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Efficient parallel algorithms for parabolic problems. (English) Zbl 1013.65090

Summary: Domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation. Implicit schemes are used in order to march with large time steps. Parallelization is realized by approximating interface values using explicit computation. Various techniques are examined, including a multistep second order explicit scheme and a one-step high-order scheme. We show that the resulting schemes are of second order global accuracy in space, and stable in the sense of S. Osher [Math. Comput. 26, 13–39 (1972; Zbl 0254.65065)] or in \(L_{\infty}\). They are optimized with respect to the parallel efficiency.

MSC:

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
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65Y05 Parallel numerical computation
65Y20 Complexity and performance of numerical algorithms
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