A domain splitting algorithm for parabolic problems. (English. German summary) Zbl 0767.65073

Blum, H.; Lisky, S.; Rannacher, R.

Computing 49, No. 1, 11-23 (1992).

Summary: In the parallel implementation of solution methods for parabolic problems one has to find a proper balance between the parallel efficiency of a fully explicit scheme and the need for stability and accuracy which requires some degree of implicitness. As a compromise a domain splitting scheme is proposed which is locally implicit on slightly overlapping subdomains but propagates the corresponding boundary data by a simple explicit process. The analysis of this algorithm shows that it has satisfactory stability and approximation properties and can be effectively parallelized. These theoretical results are confirmed by numerical tests on a transputer system.

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65L05	Numerical methods for initial value problems
65L12	Finite difference and finite volume methods for ordinary differential equations
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15	Initial value problems for second-order parabolic equations
34A34	Nonlinear ordinary differential equations and systems, general theory

Keywords:

domain decomposition; parallel time stepping; transputer system; parallel implementation; fully explicit scheme; stability; domain splitting scheme; numerical tests

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