Parallel tensor methods for high-dimensional linear PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:375

Article

Boelens, Arnout M. P.¹  Venturi, Daniele²  Tartakovsky, Daniel M.¹ 

[1] Stanford Univ, Dept Energy Resources Engn, Stanford, CA 94305 USA

[2] UC Santa Cruz, Dept Appl Math & Stat, Santa Cruz, CA 95064 USA

关键词: PDF equation;    Method of distributions;    High-dimensional PDEs;   

DOI  :  10.1016/j.jcp.2018.08.057

来源: Elsevier

【 摘 要 】

High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and Fokker-Planck equations. We develop new parallel algorithms to solve such high-dimensional PDEs. The algorithms are based on canonical and hierarchical numerical tensor methods combined with alternating least squares and hierarchical singular value decomposition. Both implicit and explicit integration schemes are presented and discussed. We demonstrate the accuracy and efficiency of the proposed new algorithms in computing the numerical solution to both an advection equation in six variables plus time and a linearized version of the Boltzmann equation. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free