ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS > Class Template Reference

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

#include <PreconditionedFEMPoissonSolver.h>

Inheritance diagram for ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >:

Collaboration diagram for ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >:

Public Types
using	Base = Poisson< FieldLHS, FieldRHS >
using	MeshType = typename FieldRHS::Mesh_t
using	PCGSolverAlgorithm_t = PCG< lhs_type, lhs_type, lhs_type, lhs_type, lhs_type, FieldLHS, FieldRHS >
using	ElementType = std::conditional_t< Dim==1, ippl::EdgeElement< Tlhs >, std::conditional_t< Dim==2, ippl::QuadrilateralElement< Tlhs >, ippl::HexahedralElement< Tlhs > > >
using	QuadratureType = GaussJacobiQuadrature< Tlhs, 5, ElementType >
using	LagrangeType = LagrangeSpace< Tlhs, Dim, 1, ElementType, QuadratureType, FieldLHS, FieldRHS >
using	lhs_type = FieldLHS
using	rhs_type = FieldRHS
enum	OutputType
using	Trhs = typename FieldRHS::value_type
using	grad_type = Field< Vector< Tlhs, Dim >, Dim, Mesh, Centering >

Public Member Functions
	PreconditionedFEMPoissonSolver ()
	PreconditionedFEMPoissonSolver (lhs_type &lhs, rhs_type &rhs)
void	setRhs (rhs_type &rhs) override
void	solve () override
	Solve the poisson equation using finite element methods. More...
int	getIterationCount ()
	Query how many iterations were required to obtain the solution the last time this solver was used. More...
Tlhs	getResidue () const
	Query the residue. More...
template<typename F >
Tlhs	getL2Error (const F &analytic)
	Query the L2-norm error compared to a given (analytical) sol. More...
Tlhs	getAvg (bool Vol=false)
	Query the average of the solution. More...
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 >	MField_t

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

Detailed Description

template<typename FieldLHS, typename FieldRHS = FieldLHS>
class ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >

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 39 of file PreconditionedFEMPoissonSolver.h.

Member Typedef Documentation

Base

template<typename FieldLHS , typename FieldRHS = FieldLHS>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::Base = Poisson<FieldLHS, FieldRHS>

Definition at line 44 of file PreconditionedFEMPoissonSolver.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>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::ElementType = std::conditional_t<Dim == 1, ippl::EdgeElement<Tlhs>, std::conditional_t<Dim == 2, ippl::QuadrilateralElement<Tlhs>, ippl::HexahedralElement<Tlhs> >>

Definition at line 53 of file PreconditionedFEMPoissonSolver.h.

grad_type

using ippl::Poisson< FieldLHS, FieldLHS >::grad_type = Field<Vector<Tlhs, Dim>, Dim, Mesh, Centering>

inherited

Definition at line 29 of file Poisson.h.

LagrangeType

template<typename FieldLHS , typename FieldRHS = FieldLHS>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::LagrangeType = LagrangeSpace<Tlhs, Dim, 1, ElementType, QuadratureType, FieldLHS, FieldRHS>

Definition at line 60 of file PreconditionedFEMPoissonSolver.h.

lhs_type

template<typename FieldLHS , typename FieldRHS = FieldLHS>

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

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>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::MeshType = typename FieldRHS::Mesh_t

Definition at line 46 of file PreconditionedFEMPoissonSolver.h.

MField_t

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

privateinherited

Definition at line 21 of file Poisson.h.

PCGSolverAlgorithm_t

template<typename FieldLHS , typename FieldRHS = FieldLHS>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::PCGSolverAlgorithm_t = PCG<lhs_type, lhs_type, lhs_type, lhs_type, lhs_type, FieldLHS, FieldRHS>

Definition at line 49 of file PreconditionedFEMPoissonSolver.h.

QuadratureType

template<typename FieldLHS , typename FieldRHS = FieldLHS>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::QuadratureType = GaussJacobiQuadrature<Tlhs, 5, ElementType>

Definition at line 58 of file PreconditionedFEMPoissonSolver.h.

rhs_type

template<typename FieldLHS , typename FieldRHS = FieldLHS>

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

Definition at line 25 of file Poisson.h.

Tlhs

template<typename FieldLHS , typename FieldRHS = FieldLHS>

using ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::Tlhs = typename FieldLHS::value_type

private

Definition at line 41 of file PreconditionedFEMPoissonSolver.h.

Trhs

using ippl::Poisson< FieldLHS, FieldLHS >::Trhs = typename FieldRHS::value_type

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

PreconditionedFEMPoissonSolver() [1/2]

template<typename FieldLHS , typename FieldRHS = FieldLHS>

ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::PreconditionedFEMPoissonSolver ( )

inline

Definition at line 63 of file PreconditionedFEMPoissonSolver.h.

PreconditionedFEMPoissonSolver() [2/2]

template<typename FieldLHS , typename FieldRHS = FieldLHS>

ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::PreconditionedFEMPoissonSolver ( lhs_type &  lhs, rhs_type &  rhs  )

inline

Definition at line 71 of file PreconditionedFEMPoissonSolver.h.

References ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateLoadVector(), IpplTimings::getTimer(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m, ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::setDefaultParameters(), IpplTimings::startTimer(), and IpplTimings::stopTimer().

