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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Modulated plane wave methods for Helmholtz problem
s in heterogeneous media - Betcke\, T (University
College London)
DTSTART;TZID=Europe/London:20111213T090000
DTEND;TZID=Europe/London:20111213T093000
UID:TALK34933AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34933
DESCRIPTION:A major challenge in seismic imaging is full wavef
orm inversion in the frequency domain. If an acous
tic model is assumed the underlying problem formul
ation is a Helmholtz equation with varying speed o
f sound. Typically\, in seismic applications the s
olution has many wavelengths across the computatio
nal domain\, leading to very large linear systems
after discretisation with standard finite element
methods. Much progress has been achieved in recent
years by the development of better preconditioner
s for the iterative solution of these linear syste
ms. But the fundamental problem of requiring many\
ndegrees of freedom per wavelength for the discret
isation remains.\n\nFor problems in homogeneous me
dia\, that is\, spatially constant wave velocity\,
plane wave finite element methods have gained sig
nificant attention. The idea is that instead of po
lynomials on each element we use a linear combinat
ion of oscillatory plane wave solutions. These bas
is functions already oscillate with the right wave
length\, leading to a significant reduction in the
required number of unknowns. However\, higher-ord
er convergence is only achieved for problems with
constant or piecewise constant media.\n\nIn this t
alk we discuss the use of modulated plane waves in
heterogeneous media\, products of low-degree poly
nomials and oscillatory plane wave solutions for a
(local) average homogeneous medium. The idea is t
hat high-order convergence in a varying medium is
recovered due to the polynomial modulation of the
plane waves. Wave directions are chosen based on i
nformation from raytracing or other fast solvers f
or the eikonal equation. This approach is related
to the Amplitude FEM originally proposed by Giladi
and Keller in 2001. However\, for the assembly of
the systems we will use a discontinuous Galerkin
method\, which allows a simple way of incorporatin
g multiple phase information in one element. We wi
ll discuss the dependence of the element sizes on
the wavelenth and the accuracy of the phase inform
ation\, and present several examples that demonstr
ate the properties of modulated plane wave methods
for heterogeneous media problems.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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