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

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A global random walk on spheres algorithm for transient heat equation and some extensions. / Sabelfeld, Karl K.

In: Monte Carlo Methods and Applications, Vol. 25, No. 1, 01.03.2019, p. 85-96.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{7a7e61a96a1348ad8b5e1117c1c1e6d0,

title = "A global random walk on spheres algorithm for transient heat equation and some extensions",

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

author = "Sabelfeld, {Karl K.}",

year = "2019",

month = mar,

day = "1",

doi = "10.1515/mcma-2019-2032",

language = "English",

volume = "25",

pages = "85--96",

journal = "Monte Carlo Methods and Applications",

issn = "0929-9629",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

RIS

TY - JOUR

T1 - A global random walk on spheres algorithm for transient heat equation and some extensions

AU - Sabelfeld, Karl K.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - cathodoluminescence imaging

KW - double randomization

KW - fundamental solution

KW - Green's function

KW - heat equation

KW - spherical integral relation,fist passage time

KW - spherical integral relation

KW - fist passage time

UR - http://www.scopus.com/inward/record.url?scp=85062232877&partnerID=8YFLogxK

U2 - 10.1515/mcma-2019-2032

DO - 10.1515/mcma-2019-2032

M3 - Article

AN - SCOPUS:85062232877

VL - 25

SP - 85

EP - 96

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 1

ER -

ID: 18680681