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

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)85-96
Число страниц12
ЖурналMonte Carlo Methods and Applications
Том25
Номер выпуска1
DOI
СостояниеОпубликовано - 1 мар 2019

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