A global linear system. More...

#include <GlobalLinSysXxtStaticCond.h>

Inheritance diagram for Nektar::MultiRegions::GlobalLinSysXxtStaticCond:

Collaboration diagram for Nektar::MultiRegions::GlobalLinSysXxtStaticCond:

Public Member Functions
	GlobalLinSysXxtStaticCond (const GlobalLinSysKey &mkey, const boost::weak_ptr< ExpList > &pExpList, const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve.
	GlobalLinSysXxtStaticCond (const GlobalLinSysKey &mkey, const boost::weak_ptr< ExpList > &pExpList, const DNekScalBlkMatSharedPtr pSchurCompl, const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC, const DNekScalBlkMatSharedPtr pInvD, const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve.
virtual	~GlobalLinSysXxtStaticCond ()
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSysXxt
	GlobalLinSysXxt (const GlobalLinSysKey &pKey, const boost::weak_ptr< ExpList > &pExp, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve.
virtual	~GlobalLinSysXxt ()
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSys
	GlobalLinSys (const GlobalLinSysKey &pKey, const boost::weak_ptr< ExpList > &pExpList, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve.
virtual	~GlobalLinSys ()
const GlobalLinSysKey &	GetKey (void) const
	Returns the key associated with the system.
const boost::weak_ptr< ExpList > &	GetLocMat (void) const
void	InitObject ()
void	Initialise (const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
void	Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve the linear system for given input and output vectors using a specified local to global map.
boost::shared_ptr< GlobalLinSys >	GetSharedThisPtr ()
	Returns a shared pointer to the current object.
int	GetNumBlocks ()
DNekScalMatSharedPtr	GetBlock (unsigned int n)
DNekScalBlkMatSharedPtr	GetStaticCondBlock (unsigned int n)
void	DropStaticCondBlock (unsigned int n)
void	SolveLinearSystem (const int pNumRows, const Array< OneD, const NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const AssemblyMapSharedPtr &locToGloMap, const int pNumDir=0)
	Solve the linear system for given input and output vectors.
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
	GlobalLinSysStaticCond (const GlobalLinSysKey &mkey, const boost::weak_ptr< ExpList > &pExpList, const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve.
virtual	~GlobalLinSysStaticCond ()

Static Public Member Functions
static GlobalLinSysSharedPtr	create (const GlobalLinSysKey &pLinSysKey, const boost::weak_ptr< ExpList > &pExpList, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
	Creates an instance of this class.

Static Public Attributes
static std::string	className
	Name of class.
static std::string	className2

Protected Member Functions
void	CreateMap (const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
virtual void	v_AssembleSchurComplement (boost::shared_ptr< AssemblyMap > locToGloMap)
	Assemble the Schur complement matrix.
virtual GlobalLinSysStaticCondSharedPtr	v_Recurse (const GlobalLinSysKey &mkey, const boost::weak_ptr< ExpList > &pExpList, const DNekScalBlkMatSharedPtr pSchurCompl, const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC, const DNekScalBlkMatSharedPtr pInvD, const boost::shared_ptr< AssemblyMap > &locToGloMap)
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSysXxt
virtual void	v_SolveLinearSystem (const int pNumRows, const Array< OneD, const NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const AssemblyMapSharedPtr &locToGloMap, const int pNumDir=0)
	Solve the linear system for given input and output vectors.
void	GlobalToLocalNoSign (const Array< OneD, const NekDouble > &global, Array< OneD, NekDouble > &local)
void	LocalToGlobalNoSign (const Array< OneD, const NekDouble > &local, Array< OneD, NekDouble > &global)
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSys
virtual DNekScalMatSharedPtr	v_GetBlock (unsigned int n)
	Retrieves the block matrix from n-th expansion using the matrix key provided by the m_linSysKey.
virtual DNekScalBlkMatSharedPtr	v_GetStaticCondBlock (unsigned int n)
	Retrieves a the static condensation block matrices from n-th expansion using the matrix key provided by the m_linSysKey.
virtual void	v_DropStaticCondBlock (unsigned int n)
	Releases the static condensation block matrices from NekManager of n-th expansion using the matrix key provided by the m_linSysKey.
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
virtual DNekScalBlkMatSharedPtr	v_PreSolve (int scLevel, NekVector< NekDouble > &F_GlobBnd)
virtual void	v_BasisTransform (Array< OneD, NekDouble > &pInOut, int offset)
virtual void	v_BasisInvTransform (Array< OneD, NekDouble > &pInOut)
virtual int	v_GetNumBlocks ()
	Get the number of blocks in this system.
virtual void	v_Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve the linear system for given input and output vectors using a specified local to global map.
virtual void	v_InitObject ()
virtual void	v_Initialise (const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Initialise this object.
void	SetupTopLevel (const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Set up the storage for the Schur complement or the top level of the multi-level Schur complement.
void	ConstructNextLevelCondensedSystem (const boost::shared_ptr< AssemblyMap > &locToGloMap)

