A posteriori error analysis for Schwarz overlapping domain decomposition methods
A posteriori error analysis for Schwarz overlapping domain decomposition methods
复制标题
DOI：
10.1007/s10543-021-00864-1
复制
发表时间：
2019-07
影响因子：
1.5
通讯作者：
J. Chaudhry;D. Estep;S. Tavener
中科院分区：
文献类型：
--
作者：
J. Chaudhry;D. Estep;S. Tavener
区域分解法是一种在高性能计算机上求解偏微分方程的数值方法。我们开发了一个基于伴随的后验误差分析的乘法和加法重叠施瓦茨区域分解方法。在用户指定的功能的解决方案（感兴趣的量）的数值误差被分解成的贡献，所产生的结果的子域之间的有限迭代和从空间离散化。空间离散化的贡献被进一步分解为每个子域产生的贡献。数值误差的这种分解被用于构造两阶段的解决方案策略，该策略通过调整对误差的相对贡献来有效地减少感兴趣的量中的误差。
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.