Journal of the Korean Society for Industrial and Applied Mathematics

  • 제12권1호
  • /
  • Pages.13-23
  • /
  • 2008
  • /
  • 1226-9433(pISSN)
  • /
  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지

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)
  • 발행 : 2008.03.25
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초록

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.

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