New matrix-by-vector multiplications based on a nonoverlapping domain decomposition data distribution
The nonoverlapping domain decomposition (DD) method allows to store vectors as accumulated or as distributed (each process stores a part of that value vectors. The case of distributed stored matrices is fully investigated, whereas the use of accumulated matrices is not customary in the DD community. This paper is concerned with the accumulated matrices and investigates conditions under which matrix-by-vector multiplications can be realized. Especially, we derive restrictions on the matrix shape and the finite element (FE) mesh. As a new result, the special structure of these admissible accumulated matrices leads directly to global incomplete factorizations as preconditioners in CG-like methods. Also, the well-known DD preconditioners fit into the general framework of the matrix-by-vector operations presented.
KeywordsParallel Iterative Solvers Incomplete Factorization Preconditioning Domain Decomposition Finite Element Method
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