A global linear system. More...

#include <GlobalLinSysDirectStaticCond.h>

Inheritance diagram for Nektar::MultiRegions::GlobalLinSysDirectStaticCond:

Collaboration diagram for Nektar::MultiRegions::GlobalLinSysDirectStaticCond:

Public Member Functions
	GlobalLinSysDirectStaticCond (const GlobalLinSysKey &mkey, const boost::weak_ptr< ExpList > &pExpList, const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve.
	GlobalLinSysDirectStaticCond (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	~GlobalLinSysDirectStaticCond ()
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSysDirect
	GlobalLinSysDirect (const GlobalLinSysKey &pKey, const boost::weak_ptr< ExpList > &pExp, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve.
virtual	~GlobalLinSysDirect ()
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
virtual void	v_AssembleSchurComplement (boost::shared_ptr< AssemblyMap > pLocToGloMap)
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 > &l2gMap)
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSysDirect
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.
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)

Private Member Functions
MatrixStorage	DetermineMatrixStorage (const boost::shared_ptr< AssemblyMap > &locToGloMap)
	Matrix Storage type for known matrices.

Additional Inherited Members
Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSysDirect
DNekLinSysSharedPtr	m_linSys
	Basic linear system object.
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 54 of file GlobalLinSysDirectStaticCond.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::GlobalLinSysDirectStaticCond::GlobalLinSysDirectStaticCond	(	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 83 of file GlobalLinSysDirectStaticCond.cpp.

References ASSERTL1, Nektar::MultiRegions::eDirectMultiLevelStaticCond, Nektar::MultiRegions::eDirectStaticCond, and Nektar::MultiRegions::GlobalLinSysKey::GetGlobalSysSolnType().

            : GlobalLinSys          (pKey, pExpList, pLocToGloMap),
              GlobalLinSysDirect    (pKey, pExpList, pLocToGloMap),
              GlobalLinSysStaticCond(pKey, pExpList, pLocToGloMap)
        {
            ASSERTL1((pKey.GetGlobalSysSolnType()==eDirectStaticCond)||
                     (pKey.GetGlobalSysSolnType()==eDirectMultiLevelStaticCond),
                     "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::GlobalLinSysDirectStaticCond::GlobalLinSysDirectStaticCond	(	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 105 of file GlobalLinSysDirectStaticCond.cpp.

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

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

Nektar::MultiRegions::GlobalLinSysDirectStaticCond::~GlobalLinSysDirectStaticCond ( )

virtual

Definition at line 127 of file GlobalLinSysDirectStaticCond.cpp.

        {
        }

Member Function Documentation

static GlobalLinSysSharedPtr Nektar::MultiRegions::GlobalLinSysDirectStaticCond::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 59 of file GlobalLinSysDirectStaticCond.h.

            {
                GlobalLinSysDirectStaticCondSharedPtr ret =
                    MemoryManager<GlobalLinSysDirectStaticCond>
                    ::AllocateSharedPtr(pLinSysKey, pExpList, pLocToGloMap);
                ret->InitObject();
                return ret;
            }

MatrixStorage Nektar::MultiRegions::GlobalLinSysDirectStaticCond::DetermineMatrixStorage ( const boost::shared_ptr< AssemblyMap > & locToGloMap )

private

Matrix Storage type for known matrices.

Definition at line 133 of file GlobalLinSysDirectStaticCond.cpp.

References Nektar::eFULL, Nektar::StdRegions::eHelmholtz, Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eLinearAdvectionDiffusionReaction, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eMass, Nektar::ePOSITIVE_DEFINITE_SYMMETRIC, Nektar::ePOSITIVE_DEFINITE_SYMMETRIC_BANDED, Nektar::MultiRegions::GlobalMatrixKey::GetMatrixType(), and Nektar::MultiRegions::GlobalLinSys::m_linSysKey.

Referenced by v_AssembleSchurComplement().

        {
            int nBndDofs  = pLocToGloMap->GetNumGlobalBndCoeffs();
            int NumDirBCs = pLocToGloMap->GetNumGlobalDirBndCoeffs();
            unsigned int rows = nBndDofs - NumDirBCs;
            int bwidth = pLocToGloMap->GetBndSystemBandWidth();
            MatrixStorage matStorage;
            
            switch(m_linSysKey.GetMatrixType())
            {
                // case for all symmetric matices
            case StdRegions::eMass:
            case StdRegions::eLaplacian:
            case StdRegions::eHelmholtz:
            case StdRegions::eHybridDGHelmBndLam:
                {
                    if( (2*(bwidth+1)) < rows)
                    {
                        matStorage = ePOSITIVE_DEFINITE_SYMMETRIC_BANDED; 
                    }
                    else
                    {
                        matStorage = ePOSITIVE_DEFINITE_SYMMETRIC;
                    }
                }
                break;
            case StdRegions::eLinearAdvectionReaction:
            case StdRegions::eLinearAdvectionDiffusionReaction:
            default:
                {
                    // Current inversion techniques do not seem to
                    // allow banded matrices to be used as a linear
                    // system
                    matStorage = eFULL;
                }
                break;
            }
            return matStorage;
        }

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

protectedvirtual

Assemble the schur complement matrix from the block matrices stored in #m_blkMatrices and the given local to global mapping information.

Parameters

locToGloMap Local to global mapping information.

Reimplemented from Nektar::MultiRegions::GlobalLinSysStaticCond.

