndDofs, 1);
//Global boundary dofs (with zeroed dirichlet values) to local boundary dofs
Vmath::Gathr(m_map.num_elements(), m_locToGloSignMult.get(), tmp.get(), m_map.get(), pLocal.get());
//Multiply by block inverse transformation matrix
F_LocBnd=invR*F_LocBnd;
//Assemble local boundary to global non-dirichlet boundary
m_locToGloMap->AssembleBnd(F_LocBnd,F_HomBnd,nDirBndDofs);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoMultiplybyInverseTransposedTransformationMatrix ( const Array< OneD, NekDouble > &  pInput,
Array< OneD, NekDouble > &  pOutput 
)
privatevirtual

Multiply by the block tranposed inverse transformation matrix.

Definition at line 1172 of file PreconditionerLowEnergy.cpp.

References ASSERTL1, Nektar::eWrapper, m_InvRTBlk, m_locToGloMap, m_map, m_multiplicity, and Vmath::Vmul().

{
int nGlobBndDofs = m_locToGloMap->GetNumGlobalBndCoeffs();
int nDirBndDofs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBndDofs = nGlobBndDofs - nDirBndDofs;
int nLocBndDofs = m_locToGloMap->GetNumLocalBndCoeffs();
ASSERTL1(pInput.num_elements() >= nGlobHomBndDofs,
"Input array is greater than the nGlobHomBndDofs");
ASSERTL1(pOutput.num_elements() >= nGlobHomBndDofs,
"Output array is greater than the nGlobHomBndDofs");
//vectors of length number of non-dirichlet boundary dofs
NekVector<NekDouble> F_GlobBnd(nGlobHomBndDofs,pInput,eWrapper);
NekVector<NekDouble> F_HomBnd(nGlobHomBndDofs,pOutput,
eWrapper);
//Block inverse transformation matrix
DNekScalBlkMat &invRT = *m_InvRTBlk;
Array<OneD, NekDouble> pLocal(nLocBndDofs, 0.0);
NekVector<NekDouble> F_LocBnd(nLocBndDofs,pLocal,eWrapper);
m_map = m_locToGloMap->GetLocalToGlobalBndMap();
m_locToGloMap->GlobalToLocalBnd(pInput,pLocal, nDirBndDofs);
//Multiply by the block transposed transformation matrix
F_LocBnd=invRT*F_LocBnd;
m_locToGloMap->AssembleBnd(pLocal,pOutput, nDirBndDofs);
Vmath::Vmul(nGlobHomBndDofs,pOutput,1,m_multiplicity,1,pOutput,1);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoPreconditioner ( const Array< OneD, NekDouble > &  pInput,
Array< OneD, NekDouble > &  pOutput 
)
privatevirtual

Apply the low energy preconditioner during the conjugate gradient routine

Definition at line 891 of file PreconditionerLowEnergy.cpp.

References Nektar::eWrapper, and m_locToGloMap.

{
int nDir = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobal = m_locToGloMap->GetNumGlobalBndCoeffs();
int nNonDir = nGlobal-nDir;
DNekBlkMat &M = (*m_BlkMat);
NekVector<NekDouble> r(nNonDir,pInput,eWrapper);
NekVector<NekDouble> z(nNonDir,pOutput,eWrapper);
z = M * r;
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoTransformFromLowEnergy ( Array< OneD, NekDouble > &  pInOut)
privatevirtual

transform the solution vector from low energy back to the original basis.

After the conjugate gradient routine the output vector is in the low energy basis and must be trasnformed back to the original basis in order to get the correct solution out. the solution vector i.e. $\mathbf{x}=\mathbf{R^{T}}\mathbf{\overline{x}}$.

Definition at line 1085 of file PreconditionerLowEnergy.cpp.

References ASSERTL1, Vmath::Assmb(), Nektar::eWrapper, m_locToGloMap, m_locToGloSignMult, m_map, m_RTBlk, and Vmath::Vcopy().

