Balancing Domain Decomposition
نویسنده
چکیده
The Neumann-Neumann algorithm is known to be an e cient domain decomposition preconditioner with unstructured subdomains for iterative solution of nite element discretizations of di cult problems with strongly discontinuous coe cients [6]. However, this algorithm su ers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems, such as those that arize in elasticity. A convergence bound independent on the number of subdomains is proved and results of computational tests are reported.
منابع مشابه
Numerical Implementation of Overlapping Balancing Domain Decomposition Methods on Unstructured Meshes
The Overlapping Balancing Domain Decomposition (OBDD) methods can be considered as an extension of the Balancing Domain Decomposition (BDD) methods to the case of overlapping subdomains. This new approach, has been proposed and studied in [4, 3]. In this paper, we will discuss its practical parallel implementation and present numerical experiments on large unstructured meshes.
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