dealii Namespace Reference

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template<typename Range , typename Domain , typename Payload = internal::LinearOperatorImplementation::EmptyPayload>
LinearOperator< Range, Domain, Payload >	projection_operator (const Range &range_exemplar, const std::vector< std::reference_wrapper< const Domain >> &local_basis, const Domain *domain_exemplar=nullptr, const Payload &payload=Payload())
	Construct a LinearOperator object that projects a vector onto a basis. More...

Function Documentation

projection_operator()

template<typename Range , typename Domain , typename Payload = internal::LinearOperatorImplementation::EmptyPayload>

LinearOperator<Range, Domain, Payload> dealii::projection_operator	(	const Range &	range_exemplar,
		const std::vector< std::reference_wrapper< const Domain >> &	local_basis,
		const Domain *	domain_exemplar = nullptr,
		const Payload &	payload = Payload()
	)

Construct a LinearOperator object that projects a vector onto a basis.

This function can be used to perform model order reduction, i.e. to project a large dimensional vector onto a smaller dimensional subspace. A typical usage of this class is the following:

// Build a reduced vector space, i.e., a VectorType (either serial or
// parallel) that is an element of the Range space of the LinearOperator
VectorType exemplar_range(...);
 
// Initialize a vector of references to the locally owned basis vectors
// onto which we want to project.
std::vector<std::reference_wrapper<VectorType>> basis(...);
 
P = projection_operator(exemplar_range, basis);
Pt = transpose_operator(P);
 
// Project a vector onto the reduced space
VectorType elements = P * v;
 
// If the basis was orthogonal, then we could compute an orthogonal
// projection of v onto the subspace identified by the basis as
VectorType  v_reduced = Pt * v;
 
// The above could also be achieved with the following:
VectorType  v_reduced = (Pt*P) * v;
 
// If we want to project an operator A onto the reduced space, we could do
// the following:
auto A_reduced = Pt*A*P;

Parameters

range_exemplar	An exmeplar vector of the range space. We'll make a few copies of this vector to allow the operator to be used with intermediate storage.
local_basis	A vector of references to the locally owned basis vectors. These vectors must be ordered according to the IndexSet Range::locally_owned_elements() of the range space.
domain_exemplar	If used in parallel, it may happen that some processes do not own any index of the Range space. In this case, you need to provide a pointer to a Domain vector to be used as an exemplar vector.

Returns

LinearOperator<Range, Domain, Payload>

Definition at line 77 of file projection_operator.h.

References VectorOperation::add, Assert, AssertDimension, StandardExceptions::ExcMessage(), and TrilinosWrappers::linear_operator().

Referenced by PDEs::Serial::ReducedLagrange< dim, spacedim >::solve().