Solution of the General Helmholtz Equation Starting from Laplace's Equation
SYRACUSE UNIV NY ELECTRICAL ENGINEERING AND COMPUTER SCIENCE DEPT
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In this paper we illustrate how to solve the general Helmholtz equation starting from Laplaces equation. The interesting point is that the Helmholtz equation has a frequency term whereas Laplaces 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.
- Numerical Mathematics
- Radiofrequency Wave Propagation