{
int nGlobBndDofs = m_locToGloMap->GetNumGlobalBndCoeffs();
int nDirBndDofs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBndDofs = nGlobBndDofs - nDirBndDofs;
int nLocBndDofs = m_locToGloMap->GetNumLocalBndCoeffs();
ASSERTL1(pInOut.num_elements() >= nGlobBndDofs,
"Output array is greater than the nGlobBndDofs");
//Block transposed transformation matrix
DNekScalBlkMat &RT = *m_RTBlk;
NekVector<NekDouble> V_GlobHomBnd(nGlobHomBndDofs,pInOut+nDirBndDofs,
eWrapper);
Array<OneD, NekDouble> pLocal(nLocBndDofs, 0.0);
NekVector<NekDouble> V_LocBnd(nLocBndDofs,pLocal,eWrapper);
m_map = m_locToGloMap->GetLocalToGlobalBndMap();
Array<OneD,NekDouble> tmp(nGlobBndDofs,0.0);
//Global boundary (less dirichlet) to local boundary
m_locToGloMap->GlobalToLocalBnd(V_GlobHomBnd,V_LocBnd, nDirBndDofs);
//Multiply by the block transposed transformation matrix
V_LocBnd=RT*V_LocBnd;
//Assemble local boundary to global boundary
Vmath::Assmb(nLocBndDofs, m_locToGloSignMult.get(),pLocal.get(), m_map.get(), tmp.get());
//Universal assemble across processors
m_locToGloMap->UniversalAssembleBnd(tmp);
//copy non-dirichlet boundary values
Vmath::Vcopy(nGlobBndDofs-nDirBndDofs, tmp.get() + nDirBndDofs, 1, pInOut.get() + nDirBndDofs, 1);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoTransformToLowEnergy ( Array< OneD, NekDouble > &  pInOut,
int  offset 
)
privatevirtual

Transform the solution vector vector to low energy.

As the conjugate gradient system is solved for the low energy basis, the solution vector $\mathbf{x}$ must be transformed to the low energy basis i.e. $\overline{\mathbf{x}}=\mathbf{R}\mathbf{x}$.

Definition at line 993 of file PreconditionerLowEnergy.cpp.

References Nektar::eWrapper, Vmath::Gathr(), m_locToGloMap, m_locToGloSignMult, m_map, m_RBlk, and Vmath::Vcopy().

{
int nGlobBndDofs = m_locToGloMap->GetNumGlobalBndCoeffs();
int nDirBndDofs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBndDofs = nGlobBndDofs - nDirBndDofs;
int nLocBndDofs = m_locToGloMap->GetNumLocalBndCoeffs();
//Non-dirichlet boundary dofs
NekVector<NekDouble> F_HomBnd(nGlobHomBndDofs,pInOut+offset,
eWrapper);
//Block transformation matrix
DNekScalBlkMat &R = *m_RBlk;
Array<OneD, NekDouble> pLocal(nLocBndDofs, 0.0);
NekVector<NekDouble> F_LocBnd(nLocBndDofs,pLocal,eWrapper);
m_map = m_locToGloMap->GetLocalToGlobalBndMap();
//Not actually needed but we should only work with the Global boundary dofs
Array<OneD,NekDouble> tmp(nGlobBndDofs,0.0);
Vmath::Vcopy(nGlobBndDofs, pInOut.get(), 1, tmp.get(), 1);
//Global boundary (with dirichlet values) to local boundary with multiplicity
Vmath::Gathr(m_map.num_elements(), m_locToGloSignMult.get(), tmp.get(), m_map.get(), pLocal.get());
//Multiply by the block transformation matrix
F_LocBnd=R*F_LocBnd;
//Assemble local boundary to global non-dirichlet Dofs
m_locToGloMap->AssembleBnd(F_LocBnd,F_HomBnd, nDirBndDofs);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_DoTransformToLowEnergy ( const Array< OneD, NekDouble > &  pInput,
Array< OneD, NekDouble > &  pOutput 
)
privatevirtual

Transform the solution vector vector to low energy.

As the conjugate gradient system is solved for the low energy basis, the solution vector $\mathbf{x}$ must be transformed to the low energy basis i.e. $\overline{\mathbf{x}}=\mathbf{R}\mathbf{x}$.

Definition at line 1034 of file PreconditionerLowEnergy.cpp.

References ASSERTL1, Nektar::eWrapper, Vmath::Gathr(), m_locToGloMap, m_locToGloSignMult, m_map, m_RBlk, and Vmath::Vcopy().

