StokesFlowAssembler< DIM > Class Template Reference

#include <StokesFlowAssembler.hpp>

Inherits AbstractContinuumMechanicsAssembler< DIM, true, true >.

Inherited by StokesFlowPreconditionerAssembler< DIM >.

Collaboration diagram for StokesFlowAssembler< DIM >:

Public Member Functions
	StokesFlowAssembler (AbstractTetrahedralMesh< DIM, DIM > pMesh, StokesFlowProblemDefinition< DIM > pProblemDefinition)
Private Member Functions
c_matrix< double, SPATIAL_BLOCK_SIZE_ELEMENTAL, SPATIAL_BLOCK_SIZE_ELEMENTAL >	ComputeSpatialSpatialMatrixTerm (c_vector< double, NUM_NODES_PER_ELEMENT > &rQuadPhi, c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &rGradQuadPhi, c_vector< double, DIM > &rX, Element< DIM, DIM > *pElement)
c_matrix< double, SPATIAL_BLOCK_SIZE_ELEMENTAL, PRESSURE_BLOCK_SIZE_ELEMENTAL >	ComputeSpatialPressureMatrixTerm (c_vector< double, NUM_NODES_PER_ELEMENT > &rQuadPhi, c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &rGradQuadPhi, 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)
c_vector< double, SPATIAL_BLOCK_SIZE_ELEMENTAL >	ComputeSpatialVectorTerm (c_vector< double, NUM_NODES_PER_ELEMENT > &rQuadPhi, c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &rGradQuadPhi, c_vector< double, DIM > &rX, Element< DIM, DIM > *pElement)
Private Attributes
StokesFlowProblemDefinition < DIM > *	mpProblemDefinition
double	mScaleFactor
Static Private Attributes
static const unsigned	NUM_VERTICES_PER_ELEMENT = DIM+1
static const unsigned	NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2
static const unsigned	SPATIAL_BLOCK_SIZE_ELEMENTAL = DIM*NUM_NODES_PER_ELEMENT
static const unsigned	PRESSURE_BLOCK_SIZE_ELEMENTAL = NUM_VERTICES_PER_ELEMENT
Friends
class	TestStokesFlowAssembler

Detailed Description

template<unsigned DIM>
class StokesFlowAssembler< DIM >

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

The matrix has the block-form (except see comment below) [A B] [B^T 0] and the vector has the block form (except see comment below) [b] [0]

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 62 of file StokesFlowAssembler.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>

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

Constructor

Parameters:

	pMesh
	pProblemDefinition

Definition at line 228 of file StokesFlowAssembler.hpp.

Member Function Documentation

template<unsigned DIM>

c_matrix<double,SPATIAL_BLOCK_SIZE_ELEMENTAL,PRESSURE_BLOCK_SIZE_ELEMENTAL> StokesFlowAssembler< DIM >::ComputeSpatialPressureMatrixTerm	(	c_vector< double, NUM_NODES_PER_ELEMENT > &	rQuadPhi,
		c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &	rGradQuadPhi,
		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]`

The matrix has the form (except see comments about ordering above) [A B ] [B^T 0 ] The function is related to the spatial-pressure block, ie matrix B.

For the (volume-integral) contribution to B from a given element, this method returns the INTEGRAND in the definition of B.

Parameters:

	rQuadPhi	All the quadratic basis functions on this element, evaluated at the current quad point
	rGradQuadPhi	Gradients of all the quadratic basis functions on this element, evaluated at the current quad point
	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 corresponding to quad point)
	pElement	Current element

Returns:: stencil matrix

Reimplemented from AbstractContinuumMechanicsAssembler< DIM, true, true >.

