HHO_fullgradientdiff

Implementation of the HHO scheme with full gradient for variable diffusion equations. More...

Classes
struct	HArDCore3D::FullGradientDiffusion
	Assemble a diffusion problem. More...

Typedefs
typedef Eigen::SparseMatrix< double >	HArDCore3D::FullGradientDiffusion::SystemMatrixType
typedef std::function< double(const VectorRd &)>	HArDCore3D::FullGradientDiffusion::ForcingTermType
typedef std::function< double(const VectorRd &)>	HArDCore3D::FullGradientDiffusion::SolutionType
typedef std::function< VectorRd(const VectorRd &)>	HArDCore3D::FullGradientDiffusion::SolutionGradientType
typedef IntegralWeight	HArDCore3D::FullGradientDiffusion::PermeabilityType

Functions
	HArDCore3D::FullGradientDiffusion::FullGradientDiffusion (const HHOSpace &hho_space, const BoundaryConditions &BC, bool use_threads, std::ostream &output=std::cout)
	Constructor.
void	HArDCore3D::FullGradientDiffusion::assembleLinearSystem (const ForcingTermType &f, const PermeabilityType &kappa, const SolutionType &u, Eigen::VectorXd &UDir)
	Assemble the global system
size_t	HArDCore3D::FullGradientDiffusion::numSCDOFs () const
	Returns the number of statically condensed DOFs (the cell DOFs)
size_t	HArDCore3D::FullGradientDiffusion::numDirDOFs () const
	Returns the number of Dirichlet DOFs.
size_t	HArDCore3D::FullGradientDiffusion::numSkeletalDOFs () const
	Returns the number of DOFs after SC but before eliminating Dirichlet DOFs.
size_t	HArDCore3D::FullGradientDiffusion::sizeSystem () const
	Returns the size of the final system, after application of SC and removal of Dirichlet BCs.
const HHOSpace &	HArDCore3D::FullGradientDiffusion::hhospace () const
	Returns the HHO space.
const Mesh &	HArDCore3D::FullGradientDiffusion::mesh () const
	Returns the mesh.
const SystemMatrixType &	HArDCore3D::FullGradientDiffusion::systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	HArDCore3D::FullGradientDiffusion::systemMatrix ()
	Returns the linear system matrix.
const Eigen::VectorXd &	HArDCore3D::FullGradientDiffusion::systemVector () const
	Returns the linear system right-hand side vector.
Eigen::VectorXd &	HArDCore3D::FullGradientDiffusion::systemVector ()
	Returns the linear system right-hand side vector.
const double &	HArDCore3D::FullGradientDiffusion::stabilizationParameter () const
	Returns the stabilization parameter (scaling)
double &	HArDCore3D::FullGradientDiffusion::stabilizationParameter ()
	Returns the stabilization parameter.
const SystemMatrixType &	HArDCore3D::FullGradientDiffusion::scMatrix () const
	Returns the static condensation recovery operator.
Eigen::VectorXd &	HArDCore3D::FullGradientDiffusion::scVector ()
	Returns the static condensation rhs.
std::vector< double >	HArDCore3D::FullGradientDiffusion::computeEnergyNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete energy norm of a family of vectors representing the dofs.

Variables
static const double	HArDCore3D::PI = boost::math::constants::pi<double>()
static const VectorRd	HArDCore3D::vec_a = VectorRd(1.,2.,3.)
static FullGradientDiffusion::SolutionType	HArDCore3D::linear_u
static FullGradientDiffusion::SolutionGradientType	HArDCore3D::linear_gradu
static FullGradientDiffusion::ForcingTermType	HArDCore3D::linear_f
static FullGradientDiffusion::PermeabilityType	HArDCore3D::linear_kappa = FullGradientDiffusion::PermeabilityType(1.)
static FullGradientDiffusion::SolutionType	HArDCore3D::trigonometric_u
static FullGradientDiffusion::SolutionGradientType	HArDCore3D::trigonometric_gradu
static FullGradientDiffusion::ForcingTermType	HArDCore3D::trigonometric_f
static FullGradientDiffusion::PermeabilityType	HArDCore3D::trigonometric_kappa = FullGradientDiffusion::PermeabilityType(1.)

Detailed Description

Implementation of the HHO scheme with full gradient for variable diffusion equations.

