projects::ipdg_stokes::post_processing Namespace Reference

Classes
class	MeshFunctionVelocity
	A MeshFunction returning the velocity computed from the basis function coefficients of a vector potential. More...

Functions
template<typename T , typename SCALAR_COEFF >
	MeshFunctionVelocity (std::shared_ptr< T >, const Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 > &) -> MeshFunctionVelocity< typename T::Scalar, SCALAR_COEFF >
template<typename MF , typename QR_SELECTOR >
double	L2norm (const std::shared_ptr< const lf::mesh::Mesh > &mesh, const MF &f, const QR_SELECTOR &qr_selector)
	Compute the \(L^2\)-norm of a vector valued function over a mesh. More...
template<typename MF_F , typename MF_GRAD , typename QR_SELECTOR >
double	DGnorm (const std::shared_ptr< const lf::mesh::Mesh > &mesh, const MF_F &f, const MF_GRAD &f_grad, const QR_SELECTOR &qr_selector)
	Compute the DG-norm of a vector valued function over a mesh. More...
lf::mesh::utils::CodimMeshDataSet< double >	extractBasisFunctionCoefficients (const std::shared_ptr< const lf::mesh::Mesh > &mesh, const lf::assemble::DofHandler &dofh, const Eigen::VectorXd &solution)
	Extract the basis function coefficients from the solution vector. More...
lf::mesh::utils::CodimMeshDataSet< Eigen::Vector2d >	extractVelocity (const std::shared_ptr< const lf::mesh::Mesh > &mesh, const lf::assemble::DofHandler &dofh, const Eigen::VectorXd &solution)
	Extract the flow velocity on cells from the solution vector. More...

Function Documentation

DGnorm()

template<typename MF_F , typename MF_GRAD , typename QR_SELECTOR >

double projects::ipdg_stokes::post_processing::DGnorm	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh,
		const MF_F &	f,
		const MF_GRAD &	f_grad,
		const QR_SELECTOR &	qr_selector
	)

Compute the DG-norm of a vector valued function over a mesh.

Template Parameters

MF_F	The type of mesh function to take the norm from
MF_GRAD	The type of the gradient of the mesh function to take the norm from
QR_SELECTOR	The type of the qr_selector parameter

Parameters

mesh	The mesh over which the function is defined
f	The function to take the norm from
f_grad	The gradient of the function to take the norm from
qr_selector	A function giving the quadrature rule to use for a given element

Returns

The DG-norm of the function over the mesh

This functoin computes the following formula

\[ ||f||_{1,h}^2 = \sum_{K\in\mathcal{M}} \int_K\! ||\nabla f(x)||^2 \,\mathrm{d}x + \sum_{e\in\mathcal{E}(\mathcal{M})} \int_e\! \frac{1}{|e|}||\left[\!\left[ f(x) \otimes n \right]\!\right]||^2 \,\mathrm{d}x \]

Definition at line 68 of file norms.h.

References projects::ipdg_stokes::mesh::computeOutwardNormals(), lf::mesh::utils::flagEntitiesOnBoundary(), lf::fe::IntegrateMeshFunction(), lf::mesh::positive, and lf::geometry::Volume().

extractBasisFunctionCoefficients()

lf::mesh::utils::CodimMeshDataSet< double > projects::ipdg_stokes::post_processing::extractBasisFunctionCoefficients	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh,
		const lf::assemble::DofHandler &	dofh,
		const Eigen::VectorXd &	solution
	)

Extract the basis function coefficients from the solution vector.

Parameters

mesh	A shared pointer to the corresponding mesh
dofh	The DOF handler for the used FE space
solution	The solution vector obtained from solving the PDE

Returns

A mesh data set mapping nodes of the mesh to the basis function coefficient associated with them

Definition at line 8 of file solution_to_mesh_data_set.cc.

References lf::assemble::DofHandler::GlobalDofIndices().

extractVelocity()

lf::mesh::utils::CodimMeshDataSet< Eigen::Vector2d > projects::ipdg_stokes::post_processing::extractVelocity	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh,
		const lf::assemble::DofHandler &	dofh,
		const Eigen::VectorXd &	solution
	)

Extract the flow velocity on cells from the solution vector.

Parameters

mesh	A shared pointer to the corresponding mesh
dofh	The DOF handler for the used FE space
solution	The solution vector obtained from solving the PDE

Returns

A mesh data set mapping cells of the mesh to the flow velocity on them

Definition at line 18 of file solution_to_mesh_data_set.cc.

References lf::assemble::DofHandler::GlobalDofIndices(), and lf::uscalfe::FeLagrangeO1Tria< SCALAR >::GradientsReferenceShapeFunctions().

L2norm()

template<typename MF , typename QR_SELECTOR >

double projects::ipdg_stokes::post_processing::L2norm	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh,
		const MF &	f,
		const QR_SELECTOR &	qr_selector
	)

Compute the \(L^2\)-norm of a vector valued function over a mesh.

Template Parameters

MF	The type of mesh function to take the norm from
QR_SELECTOR	The type of the qr_selector parameter

Parameters

mesh	The mesh over which the function is defined
f	The function to take the norm from
qr_selector	A function giving the quadrature rule to use for a given element

Returns

The \(L^2\)-norm of the function over the mesh

This function computes the value of the following formula

\[ ||f||_0^2 = \sum_{K\in\mathcal{M}} \int_K\! ||f(x)||^2 \,\mathrm{d}x \]

Definition at line 40 of file norms.h.

References lf::fe::IntegrateMeshFunction().

MeshFunctionVelocity()

template<typename T , typename SCALAR_COEFF >

projects::ipdg_stokes::post_processing::MeshFunctionVelocity	(	std::shared_ptr< T >	,
		const Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 > &
	)		-> MeshFunctionVelocity< typename T::Scalar, SCALAR_COEFF >