Analysis of Domain Decomposition Preconditioners on L-Shaped and C-Shaped Regions

摘要

This document presents an algebraic analysis of some domain decomposition preconditioners on irregular regions. The authors analyze a preconditioner proposed in another work for the interface system and prove that, for all L-shaped regions and some C-shaped regions, it produces a convergence rate that is independent of the size of the discretization and the relative shape of the subdomains (aspect ratios). Specifically, it is proven that the condition number of the preconditioned capacitance system is bound by 2.16 for all L-shaped domains. Some results for other simple irregular geometries are also given. (kr)