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Algebraic subproblem decomposition methods and parallel algorithms with monotone convergence. (English) Zbl 0793.65040

Summary: We discuss the solution of a kind of systems of algebraic equations which arise from the discretization of symmetric or nonsymmetric elliptic boundary value problems including the related problems of parabolic type, weakly nonlinear elliptic problems, and linear or nonlinear network problems. A class of algebraic subproblem decomposition methods and parallel algorithms with their iterative sequences possessing monotone convergence componentwise are proposed for these discrete systems. These methods are suitable for arbitrary domain decomposition cases with many subdomains overlapping one another.

MSC:

65H10 Numerical computation of solutions to systems of equations
65Y05 Parallel numerical computation
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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