A solver for the electric diffusion equation given by \( \nabla \times \nabla \times E + E = f \text{ in } \Omega\) and \( n \times E = 0 \text{ on } \partial \Omega\) using the Nédélec basis functions. More...

#include <FEMMaxwellDiffusionSolver.h>

Inheritance diagram for ippl::FEMMaxwellDiffusionSolver< FieldType >:

Collaboration diagram for ippl::FEMMaxwellDiffusionSolver< FieldType >:

Public Types
using	Base = Maxwell<FieldType, FieldType>
using	MeshType = typename FieldType::Mesh_t
using	PCGSolverAlgorithm_t
using	ElementType
using	QuadratureType = GaussJacobiQuadrature<T, 5, ElementType>
using	NedelecType = NedelecSpace<T, Dim, 1, ElementType, QuadratureType, FieldType>

Public Member Functions
	FEMMaxwellDiffusionSolver ()
	FEMMaxwellDiffusionSolver (FieldType &lhs, FieldType &rhs, const FEMVector< point_t > &rhsVector)
void	setRhs (FieldType &rhs, const FEMVector< point_t > &rhsVector)
void	solve () override
	Solve the equation using finite element methods.
int	getIterationCount ()
T	getResidue () const
Kokkos::View< point_t * >	reconstructToPoints (const Kokkos::View< point_t * > &positions)
	Reconstructs function values at arbitrary points in the mesh.
template<typename F>
T	getL2Error (const F &analytic)
	Given an analytical solution computes the L2 norm error.
virtual void	setSources (FieldType &four_current)
void	setEMFields (FieldType &E, FieldType &B)
void	mergeParameters (const ParameterList &params)

Protected Member Functions
virtual void	setDefaultParameters ()
	Sets the default values for the CG solver. Defaults are: max Iterations = 10, tolerance = 1e-13.

Protected Attributes
PCGSolverAlgorithm_t	pcg_algo_m
	The CG Solver we use.
std::unique_ptr< FEMVector< T > >	rhsVector_m
	FEM represenation of the rhs We use this to store the rhs b of the System Ax = b used in the Galerkin FEM scheme.
std::unique_ptr< FEMVector< T > >	lhsVector_m
	FEM represenation of the solution vector We use this to store the solution x of the System Ax = b used in the Galerkin FEM scheme.
ElementType	refElement_m
	the reference element we have.
QuadratureType	quadrature_m
	The quadrature rule we use.
NedelecType	nedelecSpace_m
	The Nedelec Space object.
ParameterList	params_m
FieldType *	JN_mp
FieldType *	En_mp
FieldType *	Bn_mp

Private Types
using	T = typename FieldType::value_type::value_type
typedef Vector< T, Dim >	point_t

Static Private Attributes
static constexpr unsigned	Dim = FieldType::dim

Detailed Description

template<typename FieldType>
class ippl::FEMMaxwellDiffusionSolver< FieldType >

A solver for the electric diffusion equation given by \( \nabla \times \nabla \times E + E = f \text{ in } \Omega\) and \( n \times E = 0 \text{ on } \partial \Omega\) using the Nédélec basis functions.

Template Parameters

FieldType The type used to represent a field on a mesh.

Definition at line 88 of file FEMMaxwellDiffusionSolver.h.

Member Typedef Documentation

◆ Base

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::Base = Maxwell<FieldType, FieldType>

Definition at line 98 of file FEMMaxwellDiffusionSolver.h.

◆ ElementType

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::ElementType

Initial value:

Definition at line 106 of file FEMMaxwellDiffusionSolver.h.

◆ MeshType

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::MeshType = typename FieldType::Mesh_t

Definition at line 99 of file FEMMaxwellDiffusionSolver.h.

◆ NedelecType

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::NedelecType = NedelecSpace<T, Dim, 1, ElementType, QuadratureType, FieldType>

Definition at line 111 of file FEMMaxwellDiffusionSolver.h.

◆ PCGSolverAlgorithm_t

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::PCGSolverAlgorithm_t

Initial value:

Definition at line 102 of file FEMMaxwellDiffusionSolver.h.

