#include <StokesFlowAssembler.hpp>

Inheritance diagram for StokesFlowAssembler< DIM >:

Collaboration diagram for StokesFlowAssembler< DIM >:

Public Member Functions
	StokesFlowAssembler (AbstractTetrahedralMesh< DIM, DIM > pMesh, StokesFlowProblemDefinition< DIM > pProblemDefinition)

Public Member Functions inherited from AbstractContinuumMechanicsAssembler< DIM, true, true >
	AbstractContinuumMechanicsAssembler (AbstractTetrahedralMesh< DIM, DIM > *pMesh)

virtual	~AbstractContinuumMechanicsAssembler ()

Public Member Functions inherited from AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >
	AbstractFeAssemblerInterface ()

void	SetMatrixToAssemble (Mat &rMatToAssemble, bool zeroMatrixBeforeAssembly=true)

void	SetVectorToAssemble (Vec &rVecToAssemble, bool zeroVectorBeforeAssembly)

void	Assemble ()

void	AssembleMatrix ()

void	AssembleVector ()

virtual	~AbstractFeAssemblerInterface ()

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

Additional Inherited Members
Protected Member Functions inherited from AbstractContinuumMechanicsAssembler< DIM, true, true >
void	DoAssemble ()

virtual 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)

virtual c_vector< double, PRESSURE_BLOCK_SIZE_ELEMENTAL >	ComputePressureVectorTerm (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)

void	AssembleOnElement (Element< DIM, DIM > &rElement, c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &rAElem, c_vector< double, STENCIL_SIZE > &rBElem)

Protected Attributes inherited from AbstractContinuumMechanicsAssembler< DIM, true, true >
AbstractTetrahedralMesh< DIM, DIM > *	mpMesh

GaussianQuadratureRule< DIM > *	mpQuadRule

Protected Attributes inherited from AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >
Vec	mVectorToAssemble

Mat	mMatrixToAssemble

bool	mAssembleMatrix

bool	mAssembleVector

bool	mZeroMatrixBeforeAssembly

bool	mZeroVectorBeforeAssembly

PetscInt	mOwnershipRangeLo

PetscInt	mOwnershipRangeHi

Static Protected Attributes inherited from AbstractContinuumMechanicsAssembler< DIM, true, true >
static const bool	BLOCK_SYMMETRIC_MATRIX

static const unsigned	NUM_VERTICES_PER_ELEMENT

static const unsigned	NUM_NODES_PER_ELEMENT

static const unsigned	SPATIAL_BLOCK_SIZE_ELEMENTAL

static const unsigned	PRESSURE_BLOCK_SIZE_ELEMENTAL

static const unsigned	STENCIL_SIZE

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 251 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
	)

inlineprivatevirtual

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 168 of file StokesFlowAssembler.hpp.

References StokesFlowAssembler< DIM >::NUM_VERTICES_PER_ELEMENT, StokesFlowAssembler< DIM >::PRESSURE_BLOCK_SIZE_ELEMENTAL, and StokesFlowAssembler< DIM >::SPATIAL_BLOCK_SIZE_ELEMENTAL.

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
	)

inlineprivatevirtual

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 113 of file StokesFlowAssembler.hpp.

References StokesFlowProblemDefinition< DIM >::GetViscosity(), and StokesFlowAssembler< DIM >::SPATIAL_BLOCK_SIZE_ELEMENTAL.

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
	)

inlineprivatevirtual

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

Implements AbstractContinuumMechanicsAssembler< DIM, true, true >.

Definition at line 217 of file StokesFlowAssembler.hpp.

References ContinuumMechanicsProblemDefinition< DIM >::GetBodyForce(), 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 86 of file StokesFlowAssembler.hpp.

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 95 of file StokesFlowAssembler.hpp.

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2

staticprivate

Number of nodes per element.

Definition at line 71 of file StokesFlowAssembler.hpp.

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::NUM_VERTICES_PER_ELEMENT = DIM+1

staticprivate

Number of vertices per element

Definition at line 68 of file StokesFlowAssembler.hpp.

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

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::PRESSURE_BLOCK_SIZE_ELEMENTAL = NUM_VERTICES_PER_ELEMENT

staticprivate

Size of the pressure block, per element, equal num_vertices times 1 (as p solved for at each vertex.

Definition at line 83 of file StokesFlowAssembler.hpp.

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

template<unsigned DIM>

const unsigned StokesFlowAssembler< DIM >::SPATIAL_BLOCK_SIZE_ELEMENTAL = DIM*NUM_NODES_PER_ELEMENT

staticprivate

Size of the spatial block, per element, equal num_nodes times DIM (as say in 2d (u,v) solved for at each node

Definition at line 77 of file StokesFlowAssembler.hpp.

Referenced by StokesFlowAssembler< DIM >::ComputeSpatialPressureMatrixTerm(), StokesFlowAssembler< DIM >::ComputeSpatialSpatialMatrixTerm(), and StokesFlowAssembler< DIM >::ComputeSpatialVectorTerm().

The documentation for this class was generated from the following file:

continuum_mechanics/src/solver/StokesFlowAssembler.hpp

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Friends

Additional Inherited Members

Detailed Description

template<unsigned DIM> class StokesFlowAssembler< DIM >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<unsigned DIM>
class StokesFlowAssembler< DIM >