An analysis of the scalar Helmholtz equation using the integral equation method

Author

Tsuchimoto, Masanori ; Yoneta, Atsuhiko ; Honma, Toshihisa ; Miya, Kenzo

Author_Institution

Nucl. Eng. Res. Lab., Tokyo Univ., Ibaraki, Japan

Volume

40

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

29

Lastpage

33

Abstract

The scalar Helmholtz equations are investigated by using the integral equation method (IEM). In the IEM analysis, the fundamental solution of the Laplace equation is used as a weighting function. Two IEM formulations are obtained: one is a standard formulation and the other is obtained from an elimination of the unknown boundary value. The accuracy and computational time of the IEM are compared with those of the finite element method in two dimensional scalar Helmholtz problems. The analysis of a resonant cavity is reduced to a simple eigenvalue problem. Resonant frequencies of the IEM agree well with those of the finite difference method. Usefulness of the IEM is confirmed through the analyses of the scalar Helmholtz equations

Keywords

cavity resonators; eigenvalues and eigenfunctions; integral equations; Laplace equation; eigenvalue problem; integral equation method; resonant cavity; scalar Helmholtz equation; weighting function; Eigenvalues and eigenfunctions; Finite difference methods; Finite element methods; Helium; Integral equations; Laplace equations; Resonance; Resonant frequency; Search methods; Strontium;

fLanguage

English

Journal_Title

Microwave Theory and Techniques, IEEE Transactions on

Publisher

ieee

ISSN

0018-9480

Type

jour

DOI

10.1109/22.108319

Filename

108319