Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources

Abstract

The method of fundamental solutions with excitation source (MFS‐ES) is a reliable method for determining the eigenvalues of a two‐dimensional hollow waveguide. However, the accuracy in MFS‐ES is extremely dependent on the choice of the auxiliary boundary. In this work, to avoid the problem, a regularized MFS‐ES (RMFS‐ES) is proposed. First, to overcome the shortcomings of MFS, a regularized method of fundamental Solutions (RMFS) is proposed by borrowing the ideas of singular boundary method (SBM) and single layer regularized meshless method (SRMM). Second, the expressions for the fundamental solutions at the singularities are given by utilizing the subtraction and adding‐back technique (SAB). Third, the excitation source method is introduced to overcome the problem that the RMFS may also have spurious frequencies. Finally, to improve the accuracy of RMFS‐ES in solving polygonal waveguide eigenvalue, a wedge scheme (WS) is given. Numerical results show that the meshless RMFS‐ES is a promising numerical method for waveguide eigenvalue problems.