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SUMMARY:WaveHoltz: Wave Based Iterative Scheme for Helmholtz Problems - Fo
 rtino Garcia (Courant Institute of Mathematical Sciences)
DTSTART:20230419T104500Z
DTEND:20230419T113000Z
UID:TALK198736@talks.cam.ac.uk
DESCRIPTION:Designing efficient iterative solvers for the Helmholtz equati
 on is notoriously difficult\, with the two main difficulties being the res
 olution requirements and the highly indefinite character of the discretize
 d system of equations. The dependence of the number of degrees of freedom 
 on the frequency of the problem requires high frequency Helmholtz solvers 
 to be: (1) parallel\, memory lean\, and scalable\, (2) high order accurate
  to overcome the penalty due to pollution/dispersion errors.\nIn this talk
  we will introduce the WaveHoltz iteration (WHI) which makes use of time-d
 omain methods for wave equations to design Helmholtz solvers. We show that
  the WaveHoltz iteration is symmetric and positive definite in the continu
 ous setting for energy conserving boundary conditions. Numerical examples 
 using various discretization techniques that demonstrate the method can be
  used to solve problems with rather high wave numbers in a memory lean and
  scalable fashion will be presented\, as well as recent extensions to prob
 lems in elastic media.\nThis is joint work with Daniel Appel&ouml\; (MSU)\
 , Olof Runborg (KTH)\, and Allen Alvarez Loya (Los Alamos National Laborat
 ory)
LOCATION:Seminar Room 1\, Newton Institute
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