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The Factorization Method for Inverse Problems$
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Andreas Kirsch and Natalia Grinberg

Print publication date: 2007

Print ISBN-13: 9780199213535

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199213535.001.0001

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The mixed boundary value problem

The mixed boundary value problem

(p.70) 3 The mixed boundary value problem
The Factorization Method for Inverse Problems

Andreas Kirsch

Natalia Grinberg

Oxford University Press

For the mixed boundary value problem, the scattering domain D consists of several components with different types of boundary conditions. The chapter begins by reviewing results on uniqueness and existence, and proves a factorization of the far field operator. Even in the case where only Dirichlet and Neumann boundary conditions occur on the different components of D (which implies normality of the far field operator), the justification of the original Factorization Method remains an open problem. However, if domains are known a priori which separate the different types of components, then a modified Factorization Method can be constructed and justified. Numerical examples are presented.

Keywords:   Helmholtz equation, mixed boundary condition, far field operator, modified Factorization Method, Dirichlet boundary conditions, Neumann boundary conditions

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