A solver for the poisson equation using finite element methods and Conjugate Gradient (CG). More...

#include <FEMPoissonSolver.h>

Inheritance diagram for ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >:

Collaboration diagram for ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >:

Public Types
using	Base = Poisson<FieldLHS, FieldRHS>
using	MeshType = typename FieldRHS::Mesh_t
using	PCGSolverAlgorithm_t
using	ElementType
using	QuadratureType = GaussJacobiQuadrature<Tlhs, QuadNumNodes, ElementType>
using	LagrangeType = LagrangeSpace<Tlhs, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS>
using	lhs_type
using	rhs_type
enum	OutputType
using	Trhs
using	grad_type

Public Member Functions
	FEMPoissonSolver ()
	FEMPoissonSolver (lhs_type &lhs, rhs_type &rhs)
void	setRhs (rhs_type &rhs) override
void	solve () override
	Solve the poisson equation using finite element methods. The problem is described by -laplace(lhs) = rhs.
int	getIterationCount ()
Tlhs	getResidue () const
template<typename F>
Tlhs	getL2Error (const F &analytic)
Tlhs	getAvg (bool Vol=false)
void	updateParameter (const std::string &key, const T &value)
void	updateParameters (const ParameterList &params)
void	mergeParameters (const ParameterList &params)
void	setLhs (lhs_type &lhs)
virtual void	setRhs (rhs_type &rhs)
virtual MField_t *	getHessian ()
void	setGradient (grad_type &grad)

Protected Member Functions
virtual void	setDefaultParameters () override

Protected Attributes
PCGSolverAlgorithm_t	pcg_algo_m
ElementType	refElement_m
QuadratureType	quadrature_m
LagrangeType	lagrangeSpace_m
ParameterList	params_m
rhs_type *	rhs_mp
lhs_type *	lhs_mp
grad_type *	grad_mp

Private Types
using	Tlhs = typename FieldLHS::value_type
typedef FieldLHS::Mesh_t	Mesh
typedef FieldLHS::Centering_t	Centering
typedef Mesh::matrix_type	Matrix_t
typedef Field< Matrix_t, Dim, Mesh, Centering Centering >	MField_t

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

Detailed Description

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>
class ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >

A solver for the poisson equation using finite element methods and Conjugate Gradient (CG).

Template Parameters

FieldLHS	field type for the left hand side
FieldRHS	field type for the right hand side

Definition at line 37 of file FEMPoissonSolver.h.

Member Typedef Documentation

◆ Base

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::Base = Poisson<FieldLHS, FieldRHS>

Definition at line 42 of file FEMPoissonSolver.h.

◆ Centering

typedef FieldLHS::Centering_t ippl::Poisson< FieldLHS, FieldLHS >::Centering

privateinherited

Definition at line 19 of file Poisson.h.

◆ ElementType

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::ElementType

Initial value:

Definition at line 51 of file FEMPoissonSolver.h.

◆ grad_type

using ippl::Poisson< FieldLHS, FieldLHS >::grad_type

inherited

Definition at line 29 of file Poisson.h.

◆ LagrangeType

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::LagrangeType = LagrangeSpace<Tlhs, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS>

Definition at line 58 of file FEMPoissonSolver.h.

◆ lhs_type

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::Poisson< FieldLHS, FieldRHS >::lhs_type

Definition at line 24 of file Poisson.h.

◆ Matrix_t

typedef Mesh::matrix_type ippl::Poisson< FieldLHS, FieldLHS >::Matrix_t

privateinherited

Definition at line 20 of file Poisson.h.

◆ Mesh

typedef FieldLHS::Mesh_t ippl::Poisson< FieldLHS, FieldLHS >::Mesh

privateinherited

Definition at line 18 of file Poisson.h.

◆ MeshType

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::MeshType = typename FieldRHS::Mesh_t

Definition at line 44 of file FEMPoissonSolver.h.

◆ MField_t

typedef Field<Matrix_t, Dim, Mesh, Centering Centering> ippl::Poisson< FieldLHS, FieldLHS >::MField_t

privateinherited

Definition at line 21 of file Poisson.h.

◆ PCGSolverAlgorithm_t

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::PCGSolverAlgorithm_t

Initial value:

Definition at line 47 of file FEMPoissonSolver.h.

◆ QuadratureType

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::QuadratureType = GaussJacobiQuadrature<Tlhs, QuadNumNodes, ElementType>

Definition at line 56 of file FEMPoissonSolver.h.

◆ rhs_type

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::Poisson< FieldLHS, FieldRHS >::rhs_type

Definition at line 25 of file Poisson.h.

