Element vector provider for Whitney one forms. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/assemble/whitney_one_vector_provider.h>

Public Member Functions
	WhitneyOneVectorProvider (const std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Vector3d &)> &f)
	Constructor. More...

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >	Eval (const lf::mesh::Entity &entity) const
	Compute the element vector for a given triangle off the mesh. More...

bool	isActive (const lf::mesh::Entity &entity) const
	All entities are regarded as active. More...

Private Attributes
const std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Vector3d &)>	f_

Detailed Description

template<typename SCALAR>
class projects::hldo_sphere::assemble::WhitneyOneVectorProvider< SCALAR >

Element vector provider for Whitney one forms.

The linear form is given by

\[ (\mathbf{v}) \mapsto \int\limits_K \mathbf{f} \cdot \mathbf{v} \,\mathrm{d}x, \quad \mathbf{f}, \mathbf{v} \in \mathbf{H}(\text{curl}_{\Gamma}, \partial\mathbf{S}) \]

The element vector provider works in a 3 dimensional world with 2 dimensional triangular cells.

Basis functions are the Whitney 1-forms, surface edge elements for \(v\)

The whitney 1-forms, surface edge elements are associated with edges and defined as

\[ \mathbf{b}_i = s_i (\lambda_i \mathbf{grad}_{\Gamma}(\lambda_{i+1}) - \lambda_{i+1} \mathbf{grad}_{\Gamma}(\lambda_{i})) \]

with \( \lambda_i \) barycentric basis functions and \( s_i \) is a sign of the function based on the relative orientation of the edge in the mesh.

Note: This class complies with the type requirements for the template argument ENTITY_VECTOR_PROVIDER of the function lf::assemble::AssembleVectorLocally().; Only triangular meshes are supported

Definition at line 56 of file whitney_one_vector_provider.h.

Constructor & Destructor Documentation

◆ WhitneyOneVectorProvider()

template<typename SCALAR >

projects::hldo_sphere::assemble::WhitneyOneVectorProvider< SCALAR >::WhitneyOneVectorProvider ( const std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Vector3d &)> & f )

inline

Constructor.

Template Parameters

SCALAR representing the scalar field, on which the codomain is based on

Parameters

f	a tangential vector field functor required to be defined on the mesh

Definition at line 67 of file whitney_one_vector_provider.h.

Member Function Documentation

◆ Eval()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > projects::hldo_sphere::assemble::WhitneyOneVectorProvider< SCALAR >::Eval ( const lf::mesh::Entity & entity ) const

inline

Compute the element vector for a given triangle off the mesh.

Parameters

entity The mesh triangle to compute the element vector for