Solution of the general Helmholtz equation starting from Laplace's equation

Tapan Kumar Sarkar, Young Seek Chung, Magdalena Salazar Palma

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Abstract

In this paper we illustrate how to solve the general Helmholtz equation starting from Laplace's equation. The interesting point is that the Helmholtz equation has a frequency term whereas Laplace's equation is the static solution of the same boundary value problem. In this new formulation the frequency dependence is manifested in the form of an excitation. A new boundary integral method for solving the general Helmholtz equation is developed. This new formulation is developed for the two-dimensional Helmholtz equation with the method of moments Laplacian solution. The main feature of this new formulation is that the boundary conditions are satisfied independent of the region node discretizations. The numerical solution of the present method is compared with finite difference and finite element solutions of the same problem. Application of this method is also presented for the computation of cut-off frequencies for some canonical waveguide structures.

Original languageEnglish (US)
Pages (from-to)187-197
Number of pages11
JournalApplied Computational Electromagnetics Society Journal
Volume17
Issue number3
StatePublished - Nov 2002

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ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Condensed Matter Physics

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