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A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems
Author(s) -
Farhat Charbel,
Chen PoShu,
Mandel Jan
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620382207
Subject(s) - feti , mortar methods , domain decomposition methods , lagrange multiplier , solver , finite element method , computer science , scalability , mathematical optimization , convergence (economics) , algorithm , computational science , parallel computing , mathematics , physics , database , thermodynamics , economics , economic growth
We 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.