Keywords: parallel solution, multi-frontal, substructure, large-scale, PC cluster.

Parallel solution methods are being implemented in various commercial finite element analysis programs as a consequence of having large-scale structural models and increased affordability and availability of parallel computing environments. The current research on the parallel solution methods based on direct solution mainly focuses on two different kinds of solution strategies: global and domain-by-domain. Global solution strategies focus on the efficient solution of the system of linear equations. They require the entire stiffness matrix to be assembled and distributed to the computers. The domain-by-domain strategies, on the other hand, perform partitioning at the structural level and as a result they parallelize not only the equation solution but also the stiffness matrix generation, assembly, element force and stress computations.

This paper presents a comparative study on two different direct parallel solution strategies for the linear solution of large scale finite element models: global and domain-by-domain. The global solution strategy was examined by utilizing the parallel multi-frontal equation solver, MUMPS [1], together with a finite element program. In a similar manner a substructure based parallel solution framework [2] was utilized for investigating the domain-by-domain strategy.

Various large-scale structural models were solved with both global and domain-by-domain solution strategies in order to illustrate the efficiencies and weaknesses of each solution strategy. The test runs were performed using Windows XP running, a homogeneous PC cluster connected with an ordinary 1 GBit network switch.

The test runs performed for this study indicate that the global solution strategy was more efficient and faster than the domain-by-domain strategy for symmetric and uniform structural models but its efficiency was decreased as the symmetry and uniformity of the models diminished. The performance of the domain-by-domain strategy improved in non-uniform models and produced competitive solution times when compared to the times of the global solution strategy.

1

P.R. Amestoy, I.S. Duff, J.-Y. L'Excellent, "Multifrontal parallel distributed symmetric and unsymmetric Solvers", Comput. Methods Appl. Engrg., 184, 501-520, 2000. doi:10.1016/S0045-7825(99)00242-X

2

O. Kurc, "Parallel Computing in Structural Engineering", VDM Verlag, Germany, 2008.

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