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

P. Sloot; Mikhail A. Bochev; M. Bubak; L.O. Hertzberger

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)

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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 language	Undefined
Pages	872-874
Number of pages	3
Publication status	Published - 1998
Event	High-Performance Computing and Networking, International Conference and Exhibition - Amsterdam, the Netherlands Duration: 21 Apr 1998 → 23 Apr 1998

Conference

Conference	High-Performance Computing and Networking, International Conference and Exhibition
Period	21/04/98 → 23/04/98
Other	Aplril 21-23, 1998

Keywords

EWI-8612
IR-66732

Access to Document

http://www.springerlink.com/content/l554v4171270/

Cite this

@conference{10d664ff7cf548cdabfad164d08456d3,

title = "Experiments with MRAI time stepping schemes on a distributed memory parallel environment",

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.",

keywords = "EWI-8612, IR-66732",

author = "P. Sloot and Bochev, {Mikhail A.} and M. Bubak and L.O. Hertzberger",

note = "Note different possible spellings of author's name: {"}Botchev{"} or {"}Bochev{"}; High-Performance Computing and Networking, International Conference and Exhibition ; Conference date: 21-04-1998 Through 23-04-1998",

year = "1998",

language = "Undefined",

pages = "872--874",

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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.

KW - EWI-8612

KW - IR-66732

M3 - Paper

SP - 872

EP - 874

T2 - High-Performance Computing and Networking, International Conference and Exhibition

Y2 - 21 April 1998 through 23 April 1998

ER -