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SUMMARY:Modulated plane wave methods for Helmholtz problems in heterogeneo
 us media - Betcke\, T (University College London)
DTSTART:20111213T090000Z
DTEND:20111213T093000Z
UID:TALK34933@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A major challenge in seismic imaging is full waveform inversio
 n in the frequency domain. If an acoustic model is assumed the underlying 
 problem formulation is a Helmholtz equation with varying speed of sound. T
 ypically\, in seismic applications the solution has many wavelengths acros
 s the computational domain\, leading to very large linear systems after di
 scretisation with standard finite element methods. Much progress has been 
 achieved in recent years by the development of better preconditioners for 
 the iterative solution of these linear systems. But the fundamental proble
 m of requiring many\ndegrees of freedom per wavelength for the discretisat
 ion remains.\n\nFor problems in homogeneous media\, that is\, spatially co
 nstant wave velocity\, plane wave finite element methods have gained signi
 ficant attention. The idea is that instead of polynomials on each element 
 we use a linear combination of oscillatory plane wave solutions. These bas
 is functions already oscillate with the right wavelength\, leading to a si
 gnificant reduction in the required number of unknowns. However\, higher-o
 rder convergence is only achieved for problems with constant or piecewise 
 constant media.\n\nIn this talk we discuss the use of modulated plane wave
 s in heterogeneous media\, products of low-degree polynomials and oscillat
 ory plane wave solutions for a (local) average homogeneous medium. The ide
 a is that high-order convergence in a varying medium is recovered due to t
 he polynomial modulation of the plane waves. Wave directions are chosen ba
 sed on information from raytracing or other fast solvers for the eikonal e
 quation. This approach is related to the Amplitude FEM originally proposed
  by Giladi and Keller in 2001. However\, for the assembly of the systems w
 e will use a discontinuous Galerkin method\, which allows a simple way of 
 incorporating multiple phase information in one element. We will discuss t
 he dependence of the element sizes on the wavelenth and the accuracy of th
 e phase information\, and present several examples that demonstrate the pr
 operties of modulated plane wave methods for heterogeneous media problems.
 \n
LOCATION:Seminar Room 1\, Newton Institute
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