Experiments with MRAI time stepping schemes on a distributed memory parallel environment

P. Sloot (Editor), Mikhail A. Bochev, M. Bubak (Editor), L.O. Hertzberger (Editor)

    Research output: Contribution to conferencePaper

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    Abstract

    Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way to apply the approach is to modify a given implicit scheme in which one is interested. Here, we present numerical results for two parallel implementations of MRAI schemes. One is based on the simple Euler Backward scheme, and the other is the MRAI-modified multistep ODE solver LSODE. On the Cray T3E and IBM SP2 platforms, the MRAI codes exhibit parallelism of explicit schemes. The model problem under consideration is the 3D spatially discretized heat equation. The speed-up results for the Cray T3E and IBM SP2 are reported.
    Original languageUndefined
    Pages872-874
    Number of pages3
    Publication statusPublished - 1998

    Keywords

    • EWI-8612
    • IR-66732

    Cite this

    Sloot, P. (Ed.), Bochev, M. A., Bubak, M. (Ed.), & Hertzberger, L. O. (Ed.) (1998). Experiments with MRAI time stepping schemes on a distributed memory parallel environment. 872-874.
    Sloot, P. (Editor) ; Bochev, Mikhail A. ; Bubak, M. (Editor) ; Hertzberger, L.O. (Editor). / Experiments with MRAI time stepping schemes on a distributed memory parallel environment. 3 p.
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    abstract = "Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way to apply the approach is to modify a given implicit scheme in which one is interested. Here, we present numerical results for two parallel implementations of MRAI schemes. One is based on the simple Euler Backward scheme, and the other is the MRAI-modified multistep ODE solver LSODE. On the Cray T3E and IBM SP2 platforms, the MRAI codes exhibit parallelism of explicit schemes. The model problem under consideration is the 3D spatially discretized heat equation. The speed-up results for the Cray T3E and IBM SP2 are reported.",
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    Sloot, P (ed.), Bochev, MA, Bubak, M (ed.) & Hertzberger, LO (ed.) 1998, 'Experiments with MRAI time stepping schemes on a distributed memory parallel environment' pp. 872-874.

    Experiments with MRAI time stepping schemes on a distributed memory parallel environment. / Sloot, P. (Editor); Bochev, Mikhail A.; Bubak, M. (Editor); Hertzberger, L.O. (Editor).

    1998. 872-874.

    Research output: Contribution to conferencePaper

    TY - CONF

    T1 - Experiments with MRAI time stepping schemes on a distributed memory parallel environment

    AU - Bochev, Mikhail A.

    A2 - Sloot, P.

    A2 - Bubak, M.

    A2 - Hertzberger, L.O.

    N1 - Note different possible spellings of author's name: "Botchev" or "Bochev"

    PY - 1998

    Y1 - 1998

    N2 - Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way to apply the approach is to modify a given implicit scheme in which one is interested. Here, we present numerical results for two parallel implementations of MRAI schemes. One is based on the simple Euler Backward scheme, and the other is the MRAI-modified multistep ODE solver LSODE. On the Cray T3E and IBM SP2 platforms, the MRAI codes exhibit parallelism of explicit schemes. The model problem under consideration is the 3D spatially discretized heat equation. The speed-up results for the Cray T3E and IBM SP2 are reported.

    AB - Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way to apply the approach is to modify a given implicit scheme in which one is interested. Here, we present numerical results for two parallel implementations of MRAI schemes. One is based on the simple Euler Backward scheme, and the other is the MRAI-modified multistep ODE solver LSODE. On the Cray T3E and IBM SP2 platforms, the MRAI codes exhibit parallelism of explicit schemes. The model problem under consideration is the 3D spatially discretized heat equation. The speed-up results for the Cray T3E and IBM SP2 are reported.

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    Sloot P, (ed.), Bochev MA, Bubak M, (ed.), Hertzberger LO, (ed.). Experiments with MRAI time stepping schemes on a distributed memory parallel environment. 1998.