Cell-Oriented Assembly of R.h.s. Galerkin

Detailed Description

Functions assembleVectorLocally() for setting entries of the vector representing the finite element Galerkin discretization of a linear functional.

Vectors

The functions differ in their arguments, but all are templated with the following types:

• ENTITY_VECTOR_PROVIDER matching the concept EntityVectorProvider
• VECTOR a generic vector type compliant with Eigen::Vector

Also refer to Lecture Document Example 2.7.4.27 and Lecture Document Example 2.7.4.39.

Functions
template<typename VECTOR, EntityVectorProvider ENTITY_VECTOR_PROVIDER>
void	lf::assemble::AssembleVectorLocally (dim_t codim, const DofHandler &dof_handler, ENTITY_VECTOR_PROVIDER &entity_vector_provider, VECTOR &resultvector)
	entity-local assembly of (right-hand-side) vectors from element vectors
template<typename VECTOR, class ENTITY_VECTOR_PROVIDER>
VECTOR	lf::assemble::AssembleVectorLocally (dim_t codim, const DofHandler &dof_handler, ENTITY_VECTOR_PROVIDER &entity_vector_provider)
	entity-local assembly of (right-hand-side) vectors from element vectors

Function Documentation

AssembleVectorLocally() [1/2]

template<typename VECTOR, class ENTITY_VECTOR_PROVIDER>

VECTOR lf::assemble::AssembleVectorLocally	(	dim_t	codim,
		const DofHandler &	dof_handler,
		ENTITY_VECTOR_PROVIDER &	entity_vector_provider )

entity-local assembly of (right-hand-side) vectors from element vectors

Template Parameters

VECTOR	a generic vector type with component access through []
entity_vector_provider	local EntityVectorProvider object (passed as non-const!)

Parameters

codim	co-dimension of entities over which assembly should be carried out
dof_handler	object providing local-to-global dof index mapping, see DofHandler
entity_vector_provider	local EntityVectorProvider object (passed as non-const!)

Returns

assembled vector as an object of a type specified by the VECTOR template argument

See also

AssembleVectorLocally(const DofHandler &dof_handler, ENTITY_VECTOR_PROVIDER &entity_vector_provider, VECTOR &resultvector)

Additional type requirements for VECTOR template argument

VECTOR must supply a setZero method for initialization with zero. All matrix types of Eigen have such a method see Eigen documentation

Definition at line 355 of file assembler.h.

References AssembleVectorLocally(), and lf::assemble::DofHandler::NumDofs().

AssembleVectorLocally() [2/2]

template<typename VECTOR, EntityVectorProvider ENTITY_VECTOR_PROVIDER>

void lf::assemble::AssembleVectorLocally	(	dim_t	codim,
		const DofHandler &	dof_handler,
		ENTITY_VECTOR_PROVIDER &	entity_vector_provider,
		VECTOR &	resultvector )

entity-local assembly of (right-hand-side) vectors from element vectors

Template Parameters

VECTOR	a generic vector type with component access through []
ENTITY_VECTOR_PROVIDER	type for objects computing entity-local vectors, models concept EntityVectorProvider

Parameters

codim	co-dimension of entities over which assembly should be carried out
dof_handler	object providing local-to-global dof index mapping, see DofHandler
entity_vector_provider	local EntityVectorProvider object (passed as non-const!)
resultvector	generic vector for returning the assembled vector

Type requirements for template arguments

• VECTOR must provide a size() method telling its length and read/write access through the [] operator.

Note

Contributions of element vectors are added to the entries of the resultvector argument. This means that resultvector has to be initialized before calling this function!

Example Usage

  // initialize a 2d mesh somehow
  std::shared_ptr<lf::mesh::Mesh> mesh;
 
  // define a EntityVectorProvider which returns the volume for every mesh cell
  struct VolumeEntityVectorProvider {
    bool isActive(const lf::mesh::Entity& e) const { return e.Codim() == 0; }
 
    Eigen::VectorXd Eval(const lf::mesh::Entity& e) const {
      return Eigen::VectorXd::Constant(1, lf::geometry::Volume(*e.Geometry()));
    }
  } entity_vector_provider;
 
  // define a dof handler which assigns a dof to every mesh cell
  lf::assemble::UniformFEDofHandler dofh(
      mesh, {{lf::base::RefEl::kTria(), 1}, {lf::base::RefEl::kQuad(), 1}});
 
  // initialize the output vector:
  Eigen::VectorXd x(dofh.NumDofs());
 
  // assemble the global vector over entities with codim=0:
  lf::assemble::AssembleVectorLocally(0, dofh, entity_vector_provider, x);
 
  // now x[dofh.GlobalDofIndices(e)[0]] will contain the volume of mesh cell e

Definition at line 299 of file assembler.h.

References lf::assemble::DofHandler::GlobalDofIndices(), lf::assemble::DofHandler::Mesh(), and lf::assemble::DofHandler::NumLocalDofs().

Referenced by AssembleVectorLocally().