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Stabilized explicit-implicit domain decomposition methods for the numerical solution of parabolic equations. (English) Zbl 1013.65106

Summary: We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition methods, which, when compared with Schwarz-algorithm-based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions. By adding a stabilization step to EIDD, the SEIDD methods retain the time-stepwise efficiency in computation and communication of the EIDD methods but exhibit much better numerical stability.
Three SEIDD algorithms are presented in this paper, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65Y05 Parallel numerical computation
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