Poisson equation, solving with DFT

Primary authors of this description:V.M.stepanenko, E.V.Mortikov, Vad.V.Voevodin (section 2.2)

1 Properties and structure of the algorithm

1.1 General description of the algorithm

The Poisson equation for the multidimensional space has the form [math] \sum_{i=1}^{N}\frac{\partial^2 \phi}{\partial x_i^2}=f,~\mathbf{x}\in D. [/math]

Here, [math]D \in \mathbb{R}^N[/math] is the domain in which the solution [math]\phi(\mathbf{x})[/math] is defined, and [math]\mathbf{x}=(x_1,...,x_N)^T[/math] is the vector of independent variables. The Poisson equation is supplemented by the boundary conditions [math] B(\phi)=F, \mathbf{x} \in \Gamma(D), [/math]