TWO-LEVEL OVERLAPPING SCHWARZ ALGORITHMS FOR A STAGGERED DISCONTINUOUS GALERKIN METHOD

被引：42

作者：

Chung, Eric T. ^{[1
]}

Kim, Hyea Hyun ^{[2
]}

Widlund, Olof B. ^{[3
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Kyung Hee Univ, Dept Appl Math, Seoul, South Korea

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 01期

基金：

美国国家科学基金会;

关键词：

domain decomposition; elliptic problems; preconditioned conjugate gradients; discontinuous Galerkin methods; staggered grids; overlapping Schwarz algorithms; DOMAIN DECOMPOSITION PRECONDITIONERS; IRREGULAR SUBDOMAINS; ELLIPTIC PROBLEMS; INTERIOR PENALTY; APPROXIMATIONS;

D O I：

10.1137/110849432

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two overlapping Schwarz algorithms are developed for a discontinuous Galerkin finite element approximation of second order scalar elliptic problems in both two and three dimensions. The discontinuous Galerkin formulation is based on a staggered discretization introduced by Chung and Engquist [SIAM J. Numer. Anal., 47 (2009), pp. 3820-3848] for the acoustic wave equation. Two types of coarse problems are introduced for the two-level Schwarz algorithms. The first is built on a nonoverlapping subdomain partition, which allows quite general subdomain partitions, and the second on introducing an additional coarse triangulation that can also be quite independent of the fine triangulation. Condition number bounds are established and numerical results are presented.

引用

页码：47 / 67

页数：21

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