Typedef Documentation

ForcingTermType

typedef std::function<double(const VectorRd &)> HArDCore3D::FullGradientDiffusion::ForcingTermType

PermeabilityType

typedef IntegralWeight HArDCore3D::FullGradientDiffusion::PermeabilityType

SolutionGradientType

typedef std::function<VectorRd(const VectorRd &)> HArDCore3D::FullGradientDiffusion::SolutionGradientType

SolutionType

typedef std::function<double(const VectorRd &)> HArDCore3D::FullGradientDiffusion::SolutionType

SystemMatrixType

typedef Eigen::SparseMatrix<double> HArDCore3D::FullGradientDiffusion::SystemMatrixType

Function Documentation

assembleLinearSystem()

void FullGradientDiffusion::assembleLinearSystem	(	const ForcingTermType &	f,
		const PermeabilityType &	kappa,
		const SolutionType &	u,
		Eigen::VectorXd &	UDir
	)

Assemble the global system

Parameters

f	Forcing term
kappa	Permeability
u	Exact solution for boundary condition
UDir	Vector filled in by Dirichlets BCs

computeEnergyNorms()

std::vector< double > FullGradientDiffusion::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

FullGradientDiffusion()

FullGradientDiffusion::FullGradientDiffusion	(	const HHOSpace &	hho_space,
		const BoundaryConditions &	BC,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

hho_space	HHO space and operators
BC	Boundary conditions
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

hhospace()

const HHOSpace & HArDCore3D::FullGradientDiffusion::hhospace ( ) const

inline

Returns the HHO space.

mesh()

const Mesh & HArDCore3D::FullGradientDiffusion::mesh ( ) const

inline

Returns the mesh.

numDirDOFs()

size_t HArDCore3D::FullGradientDiffusion::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

numSCDOFs()

size_t HArDCore3D::FullGradientDiffusion::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs (the cell DOFs)

numSkeletalDOFs()

size_t HArDCore3D::FullGradientDiffusion::numSkeletalDOFs ( ) const

inline

Returns the number of DOFs after SC but before eliminating Dirichlet DOFs.

scMatrix()

const SystemMatrixType & HArDCore3D::FullGradientDiffusion::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scVector()

Eigen::VectorXd & HArDCore3D::FullGradientDiffusion::scVector ( )

inline

Returns the static condensation rhs.

sizeSystem()

size_t HArDCore3D::FullGradientDiffusion::sizeSystem ( ) const

inline

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

stabilizationParameter() [1/2]

double & HArDCore3D::FullGradientDiffusion::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [2/2]

const double & HArDCore3D::FullGradientDiffusion::stabilizationParameter ( ) const

inline

Returns the stabilization parameter (scaling)

systemMatrix() [1/2]

SystemMatrixType & HArDCore3D::FullGradientDiffusion::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [2/2]

const SystemMatrixType & HArDCore3D::FullGradientDiffusion::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemVector() [1/2]

Eigen::VectorXd & HArDCore3D::FullGradientDiffusion::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [2/2]

const Eigen::VectorXd & HArDCore3D::FullGradientDiffusion::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

Variable Documentation

linear_f

FullGradientDiffusion::ForcingTermType HArDCore3D::linear_f

static

Initial value:

= [](const VectorRd & x) -> double {
                 return 0.;
               }

linear_gradu

FullGradientDiffusion::SolutionGradientType HArDCore3D::linear_gradu

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                     return vec_a;
                   }

linear_kappa

FullGradientDiffusion::PermeabilityType HArDCore3D::linear_kappa = FullGradientDiffusion::PermeabilityType(1.)

static

linear_u

FullGradientDiffusion::SolutionType HArDCore3D::linear_u

static

Initial value:

= [](const VectorRd & x) -> double {
                 return vec_a.dot(x) + 4.;
               }

PI

const double HArDCore3D::PI = boost::math::constants::pi<double>()

static

trigonometric_f

FullGradientDiffusion::ForcingTermType HArDCore3D::trigonometric_f

static

Initial value:

= [](const VectorRd & x) -> double {
                      return 3. * std::pow(PI, 2) * trigonometric_u(x);
                    }

trigonometric_gradu

FullGradientDiffusion::SolutionGradientType HArDCore3D::trigonometric_gradu

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                          return PI * VectorRd(
                                                     cos(PI*x(0)) * sin(PI*x(1)) * sin(PI*x(2)),
                                                     sin(PI*x(0)) * cos(PI*x(1)) * sin(PI*x(2)),
                                                     sin(PI*x(0)) * sin(PI*x(1)) * cos(PI*x(2))
                                                     );
                        }

trigonometric_kappa

FullGradientDiffusion::PermeabilityType HArDCore3D::trigonometric_kappa = FullGradientDiffusion::PermeabilityType(1.)

static

trigonometric_u

FullGradientDiffusion::SolutionType HArDCore3D::trigonometric_u

static

Initial value:

= [](const VectorRd & x) -> double {
                      return sin(PI*x(0)) * sin(PI*x(1)) * sin(PI*x(2));
                    }

vec_a

const VectorRd HArDCore3D::vec_a = VectorRd(1.,2.,3.)

static