A local domain boundary element method for solving the nonlinear fisher KPP diffusion-reaction equation. (May 2022) - Gortsas, Theodore V.; Tsinopoulos, Stephanos V.; Polyzos, Demosthenes
Abstract: The nonlinear Fisher-KPP diffusion-reaction equation has been successfully employed to model competitive processes in biological populations. A robust numerical method for solving diffusion problems is the Boundary Element Method (ΒΕΜ). However, the conventional BEM suffers from large CPU memory requirements since it leads to dense coefficient matrices and for nonlinear problems, its efficiency is further reduced due to the appearance of volume integrals. In this work, a Local Domain BEM (LD-BEM) for solving the Fisher KPP equation is presented. The domain of interest is fragmented into small subdomains and the integral representation of the problem is considered separately for each of the considered subdomains. Eliminating the fluxes at all subdomain interfaces, the proposed LD-BEM leads to sparse linear system coefficient matrices and a reduced number of degrees of freedom. Five numerical examples are solved to assess the accuracy of the proposed method.