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

Sabelfeld Karl K. ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Acad. Sci, 630090, Lavrentiev Str. 6, Novosibirsk; and Novosibirsk State University, Russia

Monte Carlo Methods and Applications, 2019, vol. 25, issue 1, 85-96

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.

Keywords: Green’s function; heat equation; fundamental solution; spherical integral relation; fist passage time; double randomization; cathodoluminescence imaging (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1515/mcma-2019-2032

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