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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 4
HIGH PERFORMANCE COMPUTING FOR COMPUTATIONAL MECHANICS Edited by: B.H.V. Topping, L. Lämmer
Chapter 7
Parallel Solution Methods for Structural Mechanics Problems L. Lämmer
University of Technology Darmstadt, Darmstadt, Germany L. Lämmer, "Parallel Solution Methods for Structural Mechanics Problems", in B.H.V. Topping, L. Lämmer, (Editors), "High Performance Computing for Computational Mechanics", SaxeCoburg Publications, Stirlingshire, UK, Chapter 7, pp 119132, 2000. doi:10.4203/csets.4.7
Abstract
Substructuring is a wellknown method to reduce the required
amount of storage for the system of equations arising from a finite element discretisation
of partial differential equation problems. The significant reduction of
main memory consumption results in faster solution procedures. The technique
is implemented both on special purpose parallel computers as well as on network
connected workstations. The method is equivalent to the nonoverlapping domain
decomposition approach. The computational domain is split into disjoint
sets of elements. Every finite element is assigned to exactly one subdomain. The
mathematical problem is split into a number of local problems to be solved in
the interior of every subdomain and an interface problem. A number of solution
techniques are available to solve these problems. The primal substructuring
method is based on the SchurComplement decomposition. The local problem
can be solved directly or iteratively and completely in parallel. The global problem
in the displacements of the coupling nodes has to be solved efficiently iteratively
only. The dual method introduces Lagrange multipliers as additional
forces to ensure the compatibility between displacements in completely decoupled
substructures. The new, dual global problem is solved iteratively, too.
The efficiency stability of the dual substructuring method is superior for a number of structural mechanics problems in comparison to the primal substructuring. Details of a portable implementation of a portable implementation framework of the presented substructuring methods will be shown. purchase the fulltext of this chapter (price £20)
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