A 3D Vector-Additive Iterative Solver for the Anisotropic Inhomogeneous Poisson Equation in the Forward EEG problem

Authors:
Vasily Volkov;Aleksei Zherdetsky;Sergei Turovets;Allen Malony
Affiliations:
Department of Mathematics and Mechanics, Belarusian State University, Minsk, Republic of Belarus 220050;Department of Mathematics and Mechanics, Belarusian State University, Minsk, Republic of Belarus 220050;NeuroInformatics Center, University of Oregon, Eugene, USA OR 97403;NeuroInformatics Center, University of Oregon, Eugene, USA OR 97403
Venue:
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Year:
2009

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Abstract

We describe a novel 3D finite difference method for solving the anisotropic inhomogeneous Poisson equation based on a multi-component additive implicit method with a 13-point stencil. The serial performance is found to be comparable to the most efficient solvers from the family of preconditioned conjugate gradient (PCG) algorithms. The proposed multi-component additive algorithm is unconditionally stable in 3D and amenable for transparent domain decomposition parallelization up to one eighth of the total grid points in the initial computational domain. Some validation and numerical examples are given.