A global random walk on spheres algorithm for transient heat equation and some extensions

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4 Citations (Scopus)

Abstract

We suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the symmetry property of the Green function and a double randomization approach. We present the gRWS method for the heat equation with arbitrary initial and boundary conditions, and the Laplace equation. Detailed description is given for 3D problems; the 2D problems can be treated analogously. Further extensions to advection-diffusion-reaction equations will be presented in a forthcoming paper.

Original languageEnglish
Pages (from-to)85-96
Number of pages12
JournalMonte Carlo Methods and Applications
Volume25
Issue number1
DOIs
Publication statusPublished - 1 Mar 2019

Keywords

  • cathodoluminescence imaging
  • double randomization
  • fundamental solution
  • Green's function
  • heat equation
  • spherical integral relation,fist passage time
  • spherical integral relation
  • fist passage time

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