{
int nGlobBndDofs = m_locToGloMap->GetNumGlobalBndCoeffs();
int nDirBndDofs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int nGlobHomBndDofs = nGlobBndDofs - nDirBndDofs;
int nLocBndDofs = m_locToGloMap->GetNumLocalBndCoeffs();
//Input/output vectors should be length nGlobHomBndDofs
ASSERTL1(pInput.num_elements() >= nGlobHomBndDofs,
"Input array is greater than the nGlobHomBndDofs");
ASSERTL1(pOutput.num_elements() >= nGlobHomBndDofs,
"Output array is greater than the nGlobHomBndDofs");
//vectors of length number of non-dirichlet boundary dofs
NekVector<NekDouble> F_GlobBnd(nGlobHomBndDofs,pInput,eWrapper);
NekVector<NekDouble> F_HomBnd(nGlobHomBndDofs,pOutput,
eWrapper);
//Block transformation matrix
DNekScalBlkMat &R = *m_RBlk;
Array<OneD, NekDouble> pLocal(nLocBndDofs, 0.0);
NekVector<NekDouble> F_LocBnd(nLocBndDofs,pLocal,eWrapper);
m_map = m_locToGloMap->GetLocalToGlobalBndMap();
// Allocated array of size number of global boundary dofs and copy
// the input array to the tmp array offset by Dirichlet boundary
// conditions.
Array<OneD,NekDouble> tmp(nGlobBndDofs,0.0);
Vmath::Vcopy(nGlobHomBndDofs, pInput.get(), 1, tmp.get() + nDirBndDofs, 1);
//Global boundary dofs (with zeroed dirichlet values) to local boundary dofs
Vmath::Gathr(m_map.num_elements(), m_locToGloSignMult.get(), tmp.get(), m_map.get(), pLocal.get());
//Multiply by the block transformation matrix
F_LocBnd=R*F_LocBnd;
//Assemble local boundary to global non-dirichlet boundary
m_locToGloMap->AssembleBnd(F_LocBnd,F_HomBnd,nDirBndDofs);
}
void Nektar::MultiRegions::PreconditionerLowEnergy::v_InitObject ( )
privatevirtual

Definition at line 73 of file PreconditionerLowEnergy.cpp.

References ASSERTL0, CreateMultiplicityMap(), Nektar::MultiRegions::eIterativeStaticCond, m_linsys, m_locToGloMap, SetupBlockTransformationMatrix(), and SetUpReferenceElements().

{
GlobalSysSolnType solvertype=m_locToGloMap->GetGlobalSysSolnType();
ASSERTL0(solvertype == MultiRegions::eIterativeStaticCond,"Solver type not valid");
boost::shared_ptr<MultiRegions::ExpList>
expList=((m_linsys.lock())->GetLocMat()).lock();
StdRegions::StdExpansionSharedPtr locExpansion;
locExpansion = expList->GetExp(0);
int nDim = locExpansion->GetShapeDimension();
ASSERTL0(nDim==3,
"Preconditioner type only valid in 3D");
//Sets up reference element and builds transformation matrix
SetUpReferenceElements();
//Set up block transformation matrix
SetupBlockTransformationMatrix();
//Sets up multiplicity map for transformation from global to local
CreateMultiplicityMap();
}
DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::v_TransformedSchurCompl ( int  offset,
const boost::shared_ptr< DNekScalMat > &  loc_mat 
)
privatevirtual

Set up the transformed block matrix system.

Sets up a block elemental matrix in which each of the block matrix is the low energy equivalent i.e. $\mathbf{S}_{2}=\mathbf{R}\mathbf{S}_{1}\mathbf{R}^{T}$

Definition at line 1216 of file PreconditionerLowEnergy.cpp.

References Nektar::eFULL, Nektar::LibUtilities::eHexahedron, Nektar::LibUtilities::ePrism, Nektar::LibUtilities::eTetrahedron, m_linsys, m_Rhex, m_Rprism, m_Rtet, m_RThex, m_RTprism, and m_RTtet.

{
boost::shared_ptr<MultiRegions::ExpList>
expList=((m_linsys.lock())->GetLocMat()).lock();
StdRegions::StdExpansionSharedPtr locExpansion;
locExpansion = expList->GetExp(offset);
unsigned int nbnd=locExpansion->NumBndryCoeffs();
unsigned int ncoeffs=locExpansion->GetNcoeffs();
unsigned int nint=ncoeffs-nbnd;
//This is the SC elemental matrix in the orginal basis (S1)
DNekScalMatSharedPtr pS1=loc_mat;
//Transformation matrices
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transmatrixmap;
map<LibUtilities::ShapeType,DNekScalMatSharedPtr> transposedtransmatrixmap;
transmatrixmap[LibUtilities::eTetrahedron]=m_Rtet;
transmatrixmap[LibUtilities::ePrism]=m_Rprism;
transmatrixmap[LibUtilities::eHexahedron]=m_Rhex;
transposedtransmatrixmap[LibUtilities::eTetrahedron]=m_RTtet;
transposedtransmatrixmap[LibUtilities::ePrism]=m_RTprism;
transposedtransmatrixmap[LibUtilities::eHexahedron]=m_RThex;
DNekScalMat &S1 = (*pS1);
MatrixStorage storage = eFULL;
DNekMatSharedPtr pS2 = MemoryManager<DNekMat>::AllocateSharedPtr(nbnd,nbnd,0.0,storage);
DNekMatSharedPtr pRS1 = MemoryManager<DNekMat>::AllocateSharedPtr(nbnd,nbnd,0.0,storage);
LibUtilities::ShapeType eType=
(expList->GetExp(offset))->DetShapeType();
//transformation matrices
DNekScalMat &R = (*(transmatrixmap[eType]));
DNekScalMat &RT = (*(transposedtransmatrixmap[eType]));
//create low energy matrix
DNekMat &RS1 = (*pRS1);
DNekMat &S2 = (*pS2);
//setup S2
RS1=R*S1;
S2=RS1*RT;
DNekScalMatSharedPtr tmp_mat;
tmp_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(1.0, pS2);
return tmp_mat;
}

