A global linear system. More...

#include <GlobalLinSysDirect.h>

Inheritance diagram for Nektar::MultiRegions::GlobalLinSysDirect:

Collaboration diagram for Nektar::MultiRegions::GlobalLinSysDirect:

Public Member Functions
	GlobalLinSysDirect (const GlobalLinSysKey &pKey, const boost::weak_ptr< ExpList > &pExp, const boost::shared_ptr< AssemblyMap > &pLocToGloMap)
	Constructor for full direct matrix solve. More...

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. More...

virtual	~GlobalLinSys ()

const GlobalLinSysKey &	GetKey (void) const
	Returns the key associated with the system. More...

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. More...

boost::shared_ptr< GlobalLinSys >	GetSharedThisPtr ()
	Returns a shared pointer to the current object. More...

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. More...

Protected Member Functions
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. More...

Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSys
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 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 Attributes
DNekLinSysSharedPtr	m_linSys
	Basic linear system object. More...

Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSys
const GlobalLinSysKey	m_linSysKey
	Key associated with this linear system. More...

const boost::weak_ptr< ExpList >	m_expList
	Local Matrix System. More...

const std::map< int, RobinBCInfoSharedPtr >	m_robinBCInfo
	Robin boundary info. More...

Detailed Description

A global linear system.

Solves a linear system using direct methods.

Consider a linear system $\boldsymbol{M\hat{u}}_g=\boldsymbol{\hat{f}}$ to be solved, where $\boldsymbol{M}$ is a matrix of type specified by mkey. This function assembles the global system matrix $\boldsymbol{M}$ out of the elemental submatrices $\boldsymbol{M}^e$ . This is equivalent to:

$\boldsymbol{M}=\boldsymbol{\mathcal{A}}^T \underline{\boldsymbol{M}}^e\boldsymbol{\mathcal{A}}.$

where the matrix $\boldsymbol{\mathcal{A}}$ is a sparse permutation matrix of size $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ . However, due to the size and sparsity of the matrix $\boldsymbol{\mathcal{A}}$ , it is more efficient to assemble the global matrix using the mapping array map $[e][i]$ contained in the input argument locToGloMap. The global assembly is then evaluated as:

$\boldsymbol{M}\left[\mathrm{\texttt{map}}[e][i]\right] \left[\mathrm{\texttt{map}}[e][j]\right] =\mathrm{\texttt{sign}}[e][i]\cdot \mathrm{\texttt{sign}}[e][j] \cdot\boldsymbol{M}^e[i][j]$

where the values sign $[e][i]$ ensure the correct connectivity.

Solves a linear system using single- or multi-level static condensation.

Definition at line 49 of file GlobalLinSysDirect.h.

Constructor & Destructor Documentation

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.

Definition at line 54 of file GlobalLinSysDirect.cpp.

                 : GlobalLinSys(pKey, pExp, pLocToGloMap)
         {
         }

Nektar::MultiRegions::GlobalLinSysDirect::~GlobalLinSysDirect ( )

virtual

Definition at line 63 of file GlobalLinSysDirect.cpp.

64 {

65 }

Member Function Documentation

void Nektar::MultiRegions::GlobalLinSysDirect::v_SolveLinearSystem	(	const int	pNumRows,
		const Array< OneD, const NekDouble > &	pInput,
		Array< OneD, NekDouble > &	pOutput,
		const AssemblyMapSharedPtr &	locToGloMap,
		const int	pNumDir = `0`
	)

protectedvirtual

Solve the linear system for given input and output vectors.

Implements Nektar::MultiRegions::GlobalLinSys.

Definition at line 68 of file GlobalLinSysDirect.cpp.

References Nektar::eWrapper, and m_linSys.

         {
             const int nHomDofs = pNumRows - pNumDir;
 
             DNekVec Vin (nHomDofs, pInput  + pNumDir);
             DNekVec Vout(nHomDofs, pOutput + pNumDir, eWrapper);
 
             m_linSys->Solve(Vin, Vout);
         }

Member Data Documentation

DNekLinSysSharedPtr Nektar::MultiRegions::GlobalLinSysDirect::m_linSys

protected

Basic linear system object.

Definition at line 61 of file GlobalLinSysDirect.h.

Referenced by Nektar::MultiRegions::GlobalLinSysDirectFull::AssembleFullMatrix(), Nektar::MultiRegions::GlobalLinSysDirectStaticCond::v_AssembleSchurComplement(), and v_SolveLinearSystem().

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation