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UID:5085@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240319T100000
DTEND;TZID=Europe/Paris:20240319T110000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-35-2/
SUMMARY: (...): Block preconditioning methods for asymptotic preserving sch
 eme arising in anisotropic elliptic problems
DESCRIPTION:: Efficient and robust iterative solvers for strongly anisotrop
 ic elliptic equations are very challenging. Indeed\, the discretization o
 f this class of problems gives rise to a linear system with a condition nu
 mber increasing with  anisotropic strength. This weakness is addressed c
 learly by adopting  the asymptotic-preserving (AP) discretizations. In th
 is work a block preconditioning method is introduced to solve the linear a
 lgebraic systems of a class of micro-macro asymptotic-preserving (MMAP) s
 cheme. The MMAP method was developed by Degond et al. in 2012 where its c
 orresponding discrete matrix has a 2x2 block structure. Motivated by appro
 ximate Schur complements\, a series of block preconditioners are construct
 ed. We first analyze a natural approximate Schur complement that is the co
 efficient matrix of the original Non-AP discretization. However it tends t
 o be singular for very small anisotropic parameters. We then improve it by
  using more suitable approximation for boundary rows of the exact Schur c
 omplement. With these block preconditioners\, a preconditioned GMRES itera
 tive method is developed to solve the discrete equations. Several numeric
 al tests show that block preconditioning methods can be a practically usef
 ul strategy with respect to grid refinement and  anisotropic strengths.
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
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 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20231029T020000
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