Field sensitivity to Lp variations of a scatterer

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:360

Article

Shipman, Stephen P.

关键词: Periodic slab;    Open waveguide;    Guided modes;    Scattering;    Helmholtz equation;    Variational calculus;    Transmission coefficient;    Sensitivity analysis;    Elliptic regularity;   

DOI  :  10.1016/j.jmaa.2009.06.025

来源: Elsevier

【 摘 要 】

For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation. which describes acoustic or electromagnetic fields. The main theorem establishes the variational (Frechet) derivative of the scattered field measured in the H-1 (root-mean-square-gradient) norm as a function of the material coefficients measured in an L-p (p-power integral) norm, with 2 < p < infinity, as long as these coefficients are bounded above and below by positive constants and do not admit resonance. The derivative is Lipschitz continuous. We also establish the variational derivative of the transmitted energy with respect to the material coefficients in L-p. (C) 2009 Elsevier Inc. All rights reserved.

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