A posteriori error analysis for Schwarz overlapping domain decomposition methods

被引：0
|
作者：
Chaudhry, Jehanzeb H. [1 ]
Estep, Donald [2 ]
Tavener, Simon J. [3 ]
机构：
[1] Univ New Mexico, Albuquerque, NM 87131 USA
[2] Simon Fraser Univ, Burnaby, BC V5A 1S6, Canada
[3] Colorado State Univ, Ft Collins, CO 80523 USA
来源：
BIT NUMERICAL MATHEMATICS | 2021年 / 61卷 / 04期
基金：
美国国家科学基金会;
关键词：
Schwarz overlapping domain decomposition; A posteriori error estimation; Adaptive computation; FINITE-VOLUME METHODS; ELLIPTIC PROBLEMS; ELEMENT;
D O I：
10.1007/s10543-021-00864-1
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive overlapping Schwarz domain decomposition methods. The numerical error in a user-specified functional of the solution (quantity of interest) is decomposed into contributions that arise as a result of the finite iteration between the subdomains and from the spatial discretization. The spatial discretization contribution is further decomposed into contributions arising from each subdomain. This decomposition of the numerical error is used to construct a two stage solution strategy that efficiently reduces the error in the quantity of interest by adjusting the relative contributions to the error.
引用
收藏
页码：1153 / 1191
页数：39
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