Nektar::MultiRegions::GlobalLinSysXxtStaticCond Class Reference

A global linear system. More...

#include <GlobalLinSysXxtStaticCond.h>

Inheritance diagram for Nektar::MultiRegions::GlobalLinSysXxtStaticCond:

Public Member Functions
	GlobalLinSysXxtStaticCond (const GlobalLinSysKey &mkey, const std::weak_ptr< ExpList > &pExpList, const std::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve. More...
	GlobalLinSysXxtStaticCond (const GlobalLinSysKey &mkey, const std::weak_ptr< ExpList > &pExpList, const DNekScalBlkMatSharedPtr pSchurCompl, const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC, const DNekScalBlkMatSharedPtr pInvD, const std::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve. More...
	~GlobalLinSysXxtStaticCond () override
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSysXxt
	GlobalLinSysXxt (const GlobalLinSysKey &pKey, const std::weak_ptr< ExpList > &pExp, const std::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve. More...
	~GlobalLinSysXxt () override
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSys
	GlobalLinSys (const GlobalLinSysKey &pKey, const std::weak_ptr< ExpList > &pExpList, const std::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve. More...
virtual	~GlobalLinSys ()
const GlobalLinSysKey &	GetKey (void) const
	Returns the key associated with the system. More...
const std::weak_ptr< ExpList > &	GetLocMat (void) const
void	InitObject ()
void	Initialise (const std::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. More...
std::shared_ptr< GlobalLinSys >	GetSharedThisPtr ()
	Returns a shared pointer to the current object. More...
int	GetNumBlocks ()
DNekScalMatSharedPtr	GetBlock (unsigned int n)
void	DropBlock (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. More...
Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
	GlobalLinSysStaticCond (const GlobalLinSysKey &mkey, const std::weak_ptr< ExpList > &pExpList, const std::shared_ptr< AssemblyMap > &locToGloMap)
	Constructor for full direct matrix solve. More...
	~GlobalLinSysStaticCond () override

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

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

Protected Member Functions
void	v_AssembleSchurComplement (std::shared_ptr< AssemblyMap > locToGloMap) override
	Assemble the Schur complement matrix. More...
GlobalLinSysStaticCondSharedPtr	v_Recurse (const GlobalLinSysKey &mkey, const std::weak_ptr< ExpList > &pExpList, const DNekScalBlkMatSharedPtr pSchurCompl, const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC, const DNekScalBlkMatSharedPtr pInvD, const std::shared_ptr< AssemblyMap > &locToGloMap) override
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSys
virtual void	v_Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)=0
	Solve a linear system based on mapping. More...
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 a basic matrix system. More...
virtual void	v_InitObject ()
virtual void	v_Initialise (const std::shared_ptr< AssemblyMap > &pLocToGloMap)
virtual int	v_GetNumBlocks ()
	Get the number of blocks in this system. More...
virtual DNekScalMatSharedPtr	v_GetBlock (unsigned int n)
	Retrieves the block matrix from n-th expansion using the matrix key provided by the m_linSysKey. More...
virtual void	v_DropBlock (unsigned int n)
	Releases the local block matrix from NekManager of n-th expansion using the matrix key provided by the m_linSysKey. More...
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. More...
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. More...
PreconditionerSharedPtr	CreatePrecon (AssemblyMapSharedPtr asmMap)
	Create a preconditioner object from the parameters defined in the supplied assembly map. More...
Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
virtual void	v_PreSolve (int scLevel, Array< OneD, NekDouble > &F_bnd)
virtual void	v_BasisFwdTransform (Array< OneD, NekDouble > &pInOut)
virtual void	v_CoeffsBwdTransform (Array< OneD, NekDouble > &pInOut)
virtual void	v_CoeffsFwdTransform (const Array< OneD, NekDouble > &pInput, Array< OneD, NekDouble > &pOutput)
virtual void	v_AssembleSchurComplement (std::shared_ptr< AssemblyMap > pLoctoGloMap)
int	v_GetNumBlocks () override
	Get the number of blocks in this system. More...
virtual GlobalLinSysStaticCondSharedPtr	v_Recurse (const GlobalLinSysKey &mkey, const std::weak_ptr< ExpList > &pExpList, const DNekScalBlkMatSharedPtr pSchurCompl, const DNekScalBlkMatSharedPtr pBinvD, const DNekScalBlkMatSharedPtr pC, const DNekScalBlkMatSharedPtr pInvD, const std::shared_ptr< AssemblyMap > &locToGloMap)=0
void	v_Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) override
	Solve the linear system for given input and output vectors using a specified local to global map. More...
void	v_InitObject () override
void	v_Initialise (const std::shared_ptr< AssemblyMap > &locToGloMap) override
	Initialise this object. More...
void	SetupTopLevel (const std::shared_ptr< AssemblyMap > &locToGloMap)
	Set up the storage for the Schur complement or the top level of the multi-level Schur complement. More...
void	ConstructNextLevelCondensedSystem (const std::shared_ptr< AssemblyMap > &locToGloMap)

Private Member Functions
void	v_SolveLinearSystem (const int pNumRows, const Array< OneD, const NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const AssemblyMapSharedPtr &locToGloMap, const int pNumDir) override
	Solve the linear system for given input and output vectors. More...

