Volume 26, Issue 3
Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition

Junhong Yue, Ming Li, Peijun Li & Xiaokai Yuan

Commun. Comput. Phys., 26 (2019), pp. 809-837.

Published online: 2019-04

Preview Full PDF 17 1549
Export citation
  • 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.

  • Keywords

Cauchy problems, meshfree, Kansa method, error analysis, LSQI problem, Tikhonov regularization.

  • AMS Subject Headings

65D15, 65N35, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-26-809, author = {}, title = {Numerical Solution of an Inverse Obstacle Scattering Problem for Elastic Waves via the Helmholtz Decomposition}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0194}, url = {http://global-sci.org/intro/article_detail/cicp/13148.html} }
Copy to clipboard
The citation has been copied to your clipboard