◆ Tlhs

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

using ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::Tlhs = typename FieldLHS::value_type

private

Definition at line 39 of file FEMPoissonSolver.h.

◆ Trhs

using ippl::Poisson< FieldLHS, FieldLHS >::Trhs

inherited

Definition at line 27 of file Poisson.h.

Member Enumeration Documentation

◆ OutputType

enum ippl::Poisson::OutputType

inherited

Represents the types of fields that should be output by the solver

Definition at line 35 of file Poisson.h.

Constructor & Destructor Documentation

◆ FEMPoissonSolver() [1/2]

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::FEMPoissonSolver ( )

inline

Definition at line 61 of file FEMPoissonSolver.h.

References Dim, lagrangeSpace_m, quadrature_m, and refElement_m.

◆ FEMPoissonSolver() [2/2]

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::FEMPoissonSolver	(	lhs_type &	lhs,
		rhs_type &	rhs )

inline

Definition at line 69 of file FEMPoissonSolver.h.

References IpplTimings::getTimer(), lagrangeSpace_m, quadrature_m, refElement_m, setDefaultParameters(), IpplTimings::startTimer(), and IpplTimings::stopTimer().

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Member Function Documentation

◆ getAvg()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

Tlhs ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::getAvg ( bool Vol = false )

inline

Query the average of the solution

Parameters

vol	Boolean indicating whether we divide by volume or not

Returns: avg (offset for null space test cases if divided by volume)

Definition at line 199 of file FEMPoissonSolver.h.

References lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp.

◆ getHessian()

virtual MField_t * ippl::Poisson< FieldLHS, FieldLHS >::getHessian ( )

inlinevirtualinherited

Get the Hessian matrix of the solution

Returns: Matrix field containing the Hessian of the lhs

Definition at line 102 of file Poisson.h.

◆ getIterationCount()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

int ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::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 176 of file FEMPoissonSolver.h.

References pcg_algo_m.

◆ getL2Error()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

template<typename F>

Tlhs ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::getL2Error ( const F & analytic )

inline

Query the L2-norm error compared to a given (analytical) sol

Returns: L2 error after last solve

Definition at line 189 of file FEMPoissonSolver.h.

References lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp.

◆ getResidue()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

Tlhs ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::getResidue ( ) const

inline

Query the residue

Returns: Residue norm from last solve

Definition at line 182 of file FEMPoissonSolver.h.

References pcg_algo_m.

◆ mergeParameters()

void ippl::Poisson< FieldLHS, FieldLHS >::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 84 of file Poisson.h.

◆ setDefaultParameters()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

virtual void ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::setDefaultParameters ( )

inlineoverrideprotectedvirtual

Utility function for initializing a solver's default parameters (to be overridden for each base class)

Reimplemented from ippl::Poisson< FieldLHS, FieldLHS >.

Definition at line 214 of file FEMPoissonSolver.h.

References ippl::Poisson< FieldLHS, FieldLHS >::params_m.

Referenced by FEMPoissonSolver().

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◆ setGradient()

void ippl::Poisson< FieldLHS, FieldLHS >::setGradient ( grad_type & grad )

inlineinherited

Set the field in which the gradient of the computed potential should be stored

Parameters

grad	Reference to field in which to store the gradient

Definition at line 109 of file Poisson.h.

◆ setLhs()

void ippl::Poisson< FieldLHS, FieldLHS >::setLhs ( lhs_type & lhs )

inlineinherited

Set the problem LHS

Parameters

lhs	Reference to problem LHS field

Definition at line 90 of file Poisson.h.

◆ setRhs() [1/2]

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

void ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::setRhs ( rhs_type & rhs )

inlineoverride

Definition at line 90 of file FEMPoissonSolver.h.

References lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldRHS >::setRhs().

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◆ setRhs() [2/2]

virtual void ippl::Poisson< FieldLHS, FieldLHS >::setRhs ( rhs_type & rhs )

inlinevirtualinherited

Set the problem RHS

Parameters

rhs	Reference to problem RHS field

Definition at line 96 of file Poisson.h.

◆ solve()

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

void ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::solve ( )

inlineoverridevirtual

Solve the poisson equation using finite element methods. The problem is described by -laplace(lhs) = rhs.

Implements ippl::Poisson< FieldLHS, FieldLHS >.

Definition at line 106 of file FEMPoissonSolver.h.

