## 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 where as the 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 Helmholte equation is developed. This new formulation is developed for the two-dimensional Helmholtz equation. The new formulation is based on 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 language | English (US) |
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Pages | 458-463 |

Number of pages | 6 |

State | Published - 2003 |

Event | 19th Annual Review of Progress in Applied Computational Electromagnetics - Monterey, CA, United States Duration: Mar 24 2003 → Mar 28 2003 |

### Other

Other | 19th Annual Review of Progress in Applied Computational Electromagnetics |
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Country/Territory | United States |

City | Monterey, CA |

Period | 3/24/03 → 3/28/03 |

## Keywords

- Helmholtz equation
- Laplace's equation
- Method of Moments
- Poisson's equation

## ASJC Scopus subject areas

- Electrical and Electronic Engineering