Additional Inherited Members
Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSysXxt
struct Xxt::crs_data *	m_crsData
Array< OneD, unsigned int >	m_Ai
Array< OneD, unsigned int >	m_Aj
Array< OneD, double >	m_Ar
Array< OneD, NekDouble >	m_locToGloSignMult
Array< OneD, int >	m_map
Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
GlobalLinSysStaticCondSharedPtr	m_recursiveSchurCompl
	Schur complement for Direct Static Condensation.
DNekScalBlkMatSharedPtr	m_schurCompl
	Block Schur complement matrix.
DNekScalBlkMatSharedPtr	m_BinvD
	Block $BD^{-1}$ matrix.
DNekScalBlkMatSharedPtr	m_C
	Block matrix.
DNekScalBlkMatSharedPtr	m_invD
	Block $D^{-1}$ matrix.
boost::shared_ptr< AssemblyMap >	m_locToGloMap
	Local to global map.
Array< OneD, NekDouble >	m_wsp
	Workspace array for matrix multiplication.

Detailed Description

A global linear system.

Definition at line 57 of file GlobalLinSysXxtStaticCond.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::GlobalLinSysXxtStaticCond::GlobalLinSysXxtStaticCond	(	const GlobalLinSysKey &	pKey,
		const boost::weak_ptr< ExpList > &	pExpList,
		const boost::shared_ptr< AssemblyMap > &	pLocToGloMap
	)

Constructor for full direct matrix solve.

For a matrix system of the form

$\left[ \begin{array}{cc} \boldsymbol{A} & \boldsymbol{B}\\ \boldsymbol{C} & \boldsymbol{D} \end{array} \right] \left[ \begin{array}{c} \boldsymbol{x_1}\\ \boldsymbol{x_2} \end{array}\right] = \left[ \begin{array}{c} \boldsymbol{y_1}\\ \boldsymbol{y_2} \end{array}\right],$

where $\boldsymbol{D}$ and $(\boldsymbol{A-BD^{-1}C})$ are invertible, store and assemble a static condensation system, according to a given local to global mapping. #m_linSys is constructed by AssembleSchurComplement().

Parameters

mKey	Associated matrix key.
pLocMatSys	LocalMatrixSystem
locToGloMap	Local to global mapping.

Definition at line 86 of file GlobalLinSysXxtStaticCond.cpp.

References ASSERTL1, Nektar::MultiRegions::eXxtMultiLevelStaticCond, Nektar::MultiRegions::eXxtStaticCond, and Nektar::MultiRegions::GlobalLinSysKey::GetGlobalSysSolnType().

            : GlobalLinSys          (pKey, pExpList, pLocToGloMap),
              GlobalLinSysXxt       (pKey, pExpList, pLocToGloMap),
              GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
        {
            ASSERTL1((pKey.GetGlobalSysSolnType()==eXxtStaticCond)||
                     (pKey.GetGlobalSysSolnType()==eXxtMultiLevelStaticCond),
                     "This constructor is only valid when using static "
                     "condensation");
            ASSERTL1(pKey.GetGlobalSysSolnType()
                        == pLocToGloMap->GetGlobalSysSolnType(),
                     "The local to global map is not set up for the requested "
                     "solution type");
        }

Nektar::MultiRegions::GlobalLinSysXxtStaticCond::GlobalLinSysXxtStaticCond	(	const GlobalLinSysKey &	mkey,
		const boost::weak_ptr< ExpList > &	pExpList,
		const DNekScalBlkMatSharedPtr	pSchurCompl,
		const DNekScalBlkMatSharedPtr	pBinvD,
		const DNekScalBlkMatSharedPtr	pC,
		const DNekScalBlkMatSharedPtr	pInvD,
		const boost::shared_ptr< AssemblyMap > &	locToGloMap
	)

Constructor for full direct matrix solve.

Definition at line 109 of file GlobalLinSysXxtStaticCond.cpp.

References Nektar::MultiRegions::GlobalLinSysStaticCond::m_BinvD, Nektar::MultiRegions::GlobalLinSysStaticCond::m_C, Nektar::MultiRegions::GlobalLinSysStaticCond::m_invD, Nektar::MultiRegions::GlobalLinSysStaticCond::m_locToGloMap, and Nektar::MultiRegions::GlobalLinSysStaticCond::m_schurCompl.