◆ point_t

template<typename FieldType>

typedef Vector<T,Dim> ippl::FEMMaxwellDiffusionSolver< FieldType >::point_t

private

Definition at line 95 of file FEMMaxwellDiffusionSolver.h.

◆ QuadratureType

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::QuadratureType = GaussJacobiQuadrature<T, 5, ElementType>

Definition at line 109 of file FEMMaxwellDiffusionSolver.h.

◆ T

template<typename FieldType>

using ippl::FEMMaxwellDiffusionSolver< FieldType >::T = typename FieldType::value_type::value_type

private

Definition at line 93 of file FEMMaxwellDiffusionSolver.h.

Constructor & Destructor Documentation

◆ FEMMaxwellDiffusionSolver() [1/2]

template<typename FieldType>

ippl::FEMMaxwellDiffusionSolver< FieldType >::FEMMaxwellDiffusionSolver ( )

inline

Definition at line 114 of file FEMMaxwellDiffusionSolver.h.

References Dim, nedelecSpace_m, quadrature_m, refElement_m, and rhsVector_m.

◆ FEMMaxwellDiffusionSolver() [2/2]

template<typename FieldType>

ippl::FEMMaxwellDiffusionSolver< FieldType >::FEMMaxwellDiffusionSolver	(	FieldType &	lhs,
		FieldType &	rhs,
		const FEMVector< point_t > &	rhsVector )

inline

Definition at line 123 of file FEMMaxwellDiffusionSolver.h.

References nedelecSpace_m, quadrature_m, refElement_m, rhsVector_m, and setDefaultParameters().

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Member Function Documentation

◆ getIterationCount()

template<typename FieldType>

int ippl::FEMMaxwellDiffusionSolver< FieldType >::getIterationCount ( )

inline

Query how many iterations were required to obtain the solution the last time this solver was used

Returns: Iteration count of last solve

Definition at line 220 of file FEMMaxwellDiffusionSolver.h.

References pcg_algo_m.

◆ getL2Error()

template<typename FieldType>

template<typename F>

T ippl::FEMMaxwellDiffusionSolver< FieldType >::getL2Error ( const F & analytic )

inline

Given an analytical solution computes the L2 norm error.

Parameters

analytical The analytical solution (functor)

Returns: error - The error ||u - analytical||_L2

Definition at line 265 of file FEMMaxwellDiffusionSolver.h.

References lhsVector_m, and nedelecSpace_m.

◆ getResidue()

template<typename FieldType>

T ippl::FEMMaxwellDiffusionSolver< FieldType >::getResidue ( ) const

inline

Query the residue

Returns: Residue norm from last solve

Definition at line 226 of file FEMMaxwellDiffusionSolver.h.

References pcg_algo_m.

◆ mergeParameters()

void ippl::Maxwell< FieldType, FieldType >::mergeParameters ( const ParameterList & params )

inlineinherited

Merges another parameter set into the solver's parameters, overwriting existing parameters in case of conflict

Parameters

params Parameter list with desired values

Definition at line 63 of file Maxwell.h.

References params_m.

◆ reconstructToPoints()

template<typename FieldType>

Kokkos::View< point_t * > ippl::FEMMaxwellDiffusionSolver< FieldType >::reconstructToPoints ( const Kokkos::View< point_t * > & positions )

inline

Reconstructs function values at arbitrary points in the mesh.

This function can be used to retrieve the values of a solution function at arbitrary points inside of the mesh.

Note: Currently the function is able to handle both cases, where we have that positions only contains positions which are inside of local domain of this MPI rank (i.e. each rank gets its own unique position ) and where positions contains the positions of all ranks (i.e. positions is the same for all ranks). If in the future it can be guaranteed, that each rank will get its own positions then certain parts of the function implementation can be removed. Instructions for this are given in the implementation itself.

Parameters

positions The points at which the function should be evaluated. A Kokkos::View which stores in each element a 2D/3D point.

Returns: The function evaluated at the given points, stored inside of Kokkos::View where each element corresponts to the function value at the point described by the same element inside of positions.

Definition at line 251 of file FEMMaxwellDiffusionSolver.h.

References lhsVector_m, and nedelecSpace_m.