Parallel Linear Systems Solvers: Sparse Iterative Methods

Vorst, Henk A. van der

doi:10.1007/978-94-009-0271-8_5

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“…However, they tend to iterate the most on the coarsest grid. (2) Krylov subspace algorithms, such as CG or GMRES [9], parallelize well and need few communications per iteration. Therefore, parallel MG is efficient only on tightly coupled systems [5].…”

Section: Introductionmentioning

confidence: 99%

A Direct Schur-Fourier Decomposition for the Solution of the Three-Dimensional Poisson Equation of Incompressible Flow Problems Using Loosely Coupled Parallel Computers

Sòria¹,

Segarra²,

Oliva³

2003

Numerical Heat Transfer, Part B: Fundamentals

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Parallel computers based on PC-class hardware (Beowulf clusters) provide a matchless computing power per cost unit. However, their network performance tends to be too low for standard parallel computational fluid dynamics (CFD) algorithms. A relevant example is the solution of the Poisson equations. The subject of this article is a direct Schur-Fourier decomposition (DSFD) algorithm that, for certain three-dimensional flows, produces an accurate solution of each Poisson equation with just one message, providing speed-ups of at least 24 in a low-cost PC cluster with a conventional network and 36 processors. Direct Numerical Simulation (DNS) of turbulent natural convection flow is used as a benchmark problem.

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Section: Introductionmentioning

confidence: 99%