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SUMMARY:Wave propagation in inhomogeneous media with quasi-Trefftz methods
  - Lise-Marie Imbert-Gerard (University of Arizona)
DTSTART:20230419T100000Z
DTEND:20230419T104500Z
UID:TALK198733@talks.cam.ac.uk
DESCRIPTION:&nbsp\; Trefftz methods rely\, in broad terms\, on the idea of
  approximating solutions to Partial Differential Equation (PDEs) via Galer
 kin methods using basis functions which are exact solutions of the PDE\, m
 aking explicit use of information about the ambient medium. But wave propa
 gation in inhomogeneous media is modeled by PDEs with variable coefficient
 s\, and in general no exact solutions are available.&nbsp\;\n&nbsp\; Quasi
 -Trefftz methods have been introduced\, in the case of the Helmholtz equat
 ion with variable coefficients\, to address this problem: they rely not on
  exact solutions to the PDE but instead of high order approximate solution
 s constructed locally. We will discuss the origin\, the construction\, and
  the properties of these so-called quasi-Trefftz functions. We will also d
 iscuss the consistency error introduced by this construction process.
LOCATION:Seminar Room 1\, Newton Institute
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