# A FINITE ELEMENT METHOD USING SINGULAR FUNCTIONS FOR HELMHOLTZ EQUATIONS: PART I

• Kim, Seok-Chan (Department of Applied Mathematics, Changwon National University) ;
• Pyo, Jae-Hong (Department of Mathematics, Kangwon National University) ;
• Lee, Jong-Sik (Department of Applied Mathematics, Changwon National University)
• Published : 2008.03.25

#### Abstract

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

#### Acknowledgement

Supported by : Korea Research Foundation