The simulation of three dimensional structural dynamics on massively parallel platforms places stringent requirements on the existing software infrastructure. A constrained and nonlinear graph partitioning problem that arises in scalable iterative substructuring methods, such as FETI methods, is identified. New sufficient criteria on a partition are presented that ensure the applicability of FE...

This paper is concerned with the construction and analysis of a parallel preconditioner for a FETI-DP system of equations arising from the nonconforming Crouzeix-Raviart finite element discretization of a model elliptic problem of second order with discontinuous coefficients. We show that the condition number of the preconditioned problem is independent of the coefficient jumps, and grows only ...

Until now, many implementations of the FETI method have been designed either as sequential codes on a single CPU, or as parallel implementations with a One Subdomain per Processor approach. This approach has been particularly typical of implementations on distributed memory architectures such as the IBM SP2. In the last couple of years, several computer manufacturers have introduced new machine...

We present a formulation of the FETI substructuring method as a matrix preconditioning algorithm and report on theoretical results and practical experience in large scale parallel implementations. The method has quasi-optimal convergence properties: the condition number can be proved to be independent of the number of subdomains, and to grow at most polylogarithmically with the number of elemen...

Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions

We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination with the principle of relativity and the presumed nature of Euclidean space a...