The Parallel Performance and Implementation of an Adaptive Multigrid Algorithm
Misra, Himanshu
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https://hdl.handle.net/2142/72209
Description
Title
The Parallel Performance and Implementation of an Adaptive Multigrid Algorithm
Author(s)
Misra, Himanshu
Issue Date
1993
Doctoral Committee Chair(s)
Parsons, Ian D.,
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Civil
Engineering, Mechanical
Abstract
An adaptive multigrid algorithm has been implemented on shared memory parallel computers to solve large-scale structural mechanics problems. The solution algorithm begins by solving the problem on the initial mesh, refining this mesh as required by the chosen adaptive scheme, and then solving the problem on the new mesh using the multigrid method and all of the previous meshes. This procedure is repeated until a sufficiently fine mesh is produced that meets the specified error tolerance. A very general scheme has been proposed to impose multi-point constraints in such a way that the parallel nature of the multigrid algorithm is maintained. The matrix-vector operations involved in the multigrid algorithm have been computed in a three stage process, each of which are performed on an element level and are fully optimized by processing blocks of elements in vector-concurrent mode. The element-by-element computations reduce the requirements on storage and are easy to parallelize. Numerical results indicate that the computational effort is approximately linearly proportional to the problem size. Maximum speed-ups of around 3.75 were achieved on a 4 processor Convex, indicating that almost 98% of the solution algorithm has been parallelized. The convergence behavior of the multigrid cycles was also studied and results obtained suggest a new approach, based on the value of the global relative percent error, for terminating multigrid iterations on a given mesh.
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