COUPLING PARAREAL WITH OPTIMIZED SCHWARZ WAVEFORM RELAXATION FOR PARABOLIC PROBLEMS

被引：7

作者：

Duc Quang Bui ^{[1
]}

Japhet, Caroline ^{[1
]}

Maday, Yvon ^{[2
,3
]}

Omnes, Pascal ^{[1
,4
]}

机构：

[1] Univ Sorbonne Paris Nord, LAGA, Lab Geometrie Anal & Applicat, CNRS,UMR 7539, F-93430 Villetaneuse, France

[2] Univ Paris, Sorbonne Univ, CNRS, Lab Jacques Louis Lions LJLL, F-75005 Paris, France

[3] Inst Univ France, F-75005 Paris, France

[4] CEA Saclay, DM2S STMF, F-91191 Gif Sur Yvette, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2022年 / 60卷 / 03期

关键词：

optimized Schwarz waveform relaxation; domain decomposition; Parareal in time algorithm; Robin transmission conditions; convergence rates; TIME DOMAIN DECOMPOSITION; POSTERIORI STOPPING CRITERIA; DISCRETIZATION; EQUATION;

D O I：

10.1137/21M1419428

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose and analyze a new parallel paradigm that uses both the time and the space directions. The original approach couples the Parareal algorithm with incomplete optimized Schwarz waveform relaxation (OSWR) iterations. The analysis of this coupled method is presented for a one-dimensional advection-reaction-diffusion equation. We also prove a general convergence result for this method via energy estimates. Numerical results for two-dimensional advection-diffusion problems and for a diffusion equation with strong heterogeneities are presented to illustrate the performance of the coupled Parareal-OSWR algorithm.

引用

页码：913 / 939

页数：27

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