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

  • Vasily Volkov
  • Aleksei Zherdetsky
  • Sergei Turovets
  • Allen Malony
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5544)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vasily Volkov
    • 1
  • Aleksei Zherdetsky
    • 1
  • Sergei Turovets
    • 2
  • Allen Malony
    • 2
  1. 1.Department of Mathematics and MechanicsBelarusian State UniversityMinskRepublic of Belarus
  2. 2.NeuroInformatics CenterUniversity of OregonEugeneUSA

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