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A FETI‐based domain decomposition technique for time‐dependent first‐order systems based on a DAE approach
Author(s) -
Nakshatrala K. B.,
Hjelmstad K. D.,
Tortorelli D. A.
Publication year - 2008
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.2303
Subject(s) - feti , mortar methods , domain decomposition methods , lagrange multiplier , coupling (piping) , interface (matter) , constraint algorithm , schur complement , algebraic equation , transient (computer programming) , mathematics , computer science , partial differential equation , algorithm , mathematical optimization , finite element method , nonlinear system , mathematical analysis , parallel computing , engineering , maximum bubble pressure method , operating system , structural engineering , mechanical engineering , eigenvalues and eigenvectors , physics , bubble , quantum mechanics
We present a novel partitioned coupling algorithm to solve first‐order time‐dependent non‐linear problems (e.g. transient heat conduction). The spatial domain is partitioned into a set of totally disconnected subdomains. The continuity conditions at the interface are modeled using a dual Schur formulation where the Lagrange multipliers represent the interface fluxes (or the reaction forces) that are required to maintain the continuity conditions. The interface equations along with the subdomain equations lead to a system of differential algebraic equations (DAEs). For the resulting equations a numerical algorithm is developed, which includes choosing appropriate constraint stabilization techniques. The algorithm first solves for the interface Lagrange multipliers, which are subsequently used to advance the solution in the subdomains. The proposed coupling algorithm enables arbitrary numeric schemes to be coupled with different time steps (i.e. it allows subcycling) in each subdomain. This implies that existing software and numerical techniques can be used to solve each subdomain separately. The coupling algorithm can also be applied to multiple subdomains and is suitable for parallel computers. We present examples showing the feasibility of the proposed coupling algorithm. Copyright © 2008 John Wiley & Sons, Ltd.