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 $\sum_{i=1}^{N}\frac{\partial^2 \phi}{\partial x_i^2}=f,~\mathbf{x}\in D.$

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