Fast low-rank solution of the Poisson equation with application to the Stokes problem

2013/06/10 by Ekaterina Muravleva, Ivan Oseledets, Muravleva, E. A. +1
Computer Science · Mathematics · Physics and Astronomy · #15A69 #65F08 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1306.2150

openalex publication_date 2013/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the problem of computing approximate solution of Poisson equation in the low-parametric tensor formats. We propose a new algorithm to compute the solution based on the cross approximation algorithm in the frequency space, and it has better complexity with respect to ranks in comparison with standard algorithms, which are based on the exponential sums approximation. To illustrate the effectiveness of our solver, we incorporate into a Uzawa solver for the Stokes problem on semi-staggered grid as a subsolver. The resulting solver outperforms the standard method for n ≥ 256.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• TT-cross approximation for multidimensional arrays

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