Member Data Documentation

string Nektar::MultiRegions::PreconditionerLowEnergy::className
static
Initial value:
GetPreconFactory().RegisterCreatorFunction(
"LowEnergyBlock",
PreconditionerLowEnergy::create,
"LowEnergy Preconditioning")

Name of class.

Registers the class with the Factory.

Definition at line 68 of file PreconditionerLowEnergy.h.

DNekBlkMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_BlkMat
protected

Definition at line 82 of file PreconditionerLowEnergy.h.

Referenced by v_BuildPreconditioner().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_bnd_mat
protected

Definition at line 83 of file PreconditionerLowEnergy.h.

DNekScalBlkMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_InvRBlk
protected

Definition at line 87 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and v_DoMultiplybyInverseTransformationMatrix().

DNekScalBlkMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_InvRTBlk
protected

Definition at line 88 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and v_DoMultiplybyInverseTransposedTransformationMatrix().

const boost::weak_ptr<GlobalLinSys> Nektar::MultiRegions::PreconditionerLowEnergy::m_linsys
protected

Definition at line 79 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), v_InitObject(), and v_TransformedSchurCompl().

boost::shared_ptr<AssemblyMap> Nektar::MultiRegions::PreconditionerLowEnergy::m_locToGloMap
protected

Definition at line 80 of file PreconditionerLowEnergy.h.

Referenced by CreateMultiplicityMap(), SetupBlockTransformationMatrix(), v_BuildPreconditioner(), v_DoMultiplybyInverseTransformationMatrix(), v_DoMultiplybyInverseTransposedTransformationMatrix(), v_DoPreconditioner(), v_DoTransformFromLowEnergy(), v_DoTransformToLowEnergy(), and v_InitObject().

Array<OneD, NekDouble> Nektar::MultiRegions::PreconditionerLowEnergy::m_locToGloSignMult
protected

Definition at line 105 of file PreconditionerLowEnergy.h.

Referenced by CreateMultiplicityMap(), v_DoMultiplybyInverseTransformationMatrix(), v_DoTransformFromLowEnergy(), and v_DoTransformToLowEnergy().

Array<OneD, int> Nektar::MultiRegions::PreconditionerLowEnergy::m_map
protected

Definition at line 107 of file PreconditionerLowEnergy.h.

Referenced by v_DoMultiplybyInverseTransformationMatrix(), v_DoMultiplybyInverseTransposedTransformationMatrix(), v_DoTransformFromLowEnergy(), and v_DoTransformToLowEnergy().

Array<OneD, NekDouble> Nektar::MultiRegions::PreconditionerLowEnergy::m_multiplicity
protected

Definition at line 106 of file PreconditionerLowEnergy.h.

Referenced by CreateMultiplicityMap(), and v_DoMultiplybyInverseTransposedTransformationMatrix().

DNekScalBlkMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RBlk
protected

Definition at line 85 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), v_BuildPreconditioner(), and v_DoTransformToLowEnergy().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rhex
protected

Definition at line 95 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rinvhex
protected

Definition at line 97 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rinvprism
protected

Definition at line 102 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rinvtet
protected

Definition at line 92 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rprism
protected

Definition at line 100 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

DNekScalBlkMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTBlk
protected

Definition at line 86 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), v_BuildPreconditioner(), and v_DoTransformFromLowEnergy().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_Rtet
protected

Definition at line 90 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RThex
protected

Definition at line 96 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTinvhex
protected

Definition at line 98 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTinvprism
protected

Definition at line 103 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTinvtet
protected

Definition at line 93 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), and SetUpReferenceElements().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTprism
protected

Definition at line 101 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

DNekScalMatSharedPtr Nektar::MultiRegions::PreconditionerLowEnergy::m_RTtet
protected

Definition at line 91 of file PreconditionerLowEnergy.h.

Referenced by SetupBlockTransformationMatrix(), SetUpReferenceElements(), v_BuildPreconditioner(), and v_TransformedSchurCompl().

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