Component mode synthesis and eigenvalues of second order operators : discretization and algorithm

— Component mode synthesis belongs to the class ofGalerkin methods and enables to compute the eigenpairs of a differential operator on a domain that can be subdivided into different subdomains on each ofwhichpartofthe eigenpairs of the same operator are assumed to be known. Energy transfer between subdomains is achieved thanks to functions defined on the whole domain and called « static modes », A new « fixed interface » method is presented, whose discretized version extends the Hurty [1965], Craig, and Bampton [1968] one. It is based on a special choice of the « static modes » as the eigenfunctions of the Poincaré-Steklov operator associated with the domain décomposition. Error bounds are derived in the case of the heat équation on a domain in IR", n ~* 2. A class of domain décomposition algorithms and several numerical tests are also presented.