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
Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSys
const GlobalLinSysKey	m_linSysKey
	Key associated with this linear system. More...
const std::weak_ptr< ExpList >	m_expList
	Local Matrix System. More...
const std::map< int, RobinBCInfoSharedPtr >	m_robinBCInfo
	Robin boundary info. More...
bool	m_verbose
Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSysStaticCond
GlobalLinSysStaticCondSharedPtr	m_recursiveSchurCompl
	Schur complement for Direct Static Condensation. More...
DNekScalBlkMatSharedPtr	m_schurCompl
	Block Schur complement matrix. More...
DNekScalBlkMatSharedPtr	m_BinvD
	Block \( BD^{-1} \) matrix. More...
DNekScalBlkMatSharedPtr	m_C
	Block \( C \) matrix. More...
DNekScalBlkMatSharedPtr	m_invD
	Block \( D^{-1} \) matrix. More...
std::weak_ptr< AssemblyMap >	m_locToGloMap
	Local to global map. More...
Array< OneD, NekDouble >	m_wsp
	Workspace array for matrix multiplication. More...
Array< OneD, const NekDouble >	m_sign

Detailed Description

A global linear system.

Definition at line 55 of file GlobalLinSysXxtStaticCond.h.

Constructor & Destructor Documentation

GlobalLinSysXxtStaticCond() [1/2]

Nektar::MultiRegions::GlobalLinSysXxtStaticCond::GlobalLinSysXxtStaticCond	(	const GlobalLinSysKey &	pKey,
		const std::weak_ptr< ExpList > &	pExpList,
		const std::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 81 of file GlobalLinSysXxtStaticCond.cpp.

    : 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");
}

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

GlobalLinSysXxtStaticCond() [2/2]

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

Constructor for full direct matrix solve.

Definition at line 101 of file GlobalLinSysXxtStaticCond.cpp.

    : 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;
}

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.

~GlobalLinSysXxtStaticCond()

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

override

Definition at line 121 of file GlobalLinSysXxtStaticCond.cpp.

{
}

Member Function Documentation

create()

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

inlinestatic

Creates an instance of this class.

Definition at line 60 of file GlobalLinSysXxtStaticCond.h.

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

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

v_AssembleSchurComplement()

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

overrideprotectedvirtual

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 130 of file GlobalLinSysXxtStaticCond.cpp.

{
    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()->GetRowComm();
    m_crsData = Xxt::Init(nLocal, vId, m_Ai, m_Aj, m_Ar, vComm);
    if (m_verbose)
    {
        Xxt::nektar_crs_stats(m_crsData);
    }
}

References Xxt::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, Nektar::MultiRegions::GlobalLinSys::m_verbose, and Xxt::nektar_crs_stats().

v_Recurse()

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

overrideprotectedvirtual

Implements Nektar::MultiRegions::GlobalLinSysStaticCond.

Definition at line 213 of file GlobalLinSysXxtStaticCond.cpp.

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

References Nektar::MemoryManager< DataType >::AllocateSharedPtr().

v_SolveLinearSystem()

void Nektar::MultiRegions::GlobalLinSysXxtStaticCond::v_SolveLinearSystem ( const int  pNumRows, const Array< OneD, const NekDouble > &  pInput, Array< OneD, NekDouble > &  pOutput, const AssemblyMapSharedPtr &  locToGloMap, const int  pNumDir  )

overrideprivatevirtual

Solve the linear system for given input and output vectors.

Implements Nektar::MultiRegions::GlobalLinSys.

Definition at line 228 of file GlobalLinSysXxtStaticCond.cpp.

{
    int nLocal = pLocToGloMap->GetLocalToGlobalBndSign().size();
    Vmath::Zero(nLocal, pOutput, 1);
 
    if (pLocToGloMap->GetSignChange())
    {
        Array<OneD, NekDouble> vlocal(nLocal);
        Vmath::Vmul(nLocal, pLocToGloMap->GetLocalToGlobalBndSign(), 1, pInput,
                    1, vlocal, 1);
 
        Xxt::Solve(pOutput, m_crsData, vlocal);
 
        Vmath::Vmul(nLocal, pLocToGloMap->GetLocalToGlobalBndSign(), 1, pOutput,
                    1, pOutput, 1);
    }
    else
    {
        Xxt::Solve(pOutput, m_crsData, pInput);
    }
}

References Nektar::MultiRegions::GlobalLinSysXxt::m_crsData, Xxt::Solve(), Vmath::Vmul(), and Vmath::Zero().

Member Data Documentation

className

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 73 of file GlobalLinSysXxtStaticCond.h.

className2

string Nektar::MultiRegions::GlobalLinSysXxtStaticCond::className2

static

Initial value:

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

Definition at line 74 of file GlobalLinSysXxtStaticCond.h.