A Highly Scalable Communication-free Domain Decomposition BIE-WOS (Boundary Integral Equation-Walk on Spheres) Method for Laplace Equations

A hybrid approach for solving Laplace equation in 3-D domains is presented. It is based on a local method for the Dirichlet-Neumann (DtN) or Neumann-Dirichlet (NtD) mapping of a Laplace equation by combining a deterministic boundary integral equation and the probabilistic Feynman–Kac formula for solutions of elliptic partial differential equations. This hybridization produces a parallel algorithm where bulk of the computation has no data communication between processors. Numerical implementation of the Feynman-Kac formula will be detailed, in particular the computation of local time for the reflective Brownian motions, by WOS or random walk on lattices, as required for the Neumann problem will be discussed. Numerical results show the robustness and parallel performance of the proposed method. (joint work with Dr. Chanhao Yan and Ms. Yijing Zhou)

Presentation Slides: PDF

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