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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 II.5

A Constrained Element-by-Element Method for Slightly Compressible and Incompressible Materials and its Parallel Implementation on Transputers

M.H.B.M. Shariff

School of Computing & Mathematics, University of Teesside, Middlesbrough, United Kingdom

Full Bibliographic Reference for this paper
M.H.B.M. Shariff, "A Constrained Element-by-Element Method for Slightly Compressible and Incompressible Materials and its Parallel Implementation on Transputers", in B.H.V. Topping, M. Papadrakakis, (Editors), "Advances in Parallel and Vector Processing for Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 53-57, 1994. doi:10.4203/ccp.20.2.5
Abstract
In this paper we report on the implementation of an iterative solver for large-scale finite element problems for slightly compressible and incompressible elastic materials based on a linear constrained conjugate gradient method developed by Shariff. For n number of degrees of freedom and m number of independent constraints the method converges (in exact arithmetic) in at most n-m iterations. A constrained variational (minimising) principle is developed to handle slightly compressible and incompressible elastic materials easily. An iterative element-by-element (EBE) algorithm is given which has an important feature that it is locally additive and easily parallelisable. Numerical studies are performed using 4 transputers. Our program attains a speed-up factor of greater than three when run on four transputers. Extension to nonlinear elasticity is currently being investigated.

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