Stability analysis of hierarchical tensor methods for time-dependent PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:409

Article

Rodgers, Abram¹  Venturi, Daniele¹ 

[1] Univ Calif Santa Cruz, Dept Appl Math, Santa Cruz, CA 95064 USA

关键词: Hierarchical tensor methods;    High-dimensional PDEs;    Linear multistep integrators;    Fokker-Plank equation;   

DOI  :  10.1016/j.jcp.2020.109341

来源: Elsevier

【 摘 要 】

We address the question of whether it is possible to stably integrate time-dependent high-dimensional linear PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for stability and convergence of tensor solutions evolving on tensor manifolds with constant rank. We also argue that the applicability of PDE solvers with explicit time-stepping may be limited by time-step restriction dependent on the dimension of the problem. Numerical applications are presented and discussed for variable coefficients linear hyperbolic and parabolic PDEs. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free