UN CO RR EC TE D PR O O F 1 Newton - Schwarz Optimised Waveform Relaxation 2 Krylov Accelerators for Nonlinear Reactive Transport 3
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چکیده
Krylov-type methods are widely used in order to accelerate the convergence of 10 Schwarz-type methods in the linear case. Authors in [2] have shown that they ac11 celerate without overhead cost the convergence speed of Schwarz methods for dif12 ferent types of transmission conditions. In the nonlinear context, the well-known 13 class of Newton-Krylov-Schwarz methods (cf. [5]) for steady-state problems or time14 dependent problems uses the following strategy: time-dependent problems are dis15 cretised uniformly in time first and then one proceeds as for steady-state problems, 16 i.e. the nonlinear problem is solved by a Newton method where the linear system 17 at each iteration is solved by a Krylov-type method preconditioned by an algebraic 18 Schwarz method. The major limitation is that NKS methods do not allow different 19 time discretisations in the subdomains since the problem is discretised in time uni20 formly up from the beginning. 21
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1 Institute of Geophysics and Planetary Physics, University of California at Los Angeles, 5 405 Hilgard Avenue, Los Angeles, CA 90024-1567, United States, 6 [email protected] 7 2 INRIA Grenoble Rhône-Alpes, Montbonnot, 38334 Saint Ismier Cedex, France and Jean 8 Kuntzmann Laboratory, BP 53, 38041 Grenoble Cedex 9, France, 9 [email protected] 10 3 University of Grenoble and Jean Kuntzm...
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تاریخ انتشار 2013