Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 3 : pp. 368–373
Abstract
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity $n^2 \log n$ on a $n \times n$ grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8697
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 3 : pp. 368–373
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: Stability of elliptic initial value problems Parabolic wave equation Inverse problems in acoustics and electromagnetics.