ippl::FEMMaxwellDiffusionSolver< FieldType > Class Template Reference

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 = CG< FEMVector< T >, FEMVector< T >, FEMVector< T >, FEMVector< T >, FEMVector< T >, FEMVector< T >, FEMVector< T > >
using	ElementType = std::conditional_t< Dim==2, ippl::QuadrilateralElement< T >, ippl::HexahedralElement< T > >
using	QuadratureType = GaussJacobiQuadrature< T, 5, ElementType >
using	NedelecType = NedelecSpace< T, Dim, 1, ElementType, QuadratureType, FieldType >

Public Member Functions
	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.
Public Member Functions inherited from ippl::Maxwell< FieldType, FieldType >
	Maxwell ()
	Maxwell (FieldType &four_current, FieldType &E, FieldType &B)
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.
Protected Attributes inherited from ippl::Maxwell< FieldType, FieldType >
ParameterList	params_m
FieldType *	JN_mp
FieldType *	En_mp
FieldType *	Bn_mp

Additional Inherited Members
Static Public Attributes inherited from ippl::Maxwell< FieldType, FieldType >
static constexpr unsigned	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.

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

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

analytic

The analytical solution functor

Returns

error - The error ||u - analytical||_L2

getResidue()

template<typename FieldType >

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

inline

Query the residue

Returns

Residue norm from last solve

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.

solve()

template<typename FieldType >

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

inlineoverridevirtual

Solve the equation using finite element methods.

Implements ippl::Maxwell< FieldType, FieldType >.

Member Data Documentation

nedelecSpace_m

template<typename FieldType >

NedelecType ippl::FEMMaxwellDiffusionSolver< FieldType >::nedelecSpace_m

protected

The Nedelec Space object.

This is the representation of the Nedelec space that we have and which we use to interact with all the Nedelec stuff.

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The documentation for this class was generated from the following file:

• ippl-src/src/MaxwellSolvers/FEMMaxwellDiffusionSolver.h