Stability analysis of numerical boundary conditions in domain decomposition algorithms

摘要

This paper discusses numerical stability of a class of non-overlapping domain decomposition algorithms. Inherent shortcomings associated with different methods for proving stability are pointed out. Von Neumann analysis yields only a necessary condition for stability because it does not consider the overall effect of the boundary conditions between subdomains. Matrix analysis produces also a necessary condition for stability since the matrices of coefficients associated with the algorithms are not symmetric. The GKSO, on the other hand, produces necessary and sufficient conditions for stability. However, it is difficult to apply systematically this analysis to the algorithms.