BIT Numerical Mathematics ( IF 1.5 ) Pub Date : 2021-04-28 , DOI: 10.1007/s10543-021-00864-1 Jehanzeb H. Chaudhry , Donald Estep , Simon J. Tavener
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.
中文翻译:
Schwarz重叠域分解方法的后验误差分析。
域分解方法被广泛用于高性能计算机上偏微分方程的数值解。我们为乘法和加法重叠Schwarz域分解方法开发了基于伴随的后验误差分析。用户指定的解决方案功能(感兴趣的数量)中的数值误差被分解为由于子域之间的有限迭代和空间离散而产生的贡献。空间离散贡献进一步分解为每个子域产生的贡献。数值误差的这种分解用于构造两阶段求解策略,该策略通过调整对误差的相对贡献来有效地减少感兴趣量中的误差。