Abstract
The slice-based substructuring methods introduced in this paper are Schur complement solvers for the decomposition of a three-dimensional domain into multiple disjoint subdomains with interior crosspoints. The subdomains are assembled into nonoverlapping slices such that the edges of each slice lie on the boundary of the given domain and the union of the faces between slices contains all of the interior vertices. For the subproblems corresponding to the various faces, a direct fast Poisson solver is used. Scalability is achieved in two stages where the slices change such that the faces between slices at one stage are orthogonal to the faces between slices at the other. The two stages guarantee a good rate of convergence of the resulting preconditioned iterative procedure, which is optimal with respect to the partitioning parameters.
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