XLEMath::PoissonSolver Class Reference

Solves "Poisson equations", such as the heat equation More...

#include <PoissonSolver.h>

Classes
struct	Flags

Public Types
enum	Method {   PreconCG, PlainCG, ForwardEuler, SOR,   Multigrid }

Public Member Functions
unsigned	Solve (ScalarField1D x, const PreparedMatrix &A, const ScalarField1D &b, Method method, Flags::BitField flags=0u) const
std::shared_ptr< PreparedMatrix >	PrepareDiffusionMatrix (float diffusionAmount, Method method, unsigned wrapEdgesFlags) const
std::shared_ptr< PreparedMatrix >	PrepareDivergenceMatrix (Method method, unsigned wrapEdgesFlags) const
	PoissonSolver (unsigned dimensionality, unsigned dimensions[])
	PoissonSolver (PoissonSolver &&moveFrom)
PoissonSolver &	operator= (PoissonSolver &&moveFrom)

Protected Attributes
std::unique_ptr< Pimpl >	_pimpl

Detailed Description

Solves "Poisson equations", such as the heat equation

A Poisson equation is a partial differential equations that involves the Laplace operator (del). The Laplace operator measures the "divergence" of a field of numbers – that is, the derivatives with respect to the cardinal axes (eg, X, Y, Z).

A Poisson equation imposes some restriction on the divergence of a number field, and we most solve to mean this restriction.

This is useful for many simulations and problems. For example, the "heat equation" is a Poisson equation – this simulates how heat (or a electro magnetic field, or other fields) diffuse in space.

We can't solve Poisson equations perfectly – we must use an estimate. There are many different methods that can produce estimates; all with different metrics for performance, accuracy and hardware suitability. Sometimes the best method to use in one case is not ideal in another.

This class aims to encapsulate the implementation details and math involved in calculating the solution – and provide a simple reusable interface.

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

• Math/PoissonSolver.h
• Math/PoissonSolver.cpp