Domain dependent Dirac's delta and derivatives with an application to electromagnetic boundary integral representations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:344

Article

Vanska, S.¹  Taskinen, M.² 

[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[2] Helsinki Univ Technol, Dept Radio Sci & Engn, FIN-02150 Espoo, Finland

关键词: Dirac's delta;    fundamental solution;    boundary integral representation;    Helmholtz equation;    Maxwell equations;   

DOI  :  10.1016/j.jmaa.2008.03.016

来源: Elsevier

【 摘 要 】

The domain dependent versions of derivatives and Dirac's delta are defined in distributional sense. These operations enable to obtain domain dependent fundamental solutions and global boundary integral representation formulae. A global representation formula is defined everywhere, also on the boundary, and includes the jump relations of the boundary. The use of the domain dependent objects can be interpreted as taking the boundary limit in prior to integrating by parts when deriving the familiar boundary integral equations. As an application, the representation formulae are obtained for the solutions of the Helmholtz equation and the Maxwell equations. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free