Multi-parameterized Schwarz alternating methods for elliptic boundary value problems

S.-B. Kim, A. Hadjidimos, E.N. Houstis and J.R. Rice

Mathematics and Computers in Simulation (MATCOM), 1996, vol. 42, issue 1, 47-76

Abstract: The convergence rate of a numerical procedure based on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVPs) depends on the selection of the so-called interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the weighted mixed interface conditions (g(u) = ωu + (1 − ω)ϖuϖn), controlled by the parameter ω, can optimize SAMs convergence rate. In this paper, we present a matrix formulation of this method based on finite difference approximation of the BVP, review its known computational behavior in terms of the parameter α = /gf(ω, h), where h is the discretization parameter and /gf is a derivable relation, and obtain analytically explicit and implicit expressions for the optimum α. Moreover, we consider a parameterized SAM where the parameter ω or α is assumed to be different in each overlapping area. For this SAM and the one-dimensional (1-D) elliptic model BVPs, we determine analytically the optimal values of αi. Furthermore, we extend some of these results to two-dimensional (2-D) elliptic problems.

Keywords: Elliptic partial differential equations; Schwarz alternating method; Jacobi, Gauss-Seidel, SOR iterative methods (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:42:y:1996:i:1:p:47-76

DOI: 10.1016/0378-4754(95)00111-5

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