The factorization method for scatterers with different physical properties

Xiaodong Liu

doi:10.3934/dcdss.2015.8.563

Article Contents

2015, Volume 8, Issue 3: 563-577. Doi: 10.3934/dcdss.2015.8.563

This issue Previous Article Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method Next Article Optimal control of magnetic fields in flow measurement

The factorization method for scatterers with different physical properties

Xiaodong Liu^1,

1.
Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190

Received: October 31, 2013

Revised: December 31, 2013

Published: June 2015

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Abstract

The scattering of time-harmonic acoustic plane waves by a mixed type scatterer is considered. Such a scatterer is given as the union of several components with different physical properties. Some of them are impenetrable obstacles with Dirichlet or impedance boundary conditions, while the others are penetrable inhomogeneous media with compact support. This paper is concerned with modifications of the factorization method for the following two basic cases, one is the scattering by a priori separated sound-soft and sound-hard obstacles, the other one is the scattering by a scatterer with impenetrable (Dirichlet) and penetrable components. The other cases can be dealt with similarly. Finally, some numerical experiments are presented to demonstrate the feasibility and effectiveness of the modified factorization methods.

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Mathematics Subject Classification: Primary: 35P25, 35R30; Secondary: 45Q05, 78A45.

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