# American Institute of Mathematical Sciences

June  2015, 8(3): 563-577. doi: 10.3934/dcdss.2015.8.563

## The factorization method for scatterers with different physical properties

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

Received  November 2013 Revised  January 2014 Published  October 2014

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.
Citation: Xiaodong Liu. The factorization method for scatterers with different physical properties. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 563-577. doi: 10.3934/dcdss.2015.8.563
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