StokesFlowPreconditionerAssembler< DIM > Class Template Reference

#include <StokesFlowPreconditionerAssembler.hpp>

Collaboration diagram for StokesFlowPreconditionerAssembler< DIM >:

Public Member Functions
	StokesFlowPreconditionerAssembler (AbstractTetrahedralMesh< DIM, DIM > pMesh, StokesFlowProblemDefinition< DIM > pProblemDefinition)
Private Member Functions
c_matrix< double, PRESSURE_BLOCK_SIZE_ELEMENTAL, PRESSURE_BLOCK_SIZE_ELEMENTAL >	ComputePressurePressureMatrixTerm (c_vector< double, NUM_VERTICES_PER_ELEMENT > &rLinearPhi, c_matrix< double, DIM, NUM_VERTICES_PER_ELEMENT > &rGradLinearPhi, c_vector< double, DIM > &rX, Element< DIM, DIM > *pElement)
Static Private Attributes
static const unsigned	NUM_VERTICES_PER_ELEMENT = DIM+1
static const unsigned	PRESSURE_BLOCK_SIZE_ELEMENTAL = NUM_VERTICES_PER_ELEMENT

Detailed Description

template<unsigned DIM>
class StokesFlowPreconditionerAssembler< DIM >

Assembler for setting up (volume-integral parts of) the preconditioner matrix used in the FEM solver Stokes' Flow.

The system matrix has the block form (except see comment below) [A B] [B^T 0] In contrast, the preconditioner is: [A B] [B^T M]

The class therefore just needs to inherit from StokesFlowAssembler, which will assemble the A,B,B^T terms, and it just has to overload the pressure-pressure block method.

NOTE: The elemental matrix and vector is as above. The full matrix and vector uses a completely different ordering: for parallelisation reasons the pressure variables are interleaved with the spatial variables and dummy pressure variables are used for internal nodes. For example, in 2d, the ordering is [U1 V1 P1 , .. , Un Vn, Pn] where n is the total number of nodes.

Definition at line 65 of file StokesFlowPreconditionerAssembler.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>

StokesFlowPreconditionerAssembler< DIM >::StokesFlowPreconditionerAssembler	(	AbstractTetrahedralMesh< DIM, DIM > *	pMesh,
		StokesFlowProblemDefinition< DIM > *	pProblemDefinition
	)			`[inline]`

Constructor

Parameters:

	pMesh	mesh
	pProblemDefinition	problem definition

Definition at line 81 of file StokesFlowPreconditionerAssembler.hpp.

Referenced by StokesFlowPreconditionerAssembler< DIM >::ComputePressurePressureMatrixTerm().

Member Function Documentation

template<unsigned DIM>

c_matrix<double,PRESSURE_BLOCK_SIZE_ELEMENTAL,PRESSURE_BLOCK_SIZE_ELEMENTAL> StokesFlowPreconditionerAssembler< DIM >::ComputePressurePressureMatrixTerm	(	c_vector< double, NUM_VERTICES_PER_ELEMENT > &	rLinearPhi,
		c_matrix< double, DIM, NUM_VERTICES_PER_ELEMENT > &	rGradLinearPhi,
		c_vector< double, DIM > &	rX,
		Element< DIM, DIM > *	pElement
	)			`[inline, private, virtual]`

For a continuum mechanics problem in mixed form (displacement-pressure or velocity-pressure), the matrix has the form (except see comments about ordering above) [A B1] [B2^T C ] The function is related to the pressure-pressure block, i.e. C

Returns:: C=M, the mass matrix.

Parameters:

	rLinearPhi	All the linear basis functions on this element, evaluated at the current quad point
	rGradLinearPhi	Gradients of all the linear basis functions on this element, evaluated at the current quad point
	rX	Current location (physical position)
	pElement	Current element