THE LEAST SQUARES TREFFTZ METHOD AND THE METHOD OF EXTERNAL SOURCE FOR THE EIGENFREQUENCIES OF WAVEGUIDES

Abstract

In this study, the least squares Trefftz method (LSTM) is adopted for analyzing the eigenfrequencies problems governed by homogeneous Helmholtz equations. The Trefftz method, one kind of boundary-type meshless collocation methods, does not need mesh generation and numerical quadrature. Since the system of linear algebraic equations obtained by Trefftz method is highly ill-conditioned, the least squares method is adopted to stabilize the numerical scheme in this study. In the eigenproblem, the response amplitudes from an external source are used to determine the resonant frequencies. By adding an external source, the homogeneous boundary condition becomes inhomogeneous. Then we can employ the LSTM to easily solve this problem. In this paper, the LSTM and the method of external source are used to solve this eigenfrequencies problems governed by Helmholtz equations. Several numerical examples are provided to verify the accuracy and the simplicity of the proposed numerical scheme.