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#### A hybrid BIE-WOS (Boundary Integral Equation-Random Walk on Spheres) Method for Laplace Equations

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**Speaker(s)**Wei Cai, Dept of Math & Stat, UNC Charlotte**Date**From 2015-04-08 To 2015-04-08**Venue**理科一号楼 1365

报告人：Wei Cai, Dept of Math & Stat, UNC Charlotte

时间：4月8日，16：00-17：00

地点：理科一号楼 1365

报告系列： 数学中心计算方法与应用实验室活动/北京计算数学学会系列报告

摘要：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)