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UID:news251@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T213252
DTSTART;TZID=Europe/Zurich:20150529T110000
SUMMARY:Seminar in Numerical Analysis: Victorita Dolean (University of Nice
 )
DESCRIPTION:For linear problems\, domain decomposition methods can be used 
 directly  as iterative solvers\, but also as preconditioners for Krylov me
 thods. In  practice\, Krylov acceleration is almost always used\, since th
 e Krylov  method finds a much better residual polynomial than the stationa
 ry  iteration\, and thus converges much faster. We show in this work that 
  also for non-linear problems\, domain decomposition methods can either be
   used directly as iterative solvers\, or one can use them as  preconditio
 ners for Newton’s method. For the concrete case of the  parallel Schwarz
  method\, we show that we obtain a preconditioner we call  RASPEN (Restric
 ted Additive Schwarz Preconditioned Exact Newton) which  is similar to ASP
 IN (Additive Schwarz Preconditioned Inexact Newton)\,  but with all compon
 ents directly defined by the iterative method. This  has the advantage tha
 t RASPEN already converges when used as an  iterative solver\, in contrast
  to ASPIN\, and we thus get a substantially  better preconditioner for New
 ton’s method. We illustrate our findings  with numerical results on the 
 Forchheimer equation and a non-linear  diffusion problem.
X-ALT-DESC:For linear problems\, domain decomposition methods can be used d
 irectly  as iterative solvers\, but also as preconditioners for Krylov met
 hods. In  practice\, Krylov acceleration is almost always used\, since the
  Krylov  method finds a much better residual polynomial than the stationar
 y  iteration\, and thus converges much faster. We show in this work that  
 also for non-linear problems\, domain decomposition methods can either be 
  used directly as iterative solvers\, or one can use them as  precondition
 ers for Newton’s method. For the concrete case of the  parallel Schwarz 
 method\, we show that we obtain a preconditioner we call  RASPEN (Restrict
 ed Additive Schwarz Preconditioned Exact Newton) which  is similar to ASPI
 N (Additive Schwarz Preconditioned Inexact Newton)\,  but with all compone
 nts directly defined by the iterative method. This  has the advantage that
  RASPEN already converges when used as an  iterative solver\, in contrast 
 to ASPIN\, and we thus get a substantially  better preconditioner for Newt
 on’s method. We illustrate our findings  with numerical results on the F
 orchheimer equation and a non-linear  diffusion problem. 
DTEND;TZID=Europe/Zurich:20150529T120000
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