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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 20
ADVANCES IN PARALLEL AND VECTOR PROCESSING FOR STRUCTURAL MECHANICS
Edited by: B.H.V. Topping and M. Papadrakakis
Paper III.1

Adaptive Finite Element Multigrid Methods on Parallel Computers

H. Misra and I.D. Parsons

Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, United States of America

Full Bibliographic Reference for this paper
H. Misra, I.D. Parsons, "Adaptive Finite Element Multigrid Methods on Parallel Computers", in B.H.V. Topping, M. Papadrakakis, (Editors), "Advances in Parallel and Vector Processing for Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 75-82, 1994. doi:10.4203/ccp.20.3.1
Abstract
Adaptive multigrid methods are described that can be used to solve large-scale structural mechanics problems on parallel computers using the finite element method. The multigrid method was efficiently implemented on shared memory parallel computers by noting that the algorithm is dominated by matrix-vector products, and then performing these operations on the element level. Not only does this approach produce efficient code, but the storage requirements are reduced, since no element stiffness matrices need to be assembled and stored. This requires the development of a method for performing element level matrix-vector multiplications for h-refined meshes. The solution of a simple test problem demonstrates the performance of the multigrid method. It was observed that a single multigrid cycle is sufficient to obtain an approximate solution to within the discretization error of the mesh being used.

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