Definition at line 181 of file GlobalLinSysDirectStaticCond.cpp.

References DetermineMatrixStorage(), ErrorUtil::efatal, Nektar::eFULL, Nektar::ePOSITIVE_DEFINITE_SYMMETRIC, Nektar::ePOSITIVE_DEFINITE_SYMMETRIC_BANDED, Nektar::eWrapper, Nektar::MultiRegions::GlobalLinSysStaticCond::m_BinvD, Nektar::MultiRegions::GlobalLinSysStaticCond::m_C, Nektar::MultiRegions::GlobalLinSysStaticCond::m_invD, Nektar::MultiRegions::GlobalLinSysDirect::m_linSys, Nektar::MultiRegions::GlobalLinSysStaticCond::m_schurCompl, and NEKERROR.

        {
            int i, j, n, cnt, gid1, gid2;
            NekDouble sign1, sign2, value;
            int nBndDofs  = pLocToGloMap->GetNumGlobalBndCoeffs();
            int NumDirBCs = pLocToGloMap->GetNumGlobalDirBndCoeffs();
            DNekScalBlkMatSharedPtr SchurCompl = m_schurCompl;
            DNekScalBlkMatSharedPtr BinvD      = m_BinvD;
            DNekScalBlkMatSharedPtr C          = m_C;
            DNekScalBlkMatSharedPtr invD       = m_invD;
            unsigned int rows = nBndDofs - NumDirBCs;
            unsigned int cols = nBndDofs - NumDirBCs;
            DNekMatSharedPtr Gmat;
            int bwidth = pLocToGloMap->GetBndSystemBandWidth();
            MatrixStorage matStorage = DetermineMatrixStorage(pLocToGloMap);
            switch(matStorage)
            {
                case ePOSITIVE_DEFINITE_SYMMETRIC_BANDED:
                {
                    try {
                        Gmat = MemoryManager<DNekMat>
                            ::AllocateSharedPtr(rows, cols, 0.0,
                                                matStorage,
                                                bwidth, bwidth);
                    }
                    catch (...) {
                        NEKERROR(ErrorUtil::efatal,
                                 "Insufficient memory for GlobalLinSys.");
                    }
                    break;
                }
                case ePOSITIVE_DEFINITE_SYMMETRIC:
                case eFULL:
                {
                    Gmat = MemoryManager<DNekMat>
                        ::AllocateSharedPtr(rows, cols, 0.0, matStorage);
                    break;
                }
                default:
                {
                    NEKERROR(ErrorUtil::efatal,
                             "Unknown matrix storage type of type not set up");
                }
            }
            
            // fill global matrix
            DNekScalMatSharedPtr loc_mat;
            int loc_lda;
            for(n = cnt = 0; n < SchurCompl->GetNumberOfBlockRows(); ++n)
            {
                loc_mat = SchurCompl->GetBlock(n,n);
                loc_lda = loc_mat->GetRows();
                // Set up  Matrix;
                for(i = 0; i < loc_lda; ++i)
                {
                    gid1  = pLocToGloMap->GetLocalToGlobalBndMap (cnt + i)
                                                                    - NumDirBCs;
                    sign1 = pLocToGloMap->GetLocalToGlobalBndSign(cnt + i);
                    if(gid1 >= 0)
                    {
                        for(j = 0; j < loc_lda; ++j)
                        {
                            gid2  = pLocToGloMap->GetLocalToGlobalBndMap(cnt+j)
                                                                 - NumDirBCs;
                            sign2 = pLocToGloMap->GetLocalToGlobalBndSign(cnt+j);
                            if(gid2 >= 0)
                            {
                                // As the global matrix should be symmetric,
                                // only add the value for the upper triangular
                                // part in order to avoid entries to be entered
                                // twice
                                if((matStorage == eFULL)||(gid2 >= gid1))
                                {
                                    value = Gmat->GetValue(gid1,gid2)
                                                + sign1*sign2*(*loc_mat)(i,j);
                                    Gmat->SetValue(gid1,gid2,value);
                                }
                            }
                        }
                    }
                }
                cnt += loc_lda;
            }
            if(rows)
            {
                PointerWrapper w = eWrapper;
                m_linSys = MemoryManager<DNekLinSys>::AllocateSharedPtr(Gmat,w);
            }
        }

GlobalLinSysStaticCondSharedPtr Nektar::MultiRegions::GlobalLinSysDirectStaticCond::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 > &	l2gMap
	)

protectedvirtual

Implements Nektar::MultiRegions::GlobalLinSysStaticCond.

Definition at line 284 of file GlobalLinSysDirectStaticCond.cpp.

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

Member Data Documentation

string Nektar::MultiRegions::GlobalLinSysDirectStaticCond::className

static

Initial value:

 GetGlobalLinSysFactory().RegisterCreatorFunction(
                    "DirectStaticCond",
                    GlobalLinSysDirectStaticCond::create,
                    "Direct static condensation.")

Name of class.

Registers the class with the Factory.

Definition at line 72 of file GlobalLinSysDirectStaticCond.h.

string Nektar::MultiRegions::GlobalLinSysDirectStaticCond::className2

static

Initial value:

 GetGlobalLinSysFactory().RegisterCreatorFunction(
                    "DirectMultiLevelStaticCond",
                    GlobalLinSysDirectStaticCond::create,
                    "Direct multi-level static condensation.")

Definition at line 73 of file GlobalLinSysDirectStaticCond.h.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation