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Computational Science, Engineering & Technology Series
ISSN 1759-3158
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

Full Bibliographic Reference for this chapter
L. Lämmer, "Parallel Solution Methods for Structural Mechanics Problems", in B.H.V. Topping, L. Lämmer, (Editors), "High Performance Computing for Computational Mechanics", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 119-132, 2000. doi:10.4203/csets.4.7
Sub-structuring is a well-known 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 non-overlapping domain decomposition approach. The computational domain is split into disjoint sets of elements. Every finite element is assigned to exactly one sub-domain. The mathematical problem is split into a number of local problems to be solved in the interior of every sub-domain and an interface problem. A number of solution techniques are available to solve these problems. The primal sub-structuring method is based on the Schur-Complement 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 sub-structuring 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 sub-structuring methods will be shown.

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