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SUMMARY:Least-Squares methods for the Monge-Ampère equation
DTSTART:20100224T160000
DTSTAMP:20260511T050500Z
UID:78a83a73f2fb7e33d92fff313baa55961c8ad455f8c51afe15a165df
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Alexandre Caboussat\nThe Monge-Ampère equation is the m
 ost important equation in the field of \nfully nonlinear partial different
 ial equations.\n\nIn this talk\, we present a least-squares framework for 
 the numerical \nsolution of the Dirichlet problem for the Monge-Ampère eq
 uation in two \ndimensions of space.\nIn order to handle those situations 
 where this problem has no classical \nsolutions\, we introduce a concept o
 f generalized solutions. We detail in \nparticular a relaxation method wel
 l-suited to the particular structure \nof the least-squares problem. This 
 iterative method allows to decouple \nthe differential operators from poin
 t-wise nonlinear problems. We \npresent fast and robust algorithms relying
  on mixed finite element \napproximations\, which couple a conjugate gradi
 ent algorithm and local \nalgebraic solvers.\n\nNumerical experiments are 
 finally presented for various examples in two \ndimensions of space.\n\nTh
 is is a joint work with Roland Glowinski (University of Houston) and Danny
  C. Sorensen (Rice University).
LOCATION:MAA112
STATUS:CONFIRMED
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