2.5D scalar Helmholtz wave solution employing the spectral Lanczos decomposition method (SLDM)

Abstract

A numerical method is derived for obtaining the solution to the 2. 5D scalar Helmholtz equation involving an arbitrary 2D lossless inhomogeneous dielectric scatterer excited by a point source in a closed waveguide. The spectral Lanczos decomposition method (SLDM) is used to solve the differential equation by polynomial approximation. Numerical results indicate that a convergent solution to the 2.5D problem in a bounded region may be achieved in O(N1.5) operations. Also, it is demonstrated that the method is accurate for resonant solutions involving eigenvalues on the order of the machine precision. Extension to lossy dielectrics and the implementation of an absorbing boundary condition are discussed.