Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation

被引：15

作者：

Bertaccini, D. ^{[1
,2
]}

Durastante, F. ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Viale Ric Sci 1, Rome, Italy

[2] Natl Res Council CNR, Ist Applicaz Calcolo IAC M Picone, Rome, Italy

[3] Univ Pisa, Dipartimento Informat, Largo Bruno Pontecorvo 3, Pisa, Italy

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 95卷

关键词：

Structured preconditioners in tensor form; Tensor trains; Fractional diffusion equations; Finite volumes; LINEAR-SYSTEMS;

D O I：

10.1016/j.aml.2019.03.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a tensor structured preconditioner for the tensor train GMRES algorithm (or TT-GMRES for short) to approximate the solution of the all-at-once formulation of time-dependent fractional partial differential equations discretized in time by linear multistep formulas used in boundary value form and in space by finite volumes. Numerical experiments show that the proposed preconditioner is efficient for very large problems and is competitive, in particular with respect to the AMEn algorithm. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：92 / 97

页数：6

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