Definition at line 145 of file StokesFlowAssembler.hpp.

template<unsigned DIM>

c_matrix<double,SPATIAL_BLOCK_SIZE_ELEMENTAL,SPATIAL_BLOCK_SIZE_ELEMENTAL> StokesFlowAssembler< DIM >::ComputeSpatialSpatialMatrixTerm	(	c_vector< double, NUM_NODES_PER_ELEMENT > &	rQuadPhi,
		c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &	rGradQuadPhi,
		c_vector< double, DIM > &	rX,
		Element< DIM, DIM > *	pElement
	)			`[inline, private, virtual]`

The matrix has the form (except see comments about ordering above) [A B ] [B^T 0 ] The function is related to the spatial-spatial block, ie matrix A.

For the (volume-integral) contribution to A from a given element, this method returns the INTEGRAND in the definition of A.

Parameters:

	rQuadPhi	All the quadratic basis functions on this element, evaluated at the current quad point
	rGradQuadPhi	Gradients of all the quadratic basis functions on this element, evaluated at the current quad point
	rX	Current location (physical position corresponding to quad point)
	pElement	Current element

Returns:: stencil matrix

Reimplemented from AbstractContinuumMechanicsAssembler< DIM, true, true >.

Definition at line 90 of file StokesFlowAssembler.hpp.

template<unsigned DIM>

c_vector<double,SPATIAL_BLOCK_SIZE_ELEMENTAL> StokesFlowAssembler< DIM >::ComputeSpatialVectorTerm	(	c_vector< double, NUM_NODES_PER_ELEMENT > &	rQuadPhi,
		c_matrix< double, DIM, NUM_NODES_PER_ELEMENT > &	rGradQuadPhi,
		c_vector< double, DIM > &	rX,
		Element< DIM, DIM > *	pElement
	)			`[inline, private, virtual]`

The matrix has the form (except see comments about ordering above) [A B ] [B^T 0 ] and the vector has the form [b1] [b2] The function is related to the spatial-block in the vector, ie b1.

For the contribution to b1 from a given element, this method should return the INTEGRAND in the definition of b1.

Parameters:

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

Returns:: stencil vector

Reimplemented from AbstractContinuumMechanicsAssembler< DIM, true, true >.

Definition at line 194 of file StokesFlowAssembler.hpp.

References StokesFlowAssembler< DIM >::mpProblemDefinition, StokesFlowAssembler< DIM >::NUM_NODES_PER_ELEMENT, and StokesFlowAssembler< DIM >::SPATIAL_BLOCK_SIZE_ELEMENTAL.

Member Data Documentation

template<unsigned DIM>

StokesFlowProblemDefinition<DIM>* StokesFlowAssembler< DIM >::mpProblemDefinition [private]

Stokes' flow problem definition

Definition at line 63 of file StokesFlowAssembler.hpp.

Referenced by StokesFlowAssembler< DIM >::ComputeSpatialVectorTerm().

template<unsigned DIM>

double StokesFlowAssembler< DIM >::mScaleFactor [private]

This variable is initialised to 1.0 and almost never changed, and is used in the spatial-spatial matrix term. One test (see TestStokesFlowAssembler) sets it to 0.0 before assembling the matrix. Basically, a different weak form USED to be implemented here (corresponding to one kind of Neumann boundary condition), and the matrix for that weak form was compared against exact solutions in this test. mScaleFactor = 0.0 corresponds to old weak form, mScaleFactor = 1 corresponds to new weak form as documented in fem implementations pdf.

Definition at line 72 of file StokesFlowAssembler.hpp.

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2 [static, private]

Number of nodes per element.

Reimplemented from AbstractContinuumMechanicsAssembler< DIM, true, true >.

Definition at line 48 of file StokesFlowAssembler.hpp.

Referenced by StokesFlowAssembler< DIM >::ComputeSpatialVectorTerm().

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::NUM_VERTICES_PER_ELEMENT = DIM+1 [static, private]

Number of vertices per element

Reimplemented from AbstractContinuumMechanicsAssembler< DIM, true, true >.

Reimplemented in StokesFlowPreconditionerAssembler< DIM >.