A Finite Element Method for Scalar Helmholtz Equation with Field Singularities

Hajime IGARASHI; Toshihisa HONMA

A Finite Element Method for Scalar Helmholtz Equation with Field Singularities

Hajime IGARASHI, Toshihisa HONMA

Full Text Views

0

Cite this

Summary :

This paper describes a finite element method to obtain an accurate solution of the scalar Helmholtz equation with field singularities. It is known that the spatial derivatives of the eigenfunction of the scalar Helmholtz equation become infinite under certain conditions. These field singularities under mine the accuracy of the numerical solutions obtained by conventional finite element methods based on piecewise polynomials. In this paper, a regularized eigenfunction is introduced by subtracting the field singularities from the original eigenfunction. The finite element method formulated in terms of the regularized eigenfunction is expected to improve the accuracy and convergence of the numerical solutions. The finite element matrices for the present method can be easily evaluated since they do not involve any singular integrands. Moreover, the Dirichlet-type boundary conditions are explicitly imposed on the variables using a transform matrix while the Neumann-type boundary conditions are implicitly imposed in the functional. The numerical results for three test problems show that the present method clearly improves the accuracy of the numerical solutions.

Publication: IEICE TRANSACTIONS on Electronics Vol.E79-C No.1 pp.131-138

Publication Date: 1996/01/25

Publicized

Online ISSN

DOI

Type of Manuscript: PAPER

Category: Electromagnetic Theory

Cite this

Copy

Hajime IGARASHI, Toshihisa HONMA, "A Finite Element Method for Scalar Helmholtz Equation with Field Singularities" in IEICE TRANSACTIONS on Electronics, vol. E79-C, no. 1, pp. 131-138, January 1996, doi: .
Abstract: This paper describes a finite element method to obtain an accurate solution of the scalar Helmholtz equation with field singularities. It is known that the spatial derivatives of the eigenfunction of the scalar Helmholtz equation become infinite under certain conditions. These field singularities under mine the accuracy of the numerical solutions obtained by conventional finite element methods based on piecewise polynomials. In this paper, a regularized eigenfunction is introduced by subtracting the field singularities from the original eigenfunction. The finite element method formulated in terms of the regularized eigenfunction is expected to improve the accuracy and convergence of the numerical solutions. The finite element matrices for the present method can be easily evaluated since they do not involve any singular integrands. Moreover, the Dirichlet-type boundary conditions are explicitly imposed on the variables using a transform matrix while the Neumann-type boundary conditions are implicitly imposed in the functional. The numerical results for three test problems show that the present method clearly improves the accuracy of the numerical solutions.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e79-c_1_131/_p

Copy

@ARTICLE{e79-c_1_131,
author={Hajime IGARASHI, Toshihisa HONMA, },
journal={IEICE TRANSACTIONS on Electronics},
title={A Finite Element Method for Scalar Helmholtz Equation with Field Singularities},
year={1996},
volume={E79-C},
number={1},
pages={131-138},
abstract={This paper describes a finite element method to obtain an accurate solution of the scalar Helmholtz equation with field singularities. It is known that the spatial derivatives of the eigenfunction of the scalar Helmholtz equation become infinite under certain conditions. These field singularities under mine the accuracy of the numerical solutions obtained by conventional finite element methods based on piecewise polynomials. In this paper, a regularized eigenfunction is introduced by subtracting the field singularities from the original eigenfunction. The finite element method formulated in terms of the regularized eigenfunction is expected to improve the accuracy and convergence of the numerical solutions. The finite element matrices for the present method can be easily evaluated since they do not involve any singular integrands. Moreover, the Dirichlet-type boundary conditions are explicitly imposed on the variables using a transform matrix while the Neumann-type boundary conditions are implicitly imposed in the functional. The numerical results for three test problems show that the present method clearly improves the accuracy of the numerical solutions.},
keywords={},
doi={},
ISSN={},
month={January},}

Copy

TY - JOUR
TI - A Finite Element Method for Scalar Helmholtz Equation with Field Singularities
T2 - IEICE TRANSACTIONS on Electronics
SP - 131
EP - 138
AU - Hajime IGARASHI
AU - Toshihisa HONMA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E79-C
IS - 1
JA - IEICE TRANSACTIONS on Electronics
Y1 - January 1996
AB - This paper describes a finite element method to obtain an accurate solution of the scalar Helmholtz equation with field singularities. It is known that the spatial derivatives of the eigenfunction of the scalar Helmholtz equation become infinite under certain conditions. These field singularities under mine the accuracy of the numerical solutions obtained by conventional finite element methods based on piecewise polynomials. In this paper, a regularized eigenfunction is introduced by subtracting the field singularities from the original eigenfunction. The finite element method formulated in terms of the regularized eigenfunction is expected to improve the accuracy and convergence of the numerical solutions. The finite element matrices for the present method can be easily evaluated since they do not involve any singular integrands. Moreover, the Dirichlet-type boundary conditions are explicitly imposed on the variables using a transform matrix while the Neumann-type boundary conditions are implicitly imposed in the functional. The numerical results for three test problems show that the present method clearly improves the accuracy of the numerical solutions.
ER -