Parallel modal synthesis methods in structural dynamics

Within the finite element framework, we deal with large-scale eigenvalue problems induced by free vibration analysis of complex structures. The classical approach for the solution of such problems consists first of reducing the number of unknowns, allowing to reduce the computational cost of eigensolver, because only the lowest eigenfrequencies are classically researched in modal analysis. Component mode synthesis (CMS) or dynamic substructuring methods are appropriate tools for this reduction. In this paper we will discuss about the parallel implementation of CMS methods. We consider, in particular, among several CMS methods [4], the fixed-interface method which we briefly recall. Assuming that the studied domain is partitioned in Ns non-overlapping substructures, the global solution of the eigenvalue problem to be solved in the domain can be written as the sum of the local solutions (fixed interface modes) to elasticity eigenproblem to be solved in each subdomain clamped on the interface, and extensions (constraint modes or coupling modes), in each subdomain, of functions which represent the motion of the interface. The dynamic behavior of the global structure can be approximated in the low frequencies range by truncating the series which represent the different spaces. It remains to define what kind of Dirichlet’s conditions has to be prescribed for the coupling of the substructures. The most classical choice [3] consists of prescribing at the discrete level the shape functions spanning the interfacial interpolation space. In this case, all the motions of the interface are represented, but, the number of constraint modes is equal to the number of degrees of freedom (d.o.f.) of the interface. From the parallel point of view the constraint and the fixed interface modes can be computed independently in each subdomain. An other choice, proposed by Bourquin [1], consists of filtering information in order to represent the interface’s motion only in the low frequency range, thanks to a spectral decomposition of the interface operator coupling subdomains. However, the computation of the coupling modes involves all the subdomains. We propose a parallel implementation of these methods [5] thanks to the use of techniques arising in domain decomposition.