A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems

Abstract

AbstractWe present a new efficient and scalable domain decomposition method for solving implicitly linear and non‐linear time‐dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time‐independent problems. Computational results confirm that the optimal convergence properties of the time‐independent FETI method are preserved in the time‐dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large‐scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time‐dependent problems, including the fictitious domain decomposition method.