Singular value expansion for the Green function of Helmholtz operator

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:377

Article

Egidi, Nadaniela¹  Maponi, Pierluigi¹ 

[1] Univ Camerino, Scuola Sci & Tecnol, I-62032 Camerino, MC, Italy

关键词: Singular value expansion;    Helmholtz operator;   

DOI  :  10.1016/j.jmaa.2010.11.045

来源: Elsevier

【 摘 要 】

We consider the integral operator defined on a circular disk, and with kernel the Green function of the Helmholtz operator. We present an analytic framework for the explicit computation of the singular system of this kernel. In particular, the main formulas of this framework are given by a characteristic equation for the singular values and explicit expressions for the corresponding singular functions. We provide also a property of the singular values, that gives an important information for the numerical evaluation of the singular system. Finally, we present a simple numerical experiment, where the singular system computed by a simple implementation of these analytic formulas is compared with the singular system obtained by a discretization of the Green function of the Helmholtz operator. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free