            : GlobalLinSys          (pKey, pExpList, pLocToGloMap),
              GlobalLinSysXxt       (pKey, pExpList, pLocToGloMap),
              GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
        {
            m_schurCompl  = pSchurCompl;
            m_BinvD       = pBinvD;
            m_C           = pC;
            m_invD        = pInvD;
            m_locToGloMap = pLocToGloMap;
        }

Nektar::MultiRegions::GlobalLinSysXxtStaticCond::~GlobalLinSysXxtStaticCond ( )

virtual

Definition at line 133 of file GlobalLinSysXxtStaticCond.cpp.

        {
        }

Member Function Documentation

static GlobalLinSysSharedPtr Nektar::MultiRegions::GlobalLinSysXxtStaticCond::create	(	const GlobalLinSysKey &	pLinSysKey,
		const boost::weak_ptr< ExpList > &	pExpList,
		const boost::shared_ptr< AssemblyMap > &	pLocToGloMap
	)

inlinestatic

Creates an instance of this class.

Definition at line 62 of file GlobalLinSysXxtStaticCond.h.

            {
                GlobalLinSysSharedPtr p = MemoryManager<
                    GlobalLinSysXxtStaticCond>::AllocateSharedPtr(
                        pLinSysKey, pExpList, pLocToGloMap);
                p->InitObject();
                return p;
            }

void Nektar::MultiRegions::GlobalLinSysXxtStaticCond::CreateMap ( const boost::shared_ptr< AssemblyMap > & pLocToGloMap )

protected

Create the inverse multiplicity map.

Parameters

locToGloMap Local to global mapping information.

Definition at line 142 of file GlobalLinSysXxtStaticCond.cpp.

References Nektar::MultiRegions::GlobalLinSysXxt::m_locToGloSignMult, and Nektar::MultiRegions::GlobalLinSysXxt::m_map.

Referenced by v_AssembleSchurComplement().

        {
            const Array<OneD, const int> &vMap
                                    = pLocToGloMap->GetLocalToGlobalBndMap();
            unsigned int nGlo       = pLocToGloMap->GetNumGlobalBndCoeffs();
            unsigned int nEntries   = pLocToGloMap->GetNumLocalBndCoeffs();
            unsigned int i;
            // Count the multiplicity of each global DOF on this process
            Array<OneD, NekDouble> vCounts(nGlo, 0.0);
            for (i = 0; i < nEntries; ++i)
            {
                vCounts[vMap[i]] += 1.0;
            }
            // Get universal multiplicity by globally assembling counts
            pLocToGloMap->UniversalAssembleBnd(vCounts);
            // Construct a map of 1/multiplicity for use in XXT solve
            m_locToGloSignMult = Array<OneD, NekDouble>(nEntries);
            for (i = 0; i < nEntries; ++i)
            {
                m_locToGloSignMult[i] = 1.0/vCounts[vMap[i]];
            }
            m_map = pLocToGloMap->GetLocalToGlobalBndMap();
        }

void Nektar::MultiRegions::GlobalLinSysXxtStaticCond::v_AssembleSchurComplement ( boost::shared_ptr< AssemblyMap > pLocToGloMap )

protectedvirtual

Assemble the Schur complement matrix.

Construct the local matrix row index, column index and value index arrays and initialize the XXT data structure with this information.

Parameters

locToGloMap Local to global mapping information.

Reimplemented from Nektar::MultiRegions::GlobalLinSysStaticCond.

Definition at line 176 of file GlobalLinSysXxtStaticCond.cpp.

References CreateMap(), Gs::Init(), Nektar::MultiRegions::GlobalLinSysXxt::m_Ai, Nektar::MultiRegions::GlobalLinSysXxt::m_Aj, Nektar::MultiRegions::GlobalLinSysXxt::m_Ar, Nektar::MultiRegions::GlobalLinSysXxt::m_crsData, Nektar::MultiRegions::GlobalLinSys::m_expList, Nektar::MultiRegions::GlobalLinSysStaticCond::m_schurCompl, and Xxt::nektar_crs_stats().