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Member Function Documentation

getAvg()

template<typename FieldLHS , typename FieldRHS = FieldLHS>

Tlhs ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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 277 of file PreconditionedFEMPoissonSolver.h.

References ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::computeAvg(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp.

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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>

int ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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 254 of file PreconditionedFEMPoissonSolver.h.

References ippl::CG< OperatorRet, LowerRet, UpperRet, UpperLowerRet, InverseDiagRet, DiagRet, FieldLHS, FieldRHS >::getIterationCount(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::pcg_algo_m.

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getL2Error()

template<typename FieldLHS , typename FieldRHS = FieldLHS>

template<typename F >

Tlhs ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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 267 of file PreconditionedFEMPoissonSolver.h.

References ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::computeErrorL2(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp.

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getResidue()

template<typename FieldLHS , typename FieldRHS = FieldLHS>

Tlhs ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::getResidue ( ) const

inline

Query the residue.

Returns

Residue norm from last solve

Definition at line 260 of file PreconditionedFEMPoissonSolver.h.

References ippl::CG< OperatorRet, LowerRet, UpperRet, UpperLowerRet, InverseDiagRet, DiagRet, FieldLHS, FieldRHS >::getResidue(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::pcg_algo_m.

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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>

virtual void ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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 292 of file PreconditionedFEMPoissonSolver.h.

References ippl::ParameterList::add(), Physics::e, and ippl::Poisson< FieldLHS, FieldLHS >::params_m.

Referenced by ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::PreconditionedFEMPoissonSolver().

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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]

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.

setRhs() [2/2]

template<typename FieldLHS , typename FieldRHS = FieldLHS>

void ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::setRhs ( rhs_type &  rhs )

inlineoverride

Definition at line 92 of file PreconditionedFEMPoissonSolver.h.

References ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateLoadVector(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::initialize(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m, and ippl::Poisson< FieldLHS, FieldRHS >::setRhs().

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solve()

template<typename FieldLHS , typename FieldRHS = FieldLHS>

void ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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 108 of file PreconditionedFEMPoissonSolver.h.

References ippl::BConds< Field, Dim >::assignGhostToPhysical(), ippl::CONSTANT_FACE, ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_diag(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_inversediag(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_lift(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_lower(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_upper(), ippl::LagrangeSpace< T, Dim, Order, ElementType, QuadratureType, FieldLHS, FieldRHS >::evaluateAx_upperlower(), ippl::FiniteElementSpace< T, Dim, NumElementDOFs, ElementType, QuadratureType, FieldLHS, FieldRHS >::getElementMeshVertexPoints(), IpplTimings::getTimer(), ippl::grad(), ippl::Poisson< FieldLHS, FieldRHS >::GRAD, ippl::Poisson< FieldLHS, FieldLHS >::grad_mp, ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m, ippl::Poisson< FieldLHS, FieldLHS >::lhs_mp, ippl::Poisson< FieldLHS, FieldLHS >::params_m, ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::pcg_algo_m, ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::refElement_m, ippl::Poisson< FieldLHS, FieldLHS >::rhs_mp, ippl::CG< OperatorRet, LowerRet, UpperRet, UpperLowerRet, InverseDiagRet, DiagRet, FieldLHS, FieldRHS >::setOperator(), ippl::PCG< OperatorRet, LowerRet, UpperRet, UpperLowerRet, InverseDiagRet, DiagRet, FieldLHS, FieldRHS >::setPreconditioner(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve(), IpplTimings::startTimer(), and IpplTimings::stopTimer().

Referenced by ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::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>

constexpr unsigned ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::Dim = FieldLHS::dim

staticconstexprprivate

Definition at line 40 of file PreconditionedFEMPoissonSolver.h.

grad_mp

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

protectedinherited

Definition at line 125 of file Poisson.h.

lagrangeSpace_m

template<typename FieldLHS , typename FieldRHS = FieldLHS>

LagrangeType ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::lagrangeSpace_m

protected

Definition at line 299 of file PreconditionedFEMPoissonSolver.h.

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

lhs_mp

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

protectedinherited

Definition at line 123 of file Poisson.h.

params_m

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

protectedinherited

Definition at line 120 of file Poisson.h.

pcg_algo_m

template<typename FieldLHS , typename FieldRHS = FieldLHS>

PCGSolverAlgorithm_t ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::pcg_algo_m

protected

Definition at line 290 of file PreconditionedFEMPoissonSolver.h.

Referenced by ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::getIterationCount(), ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::getResidue(), and ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

quadrature_m

template<typename FieldLHS , typename FieldRHS = FieldLHS>

QuadratureType ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::quadrature_m

protected

Definition at line 298 of file PreconditionedFEMPoissonSolver.h.

refElement_m

template<typename FieldLHS , typename FieldRHS = FieldLHS>

ElementType ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::refElement_m

protected

Definition at line 297 of file PreconditionedFEMPoissonSolver.h.

Referenced by ippl::PreconditionedFEMPoissonSolver< FieldLHS, FieldRHS >::solve().

rhs_mp

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

protectedinherited

Definition at line 122 of file Poisson.h.

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

• PreconditionedFEMPoissonSolver.h