Adjoint state method for time-harmonic scattering problems with boundary perturbations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:428

Article

Adriaens, Xavier¹  Henrotte, Francois^1,2  Geuzaine, Christophe¹ 

[1] Univ Liege, Dept Elect Engn & Comp Sci, Liege, Belgium

[2] Catholic Univ Louvain, EPL iMMC MEMA, Louvain, Belgium

关键词: Adjoint method;    Boundary sensitivity;    Time-harmonic wave scattering;    Optimization;    Finite element method;   

DOI  :  10.1016/j.jcp.2020.109981

来源: Elsevier

【 摘 要 】

Knowing how the solution to time-harmonic wave scattering problems depends on medium properties and boundary conditions is pivotal in wave-based inverse problems, e.g. for imaging. This paper is devoted to the exposition of a computationally efficient method, called the adjoint state method, that allows to quantify the influence of media properties, directly and through boundary conditions, in the study of acoustic, electromagnetic and elastic time-harmonic waves. Firstly, the adjoint state method is derived for general boundary value problems. A continuous (rather than discrete) formalism is adopted in order to highlight the role of the boundary terms. Then, the method is applied systematically to acoustic, electromagnetic and elastic scattering problems with impedance boundary conditions, making use of the similitude between the three problems. Finally, numerical examples solved using the finite element method are presented to demonstrate the validity of the proposed method. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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