Premium
Multi‐time‐step and two‐scale domain decomposition method for non‐linear structural dynamics
Author(s) -
Gravouil A.,
Combescure A.
Publication year - 2003
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.826
Subject(s) - conjugate gradient method , domain decomposition methods , scale (ratio) , multigrid method , relaxation (psychology) , algorithm , linear scale , mathematical optimization , computer science , mathematics , spacetime , space (punctuation) , linear system , grid , mathematical analysis , geometry , partial differential equation , finite element method , psychology , social psychology , physics , geodesy , quantum mechanics , thermodynamics , geography , operating system
In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two‐scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale. For non‐linear problems, we propose an algorithm with a single iteration level to deal with both the non‐linear equilibrium and the two space scales thanks to a two‐grid method in which the relaxation steps are performed using a non‐linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.