References ippl::CONSTANT_FACE, ippl::get(), IpplTimings::getTimer(), ippl::Poisson< FieldLHS, FieldRHS >::GRAD, ippl::grad(), ippl::Poisson< FieldLHS, FieldLHS >::grad_mp, lagrangeSpace_m, ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp, ippl::Poisson< FieldLHS, FieldLHS >::params_m, pcg_algo_m, refElement_m, ippl::Poisson< FieldLHS, FieldLHS >::rhs_mp, solve(), IpplTimings::startTimer(), and IpplTimings::stopTimer().

Referenced by solve().

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◆ updateParameter()

void ippl::Poisson< FieldLHS, FieldLHS >::updateParameter	(	const std::string &	key,
		const T &	value )

inlineinherited

Update one of the solver's parameters

Parameters

key	The parameter key
value	The new value

Exceptions

IpplException Fails if there is no existing parameter with the given key

Definition at line 67 of file Poisson.h.

◆ updateParameters()

void ippl::Poisson< FieldLHS, FieldLHS >::updateParameters ( const ParameterList & params )

inlineinherited

Updates all solver parameters based on values in another parameter set

Parameters

params Parameter list with updated values

Exceptions

IpplException Fails if the provided parameter list includes keys not already present

Definition at line 77 of file Poisson.h.

Member Data Documentation

◆ Dim

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

unsigned ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::Dim = FieldLHS::dim

staticconstexprprivate

Definition at line 38 of file FEMPoissonSolver.h.

Referenced by FEMPoissonSolver().

◆ grad_mp

grad_type* ippl::Poisson< FieldLHS, FieldLHS >::grad_mp

protectedinherited

Definition at line 125 of file Poisson.h.

Referenced by ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::solve(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

◆ lagrangeSpace_m

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

LagrangeType ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::lagrangeSpace_m

protected

Definition at line 221 of file FEMPoissonSolver.h.

Referenced by FEMPoissonSolver(), FEMPoissonSolver(), getAvg(), getL2Error(), setRhs(), and solve().

◆ lhs_mp

lhs_type* ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp

protectedinherited

Definition at line 123 of file Poisson.h.

Referenced by ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::getAvg(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::getAvg(), ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::getL2Error(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::getL2Error(), ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::solve(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

◆ params_m

ParameterList ippl::Poisson< FieldLHS, FieldLHS >::params_m

protectedinherited

Definition at line 120 of file Poisson.h.

Referenced by ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::setDefaultParameters(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::setDefaultParameters(), ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::solve(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

◆ pcg_algo_m

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

PCGSolverAlgorithm_t ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::pcg_algo_m

protected

Definition at line 212 of file FEMPoissonSolver.h.

Referenced by getIterationCount(), getResidue(), and solve().

◆ quadrature_m

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

QuadratureType ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::quadrature_m

protected

Definition at line 220 of file FEMPoissonSolver.h.

Referenced by FEMPoissonSolver(), and FEMPoissonSolver().

◆ refElement_m

template<typename FieldLHS, typename FieldRHS = FieldLHS, unsigned Order = 1, unsigned QuadNumNodes = 5>

ElementType ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::refElement_m

protected

Definition at line 219 of file FEMPoissonSolver.h.

Referenced by FEMPoissonSolver(), FEMPoissonSolver(), and solve().

◆ rhs_mp

rhs_type* ippl::Poisson< FieldLHS, FieldLHS >::rhs_mp

protectedinherited

Definition at line 122 of file Poisson.h.

Referenced by ippl::FEMPoissonSolver< FieldLHS, FieldRHS, Order, QuadNumNodes >::solve(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

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

FEMPoissonSolver.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Types

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ Centering

◆ ElementType

◆ grad_type

◆ LagrangeType

◆ lhs_type

◆ Matrix_t

◆ Mesh

◆ MeshType

◆ MField_t

◆ PCGSolverAlgorithm_t

◆ QuadratureType

◆ rhs_type

◆ Tlhs

◆ Trhs

Member Enumeration Documentation

◆ OutputType

Constructor & Destructor Documentation

◆ FEMPoissonSolver() [1/2]

◆ FEMPoissonSolver() [2/2]

Member Function Documentation

◆ getAvg()

◆ getHessian()

◆ getIterationCount()

◆ getL2Error()

◆ getResidue()

◆ mergeParameters()

◆ setDefaultParameters()

◆ setGradient()

◆ setLhs()

◆ setRhs() [1/2]

◆ setRhs() [2/2]

◆ solve()

◆ updateParameter()

◆ updateParameters()

Member Data Documentation

◆ Dim

◆ grad_mp

◆ lagrangeSpace_m

◆ lhs_mp

◆ params_m

◆ pcg_algo_m

◆ quadrature_m

◆ refElement_m

◆ rhs_mp