        {
            CreateMap(pLocToGloMap);
            ExpListSharedPtr vExp = m_expList.lock();
            unsigned int nElmt = m_schurCompl->GetNumberOfBlockRows();
            DNekScalMatSharedPtr loc_mat;
            unsigned int iCount     = 0;
            unsigned int rCount     = 0;
            unsigned int nRows      = 0;
            unsigned int nEntries   = 0;
            unsigned int numDirBnd  = pLocToGloMap->GetNumGlobalDirBndCoeffs();
            unsigned int nLocal     = pLocToGloMap->GetNumLocalBndCoeffs();
            const Array<OneD, NekDouble> &vMapSign
                                    = pLocToGloMap->GetLocalToGlobalBndSign();
            bool doSign = pLocToGloMap->GetSignChange();
            unsigned int i = 0, j = 0, k = 0, n = 0;
            int gid1;
            Array<OneD, unsigned int> vSizes(nElmt);
            // First construct a map of the number of local DOFs in each block
            // and the number of matrix entries for each block
            for (n = 0; n < nElmt; ++n)
            {
                loc_mat = m_schurCompl->GetBlock(n,n);
                vSizes[n] = loc_mat->GetRows();
                nEntries += vSizes[n]*vSizes[n];
            }
            // Set up i-index, j-index and value arrays
            m_Ai = Array<OneD, unsigned int>(nEntries);
            m_Aj = Array<OneD, unsigned int>(nEntries);
            m_Ar = Array<OneD, double>(nEntries, 0.0);
            // Set up the universal ID array for XXT
            Array<OneD, unsigned long> vId(nLocal);
            // Loop over each elemental block, extract matrix indices and value
            // and set the universal ID array
            for(n = iCount = 0; n < nElmt; ++n)
            {
                loc_mat = m_schurCompl->GetBlock(n,n);
                nRows = loc_mat->GetRows();
                for(i = 0; i < nRows; ++i)
                {
                    gid1 = pLocToGloMap->GetLocalToGlobalBndMap(iCount + i);
                    for(j = 0; j < nRows; ++j)
                    {
                            k = rCount + i*vSizes[n] + j;
                            m_Ai[k] = iCount + i;
                            m_Aj[k] = iCount + j;
                            m_Ar[k] = (*loc_mat)(i,j);
                            if (doSign)
                            {
                                m_Ar[k] *= vMapSign[iCount+i]*vMapSign[iCount+j];
                            }
                    }
                    // Dirichlet DOFs are not included in the solve, so we set
                    // these to the special XXT id=0.
                    if (gid1 < numDirBnd)
                    {
                        vId[iCount + i] = 0;
                    }
                    else
                    {
                        vId[iCount + i]
                            = pLocToGloMap->GetGlobalToUniversalBndMap()[gid1];
                    }
                }
                iCount += vSizes[n];
                rCount += vSizes[n]*vSizes[n];
            }
            // Set up XXT and output some stats
            LibUtilities::CommSharedPtr vComm = pLocToGloMap->GetComm();
            m_crsData = Xxt::Init(nLocal, vId, m_Ai, m_Aj, m_Ar, vComm);
            Xxt::nektar_crs_stats(m_crsData);
        }

GlobalLinSysStaticCondSharedPtr Nektar::MultiRegions::GlobalLinSysXxtStaticCond::v_Recurse	(	const GlobalLinSysKey &	mkey,
		const boost::weak_ptr< ExpList > &	pExpList,
		const DNekScalBlkMatSharedPtr	pSchurCompl,
		const DNekScalBlkMatSharedPtr	pBinvD,
		const DNekScalBlkMatSharedPtr	pC,
		const DNekScalBlkMatSharedPtr	pInvD,
		const boost::shared_ptr< AssemblyMap > &	locToGloMap
	)

protectedvirtual

Implements Nektar::MultiRegions::GlobalLinSysStaticCond.

Definition at line 258 of file GlobalLinSysXxtStaticCond.cpp.

        {
            GlobalLinSysXxtStaticCondSharedPtr sys = MemoryManager<
                GlobalLinSysXxtStaticCond>::AllocateSharedPtr(
                    mkey, pExpList, pSchurCompl, pBinvD, pC, pInvD, l2gMap);
            sys->Initialise(l2gMap);
            return sys;
        }

Member Data Documentation

string Nektar::MultiRegions::GlobalLinSysXxtStaticCond::className

static

Initial value:

 GetGlobalLinSysFactory().RegisterCreatorFunction(
                    "XxtStaticCond",
                    GlobalLinSysXxtStaticCond::create,
                    "Iterative static condensation.")

Name of class.

Registers the class with the Factory.

Definition at line 76 of file GlobalLinSysXxtStaticCond.h.

string Nektar::MultiRegions::GlobalLinSysXxtStaticCond::className2

static

Initial value:

 GetGlobalLinSysFactory().RegisterCreatorFunction(
                    "XxtMultiLevelStaticCond",
                    GlobalLinSysXxtStaticCond::create,
                    "Xxt multi-level static condensation.")

Definition at line 77 of file GlobalLinSysXxtStaticCond.h.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation