HArDCore2D::Stokes Struct Reference

Class for Stokes model. More...

#include <hho-stokes.hpp>

Public Types
typedef Eigen::SparseMatrix< double >	SystemMatrixType
typedef std::function< VectorRd(const VectorRd &)>	MomentumForcingTermType
typedef std::function< double(const VectorRd &)>	CompressibilityForcingTermType
typedef std::function< VectorRd(const VectorRd &)>	VelocityType
typedef std::function< MatrixRd(const VectorRd &)>	VelocityGradientType
typedef std::function< double(const VectorRd &)>	PressureType
typedef std::function< VectorRd(const VectorRd &)>	PressureGradientType
typedef IntegralWeight	ViscosityType
typedef Eigen::SparseMatrix< double >	SystemMatrixType
typedef std::function< VectorRd(const VectorRd &)>	MomentumForcingTermType
typedef std::function< double(const VectorRd &)>	CompressibilityForcingTermType
typedef std::function< VectorRd(const VectorRd &)>	VelocityType
typedef std::function< MatrixRd(const VectorRd &)>	VelocityGradientType
typedef std::function< double(const VectorRd &)>	PressureType
typedef std::function< VectorRd(const VectorRd &)>	PressureGradientType
typedef IntegralWeight	ViscosityType

Public Member Functions
	Stokes (const VHHOSpace &vhho_space, const GlobalDOFSpace &p_space, const BoundaryConditions &BC, bool use_threads, std::ostream &output=std::cout)
	Constructor.
void	assembleLinearSystem (const MomentumForcingTermType &f, const CompressibilityForcingTermType &g, const ViscosityType &mu, const VelocityType &u, Eigen::VectorXd &UDir)
	Assemble the global system
size_t	nloc_sc_u () const
	Returns the local number of velocity statically condensed DOFs.
size_t	nloc_sc_p () const
	Returns the local number of pressure statically condensed DOFs.
size_t	numSCDOFs_u () const
	Returns the number of velocity statically condensed DOFs.
size_t	numSCDOFs_p () const
	Returns the number of pressure statically condensed DOFs.
size_t	numSCDOFs () const
	Returns the number of statically condensed DOFs.
size_t	numDirDOFs () const
	Returns the number of Dirichlet DOFs.
size_t	dimVelocity () const
	Returns the dimension of velocity space.
size_t	dimPressure () const
	Returns the dimension of pressure space.
size_t	numNonSCDOFs () const
	Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.
size_t	sizeSystem () const
	Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.
const VHHOSpace &	vhhospace () const
	Returns the velocity space.
const GlobalDOFSpace &	pspace () const
	Returns the pressure space.
const Mesh &	mesh () const
	Returns the mesh.
const SystemMatrixType &	systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	systemMatrix ()
	Returns the linear system matrix.
const Eigen::VectorXd &	systemVector () const
	Returns the linear system right-hand side vector.
Eigen::VectorXd &	systemVector ()
	Returns the linear system right-hand side vector.
const double &	stabilizationParameter () const
	Returns the stabilization parameter (scaling)
double &	stabilizationParameter ()
	Returns the stabilization parameter.
const SystemMatrixType &	scMatrix () const
	Returns the static condensation recovery operator.
Eigen::VectorXd &	scVector ()
	Returns the static condensation rhs.
Eigen::VectorXd	interpolate (const VelocityType &u, const PressureType &p, const int doe_cell=-1, const int doe_face=-1) const
	Interpolates velocity and pressure.
std::vector< double >	computeEnergyNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete energy norm of a family of vectors representing the dofs.
	Stokes (const VHHOSpace &vhho_space, const GlobalDOFSpace &p_space, const BoundaryConditions &BC, bool use_threads, std::ostream &output=std::cout)
	Constructor.
void	assembleLinearSystem (const MomentumForcingTermType &f, const CompressibilityForcingTermType &g, const ViscosityType &mu, const VelocityType &u, Eigen::VectorXd &UDir, Eigen::VectorXd &u0, double &time_step)
	Assemble the global system
size_t	nloc_sc_u () const
	Returns the local number of velocity statically condensed DOFs.
size_t	nloc_sc_p () const
	Returns the local number of pressure statically condensed DOFs.
size_t	numSCDOFs_u () const
	Returns the number of velocity statically condensed DOFs.
size_t	numSCDOFs_p () const
	Returns the number of pressure statically condensed DOFs.
size_t	numSCDOFs () const
	Returns the number of statically condensed DOFs.
size_t	numDirDOFs () const
	Returns the number of Dirichlet DOFs.
size_t	dimVelocity () const
	Returns the dimension of velocity space.
size_t	dimPressure () const
	Returns the dimension of pressure space.
size_t	numNonSCDOFs () const
	Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.
size_t	sizeSystem () const
	Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.
const VHHOSpace &	vhhospace () const
	Returns the velocity space.
const GlobalDOFSpace &	pspace () const
	Returns the pressure space.
const Mesh &	mesh () const
	Returns the mesh.
const SystemMatrixType &	systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	systemMatrix ()
	Returns the linear system matrix.
const Eigen::VectorXd &	systemVector () const
	Returns the linear system right-hand side vector.
Eigen::VectorXd &	systemVector ()
	Returns the linear system right-hand side vector.
const double &	stabilizationParameter () const
	Returns the stabilization parameter (scaling)
double &	stabilizationParameter ()
	Returns the stabilization parameter.
const SystemMatrixType &	scMatrix () const
	Returns the static condensation recovery operator.
Eigen::VectorXd &	scVector ()
	Returns the static condensation rhs.
Eigen::VectorXd	interpolate (const VelocityType &u, const PressureType &p, const int doe_cell=-1, const int doe_face=-1) const
	Interpolates velocity and pressure.
std::vector< double >	computeEnergyNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete energy norm of a family of vectors representing the dofs.
Eigen::VectorXd	pressureVertexValues (const Eigen::VectorXd &p) const
	Create vertex values for the pressure (from the element values), for plotting.

Detailed Description

Class for Stokes model.

The global unknowns are in the following order:

• Dirichlets dofs of the velocity (Dirichlet faces must be numbered first in the mesh)
• Face and then element unknowns of the velocity
• Element unknowns of the pressure
• Lagrange multiplier The statically condenseds dofs for the velocity are the element unknowns of the velocity, and all dofs but the first one in each element for the pressure.

Member Typedef Documentation

CompressibilityForcingTermType [1/2]

typedef std::function<double(const VectorRd &)> HArDCore2D::Stokes::CompressibilityForcingTermType

CompressibilityForcingTermType [2/2]

typedef std::function<double(const VectorRd &)> HArDCore2D::Stokes::CompressibilityForcingTermType

MomentumForcingTermType [1/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::MomentumForcingTermType

MomentumForcingTermType [2/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::MomentumForcingTermType

PressureGradientType [1/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::PressureGradientType

PressureGradientType [2/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::PressureGradientType

PressureType [1/2]

typedef std::function<double(const VectorRd &)> HArDCore2D::Stokes::PressureType

PressureType [2/2]

typedef std::function<double(const VectorRd &)> HArDCore2D::Stokes::PressureType

SystemMatrixType [1/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::Stokes::SystemMatrixType

SystemMatrixType [2/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::Stokes::SystemMatrixType

VelocityGradientType [1/2]

typedef std::function<MatrixRd(const VectorRd &)> HArDCore2D::Stokes::VelocityGradientType

VelocityGradientType [2/2]

typedef std::function<MatrixRd(const VectorRd &)> HArDCore2D::Stokes::VelocityGradientType

VelocityType [1/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::VelocityType

VelocityType [2/2]

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::Stokes::VelocityType

ViscosityType [1/2]

typedef IntegralWeight HArDCore2D::Stokes::ViscosityType

ViscosityType [2/2]

typedef IntegralWeight HArDCore2D::Stokes::ViscosityType

Constructor & Destructor Documentation

Stokes() [1/2]

Stokes::Stokes	(	const VHHOSpace &	vhho_space,
		const GlobalDOFSpace &	p_space,
		const BoundaryConditions &	BC,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

vhho_space	Velocity space and operators
p_space	Space for the pressure
BC	Boundary conditions
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

Stokes() [2/2]

HArDCore2D::Stokes::Stokes	(	const VHHOSpace &	vhho_space,
		const GlobalDOFSpace &	p_space,
		const BoundaryConditions &	BC,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

vhho_space	Velocity space and operators
p_space	Space for the pressure
BC	Boundary conditions
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

Member Function Documentation

assembleLinearSystem() [1/2]

void Stokes::assembleLinearSystem	(	const MomentumForcingTermType &	f,
		const CompressibilityForcingTermType &	g,
		const ViscosityType &	mu,
		const VelocityType &	u,
		Eigen::VectorXd &	UDir
	)

Assemble the global system

Parameters

f	Forcing term
g	Forcing term for the divergence equation
mu	Viscosity
u	Exact solution for boundary condition
UDir	Vector filled in by Dirichlets BCs

assembleLinearSystem() [2/2]

void Stokes::assembleLinearSystem	(	const MomentumForcingTermType &	f,
		const CompressibilityForcingTermType &	g,
		const ViscosityType &	mu,
		const VelocityType &	u,
		Eigen::VectorXd &	UDir,
		Eigen::VectorXd &	u0,
		double &	time_step
	)

Assemble the global system

Parameters

f	Forcing term
g	Forcing term for the divergence equation
mu	Viscosity
u	Exact solution for boundary condition
UDir	Vector filled in by Dirichlets BCs

computeEnergyNorms() [1/2]

std::vector< double > Stokes::computeEnergyNorms

(

const std::vector< Eigen::VectorXd > &

list_dofs

)

const

Compute the discrete energy norm of a family of vectors representing the dofs.

Parameters

list_dofs

The list of vectors representing the dofs

computeEnergyNorms() [2/2]

std::vector< double > HArDCore2D::Stokes::computeEnergyNorms

(

const std::vector< Eigen::VectorXd > &

list_dofs

)

const

Compute the discrete energy norm of a family of vectors representing the dofs.

Parameters

list_dofs

The list of vectors representing the dofs

dimPressure() [1/2]

size_t HArDCore2D::Stokes::dimPressure ( ) const

inline

Returns the dimension of pressure space.

dimPressure() [2/2]

size_t HArDCore2D::Stokes::dimPressure ( ) const

inline

Returns the dimension of pressure space.

dimVelocity() [1/2]

size_t HArDCore2D::Stokes::dimVelocity ( ) const

inline

Returns the dimension of velocity space.

dimVelocity() [2/2]

size_t HArDCore2D::Stokes::dimVelocity ( ) const

inline

Returns the dimension of velocity space.

interpolate() [1/2]

Eigen::VectorXd Stokes::interpolate	(	const VelocityType &	u,
		const PressureType &	p,
		const int	doe_cell = -1,
		const int	doe_face = -1
	)		const

Interpolates velocity and pressure.

Parameters

u	Continuous velocity to interpolate
p	Continuous pressure to interpolate
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

interpolate() [2/2]

Eigen::VectorXd HArDCore2D::Stokes::interpolate	(	const VelocityType &	u,
		const PressureType &	p,
		const int	doe_cell = -1,
		const int	doe_face = -1
	)		const

Interpolates velocity and pressure.

Parameters

u	Continuous velocity to interpolate
p	Continuous pressure to interpolate
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

mesh() [1/2]

const Mesh & HArDCore2D::Stokes::mesh ( ) const

inline

Returns the mesh.

mesh() [2/2]

const Mesh & HArDCore2D::Stokes::mesh ( ) const

inline

Returns the mesh.

nloc_sc_p() [1/2]

size_t HArDCore2D::Stokes::nloc_sc_p ( ) const

inline

Returns the local number of pressure statically condensed DOFs.

nloc_sc_p() [2/2]

size_t HArDCore2D::Stokes::nloc_sc_p ( ) const

inline

Returns the local number of pressure statically condensed DOFs.

nloc_sc_u() [1/2]

size_t HArDCore2D::Stokes::nloc_sc_u ( ) const

inline

Returns the local number of velocity statically condensed DOFs.

nloc_sc_u() [2/2]

size_t HArDCore2D::Stokes::nloc_sc_u ( ) const

inline

Returns the local number of velocity statically condensed DOFs.

numDirDOFs() [1/2]

size_t HArDCore2D::Stokes::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

numDirDOFs() [2/2]

size_t HArDCore2D::Stokes::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

numNonSCDOFs() [1/2]

size_t HArDCore2D::Stokes::numNonSCDOFs ( ) const

inline

Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.

numNonSCDOFs() [2/2]

size_t HArDCore2D::Stokes::numNonSCDOFs ( ) const

inline

Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.

numSCDOFs() [1/2]

size_t HArDCore2D::Stokes::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs.

numSCDOFs() [2/2]

size_t HArDCore2D::Stokes::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs.

numSCDOFs_p() [1/2]

size_t HArDCore2D::Stokes::numSCDOFs_p ( ) const

inline

Returns the number of pressure statically condensed DOFs.

numSCDOFs_p() [2/2]

size_t HArDCore2D::Stokes::numSCDOFs_p ( ) const

inline

Returns the number of pressure statically condensed DOFs.

numSCDOFs_u() [1/2]

size_t HArDCore2D::Stokes::numSCDOFs_u ( ) const

inline

Returns the number of velocity statically condensed DOFs.

numSCDOFs_u() [2/2]

size_t HArDCore2D::Stokes::numSCDOFs_u ( ) const

inline

Returns the number of velocity statically condensed DOFs.

pressureVertexValues()

Eigen::VectorXd Stokes::pressureVertexValues

(

const Eigen::VectorXd &

p

)

const

Create vertex values for the pressure (from the element values), for plotting.

Parameters

p	Vector of pressure DOFs

pspace() [1/2]

const GlobalDOFSpace & HArDCore2D::Stokes::pspace ( ) const

inline

Returns the pressure space.

pspace() [2/2]

const GlobalDOFSpace & HArDCore2D::Stokes::pspace ( ) const

inline

Returns the pressure space.

scMatrix() [1/2]

const SystemMatrixType & HArDCore2D::Stokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scMatrix() [2/2]

const SystemMatrixType & HArDCore2D::Stokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scVector() [1/2]

Eigen::VectorXd & HArDCore2D::Stokes::scVector ( )

inline

Returns the static condensation rhs.

scVector() [2/2]

Eigen::VectorXd & HArDCore2D::Stokes::scVector ( )

inline

Returns the static condensation rhs.

sizeSystem() [1/2]

size_t HArDCore2D::Stokes::sizeSystem ( ) const

inline

Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.

sizeSystem() [2/2]

size_t HArDCore2D::Stokes::sizeSystem ( ) const

inline

Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.

stabilizationParameter() [1/4]

double & HArDCore2D::Stokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [2/4]

double & HArDCore2D::Stokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [3/4]

const double & HArDCore2D::Stokes::stabilizationParameter ( ) const

inline

Returns the stabilization parameter (scaling)

stabilizationParameter() [4/4]

const double & HArDCore2D::Stokes::stabilizationParameter ( ) const

inline

Returns the stabilization parameter (scaling)

systemMatrix() [1/4]

SystemMatrixType & HArDCore2D::Stokes::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [2/4]

SystemMatrixType & HArDCore2D::Stokes::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [3/4]

const SystemMatrixType & HArDCore2D::Stokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemMatrix() [4/4]

const SystemMatrixType & HArDCore2D::Stokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemVector() [1/4]

Eigen::VectorXd & HArDCore2D::Stokes::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [2/4]

Eigen::VectorXd & HArDCore2D::Stokes::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [3/4]

const Eigen::VectorXd & HArDCore2D::Stokes::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

systemVector() [4/4]

const Eigen::VectorXd & HArDCore2D::Stokes::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

vhhospace() [1/2]

const VHHOSpace & HArDCore2D::Stokes::vhhospace ( ) const

inline

Returns the velocity space.

vhhospace() [2/2]

const VHHOSpace & HArDCore2D::Stokes::vhhospace ( ) const

inline

Returns the velocity space.

---

The documentation for this struct was generated from the following files:

• Schemes/HHO-ns/hho-stokes.hpp
• Schemes/HHO-ns/hho-ustokes.hpp
• Schemes/HHO-ns/hho-stokes.cpp
• Schemes/HHO-ns/hho-ustokes.cpp