Parallelization of a finite volumes discretization for anisotropic diffusion problems using an improved Schur complement technique

Abstract

<p style='text-indent:20px;'>We present in this paper a new algorithm combining a finite volume method with an improved Schur complement technique to solve <inline-formula><tex-math id="M1">\begin{document}$ 2D $\end{document}</tex-math></inline-formula> anisotropic diffusion problems on general meshes. After having proved the convergence of the finite volume method, we have given a description of the proposed algorithm in the case of two nonoverlapping subdomains. Several numerical tests are achieved which illustrate the theoretical results of convergence of the finite volume method and show the advantages of the proposed algorithm.