SOLUTION TO THE GENERAL HELMHOLTZ EQUATION STARTING FROM LAPLACE EQUATION
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SOLUTION TO THE GENERAL HELMHOLTZ EQUATION STARTING FROM LAPLACE EQUATIONAbstract
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 his 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. 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.
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