Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition
Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 809–837
Abstract
Consider an inverse obstacle scattering problem in an open space which is filled with a homogeneous and isotropic elastic medium. The inverse problem is to determine the obstacle's surface from the measurement of the displacement on an artificial boundary enclosing the obstacle. In this paper, a new approach is proposed for numerical solution of the inverse problem. By introducing two scalar potential functions, the method uses the Helmholtz decomposition to split the displacement of the elastic wave equation into the compressional and shear waves, which satisfy a coupled boundary value problem of the Helmholtz equations. The domain derivative is studied for the coupled Helmholtz system. In particular, we show that the domain derivative of the potentials is the Helmholtz decomposition of the domain derivative of the displacement for the elastic wave equation. Numerical results are presented to demonstrate the effectiveness of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0194
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 809–837
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: The elastic wave equation inverse obstacle scattering domain derivative the Helmholtz decomposition.
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