Parallel multigrid waveform relaxation for parabolic problems

Auteurs

• Stefan Vandewalle

Paramètres

• Mathématiques

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This text presents a comprehensive overview of numerical simulation and parallel processing, focusing on time-dependent processes. It begins with an introduction to waveform relaxation methods, detailing their basic concepts, classifications, and convergence results, particularly for linear systems. The discussion extends to acceleration techniques and concludes with remarks on the methods' effectiveness. The application of waveform relaxation to initial boundary value problems is explored, including standard methods, linear multigrid acceleration, convergence analysis, and experimental results. Nonlinear multigrid approaches and a multigrid method on a space-time grid are also examined. The text further delves into time-periodic problems, comparing standard solvers with time-periodic waveform relaxation and analyzing both continuous and discrete-time iterations, along with multigrid acceleration techniques. An introduction to parallel computing follows, discussing classifications, hypercube topology, and performance parameters. The parallel implementation of standard parabolic marching schemes is detailed, including problem discretization, explicit update steps, multigrid solvers, and timing results. The computational complexity of multigrid waveform relaxation is addressed, focusing on arithmetic complexity and parallel implementation. Case studies illustrate programming considerations and results for various initial bou

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• Année de publication: 1993