Unstructured multigrid strategies on massively parallel computers: a case for integrated design

Multigrid techniques have been used successfully in practice to speed up the convergence of computationally intensive, PDE iterative solution schemes. Instead of iterating to termination accuracy on a fine grid, multigrid algorithms move computation among a hierarchy of grids. Adapting structured mu...

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Published in:Hawaii International Conference on System Sciences, 27th. Vol. 5: Biotechnology Vol. 2; pp. 169 - 178
Main Authors: Dorward, Matheson, Tarjan
Format: Conference Proceeding
Language:English
Published: IEEE Comput. Soc. Press 1994
Subjects:
Convergence of numerical methods
Design methodology
Iterative methods
Parallel algorithms
Partial differential equations
ISBN:0818650907, 9780818650901
Online Access:Get full text
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Abstract Multigrid techniques have been used successfully in practice to speed up the convergence of computationally intensive, PDE iterative solution schemes. Instead of iterating to termination accuracy on a fine grid, multigrid algorithms move computation among a hierarchy of grids. Adapting structured multigrid techniques to unstructured mesh hierarchies requires a substantial increase in preprocessing tasks such as mesh generation, discretization, and the construction of inter-mesh transfer operators. In addition, the current generation of medium-grained parallel supercomputers requires a set of good domain partitions for efficient parallel execution. We present three practical strategies to efficiently accomplish these preprocessing tasks. These strategies were designed to address large problem sizes by using fast, simple heuristics. We present analytical and experimental work demonstrating the viability of these strategies. Issues and directions are presented for future work toward the goal of efficient implementing 3D unstructured multigrid algorithms on the current generation of supercomputers.< >
AbstractList Multigrid techniques have been used successfully in practice to speed up the convergence of computationally intensive, PDE iterative solution schemes. Instead of iterating to termination accuracy on a fine grid, multigrid algorithms move computation among a hierarchy of grids. Adapting structured multigrid techniques to unstructured mesh hierarchies requires a substantial increase in preprocessing tasks such as mesh generation, discretization, and the construction of inter-mesh transfer operators. In addition, the current generation of medium-grained parallel supercomputers requires a set of good domain partitions for efficient parallel execution. We present three practical strategies to efficiently accomplish these preprocessing tasks. These strategies were designed to address large problem sizes by using fast, simple heuristics. We present analytical and experimental work demonstrating the viability of these strategies. Issues and directions are presented for future work toward the goal of efficient implementing 3D unstructured multigrid algorithms on the current generation of supercomputers.< >
Author Dorward
Tarjan
Matheson
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  surname: Tarjan
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PublicationTitle Hawaii International Conference on System Sciences, 27th. Vol. 5: Biotechnology
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Snippet Multigrid techniques have been used successfully in practice to speed up the convergence of computationally intensive, PDE iterative solution schemes. Instead...
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StartPage 169
SubjectTerms Convergence of numerical methods
Design methodology
Iterative methods
Parallel algorithms
Partial differential equations
Title Unstructured multigrid strategies on massively parallel computers: a case for integrated design
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