Items related to solving a Poisson equation \(-\Delta u(x)=f(x)\). More...

Classes
struct	FirstOrderSystem
	The Poisson equation formulated as a set of coupled first-order PDEs. More...

struct	Fluxes< Dim, Geometry::Curved, DataType >
	Compute the fluxes \(F^i\) for the curved-space Poisson equation on a spatial metric \(\gamma_{ij}\). More...

struct	Fluxes< Dim, Geometry::FlatCartesian, DataType >
	Compute the fluxes \(F^i\) for the Poisson equation on a flat metric in Cartesian coordinates. More...

struct	Sources< Dim, Geometry::Curved, DataType >
	Add the sources \(S\) for the curved-space Poisson equation on a spatial metric \(\gamma_{ij}\). More...

Enumerations
enum class	Geometry { FlatCartesian , Curved }
	Types of background geometries for the Poisson equation. More...

Functions
template<typename DataType , size_t Dim>
void	flat_cartesian_fluxes (gsl::not_null< tnsr::I< DataType, Dim > * > flux_for_field, const tnsr::i< DataType, Dim > &field_gradient)
	Compute the fluxes \(F^i=\partial_i u(x)\) for the Poisson equation on a flat spatial metric in Cartesian coordinates.

template<typename DataType , size_t Dim>
void	curved_fluxes (gsl::not_null< tnsr::I< DataType, Dim > * > flux_for_field, const tnsr::II< DataVector, Dim > &inv_spatial_metric, const tnsr::i< DataType, Dim > &field_gradient)
	Compute the fluxes \(F^i=\gamma^{ij}\partial_j u(x)\) for the curved-space Poisson equation on a spatial metric \(\gamma_{ij}\).

template<typename DataType , size_t Dim>
void	fluxes_on_face (gsl::not_null< tnsr::I< DataType, Dim > * > flux_for_field, const tnsr::I< DataVector, Dim > &face_normal_vector, const Scalar< DataType > &field)
	Compute the fluxes \(F^i=\gamma^{ij} n_j u\) where \(n_j\) is the `face_normal`. More...

template<typename DataType , size_t Dim>
void	add_curved_sources (gsl::not_null< Scalar< DataType > * > source_for_field, const tnsr::i< DataVector, Dim > &christoffel_contracted, const tnsr::I< DataType, Dim > &flux_for_field)
	Add the sources \(S=-\Gamma^i_{ij}v^j\) for the curved-space Poisson equation on a spatial metric \(\gamma_{ij}\). More...

Detailed Description

Items related to solving a Poisson equation \(-\Delta u(x)=f(x)\).

Enumeration Type Documentation

strong

Types of background geometries for the Poisson equation.

Enumerator
FlatCartesian	Euclidean (flat) manifold with Cartesian coordinates, i.e. the metric has components \(\gamma_{ij} = \delta_{ij}\) in these coordinates and thus all Christoffel symbols vanish: \(\Gamma^i_{jk}=0\).
Curved	The manifold is either curved or employs curved coordinates, so non-vanishing Christoffel symbols must be taken into account.

template<typename DataType , size_t Dim>

void Poisson::add_curved_sources	(	gsl::not_null< Scalar< DataType > * >	source_for_field,
		const tnsr::i< DataVector, Dim > &	christoffel_contracted,
		const tnsr::I< DataType, Dim > &	flux_for_field
	)

Add the sources \(S=-\Gamma^i_{ij}v^j\) for the curved-space Poisson equation on a spatial metric \(\gamma_{ij}\).

These sources arise from the non-principal part of the Laplacian on a non-Euclidean background.

template<typename DataType , size_t Dim>

void Poisson::fluxes_on_face	(	gsl::not_null< tnsr::I< DataType, Dim > * >	flux_for_field,
		const tnsr::I< DataVector, Dim > &	face_normal_vector,
		const Scalar< DataType > &	field
	)

Compute the fluxes \(F^i=\gamma^{ij} n_j u\) where \(n_j\) is the face_normal.

The face_normal_vector is \(\gamma^{ij} n_j\).