Manicore::MaxwellProblem Class Reference

2 dimensional Maxwell equation on a manifold without boundary More...

#include <maxwell.hpp>

Collaboration diagram for Manicore::MaxwellProblem:

Public Types
typedef Eigen::SparseMatrix< double >	SystemMatrixType
	Type used to store the system. More...
typedef Eigen::SparseLU< SystemMatrixType, Eigen::COLAMDOrdering< int > >	SolverType
	Type used to store the solver. More...

Public Member Functions
	MaxwellProblem (const Mesh< 2 > &mesh, int degree, double timestep, bool use_threads=true, std::array< int, 2 > const *dqr=nullptr, std::ostream &output=std::cout)
size_t	dimensionH () const
	Return the number of unknowns attached to the space of harmonic 0 forms. More...
size_t	dimensionG () const
	Return the number of unknowns attached to the space of 0 forms. More...
size_t	dimensionE () const
	Return the number of unknowns attached to the space of 1 forms. More...
size_t	dimensionB () const
	Return the number of unknowns attached to the space of 2 forms. More...
size_t	dimensionSystem () const
	Return the total number of unknowns. More...
DDR_Spaces< 2 > const &	ddrcore () const
	Return the associated DDR_Spaces. More...
double	timeStep () const
	Return the time-step. More...
void	assembleRHS (Eigen::Ref< const Eigen::VectorXd > const &rho, Eigen::Ref< const Eigen::VectorXd > const &J, Eigen::Ref< const Eigen::VectorXd > const &EOld, Eigen::Ref< const Eigen::VectorXd > const &BOld)
	Assemble the Right-Hand side from the given interpolates. More...
void	compute ()
	Setup the solver. More...
bool	validateSolution (Eigen::Ref< const Eigen::VectorXd > const &u) const
	Check if the vector u if a solution up to a given relative accuracy. More...
Eigen::VectorXd	solve ()
	Solve the system and return the solution. More...
Eigen::VectorXd	solve (const Eigen::VectorXd &rhs)
	Solve the system for the given Right-Hand side and return the solution. More...
template<typename Derived >
double	norm (Eigen::MatrixBase< Derived > const &E, size_t k) const
	Compute the discrete norm of a \(k\)-form. More...
template<typename Derived >
double	normd (Eigen::MatrixBase< Derived > const &E, size_t k) const
	Compute the discrete norm of the differential of a \(k\)-form. More...

Static Public Attributes
static constexpr std::string_view	SolverName = "SparseLU"
	Name of the solver. More...

Detailed Description

2 dimensional Maxwell equation on a manifold without boundary

Provides the logic to assemble and solve the system See the related paper.

Member Typedef Documentation

SolverType

typedef Eigen::SparseLU<SystemMatrixType,Eigen::COLAMDOrdering<int> > Manicore::MaxwellProblem::SolverType

Type used to store the solver.

SystemMatrixType

typedef Eigen::SparseMatrix<double> Manicore::MaxwellProblem::SystemMatrixType

Type used to store the system.

Constructor & Destructor Documentation

MaxwellProblem()

Manicore::MaxwellProblem::MaxwellProblem	(	const Mesh< 2 > &	mesh,
		int	degree,
		double	timestep,
		bool	use_threads = true,
		std::array< int, 2 > const *	dqr = nullptr,
		std::ostream &	output = std::cout
	)

Parameters

mesh	Mesh to use
degree	Polynomial degree
timestep	Time-step to use in the scheme
use_threads	Enable pthreads parallelism
dqr	Degree of quadrature used to generate the mass matrices. It cannot be exact for generic metric and default to a pretty high degree. Use a lower degree if the metric and cells are almost flat.
output	Output stream for status messages.

Member Function Documentation

assembleRHS()

void Manicore::MaxwellProblem::assembleRHS	(	Eigen::Ref< const Eigen::VectorXd > const &	rho,
		Eigen::Ref< const Eigen::VectorXd > const &	J,
		Eigen::Ref< const Eigen::VectorXd > const &	EOld,
		Eigen::Ref< const Eigen::VectorXd > const &	BOld
	)

Assemble the Right-Hand side from the given interpolates.

Parameters

rho	Interpolate of the electric charge (0 form)
J	Interpolate of the current (1 form)
EOld	Previous value of E_h
BOld	Previous value of B_h

compute()

void Manicore::MaxwellProblem::compute

(

)

Setup the solver.

ddrcore()

DDR_Spaces<2> const& Manicore::MaxwellProblem::ddrcore ( ) const

inline

Return the associated DDR_Spaces.

dimensionB()

size_t Manicore::MaxwellProblem::dimensionB ( ) const

inline

Return the number of unknowns attached to the space of 2 forms.

dimensionE()

size_t Manicore::MaxwellProblem::dimensionE ( ) const

inline

Return the number of unknowns attached to the space of 1 forms.

dimensionG()

size_t Manicore::MaxwellProblem::dimensionG ( ) const

inline

Return the number of unknowns attached to the space of 0 forms.

dimensionH()

size_t Manicore::MaxwellProblem::dimensionH ( ) const

inline

Return the number of unknowns attached to the space of harmonic 0 forms.

dimensionSystem()

size_t Manicore::MaxwellProblem::dimensionSystem ( ) const

inline

Return the total number of unknowns.

norm()

template<typename Derived >

double Manicore::MaxwellProblem::norm	(	Eigen::MatrixBase< Derived > const &	E,
		size_t	k
	)		const

Compute the discrete norm of a \(k\)-form.

Compute \( \Vert E \Vert_{h,k} \)

Parameters

E	Discrete form
k	Form degree

normd()

template<typename Derived >

double Manicore::MaxwellProblem::normd	(	Eigen::MatrixBase< Derived > const &	E,
		size_t	k
	)		const

Compute the discrete norm of the differential of a \(k\)-form.

Compute \( \Vert d_h^k E \Vert_{h,k+1} \)

Parameters

E	Discrete form
k	Form degree

solve() [1/2]

Eigen::VectorXd Manicore::MaxwellProblem::solve

(

)

Solve the system and return the solution.

solve() [2/2]

Eigen::VectorXd Manicore::MaxwellProblem::solve

(

const Eigen::VectorXd &

rhs

)

Solve the system for the given Right-Hand side and return the solution.

timeStep()

double Manicore::MaxwellProblem::timeStep ( ) const

inline

Return the time-step.

validateSolution()

bool Manicore::MaxwellProblem::validateSolution

(

Eigen::Ref< const Eigen::VectorXd > const &

u

)

const

Check if the vector u if a solution up to a given relative accuracy.

Member Data Documentation

SolverName

constexpr std::string_view Manicore::MaxwellProblem::SolverName = "SparseLU"

staticconstexpr

Name of the solver.

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

• Schemes/Maxwell2D/maxwell.hpp