Waveguide boundary spectral finite elements

A waveguide boundary spectral finite element method (SFEM) is developed for the study of acoustical wave propagation in non-uniform waveguide-like geometries. The formulation is based on a variational approach using a mixture of non-internal node element shape functions and wave solutions. The numerical method provides solutions to acoustic duct or fluid waveguide environments which may be divided into uniform cross-sectional regions. Trial functions are determined by solution of an eigenvalue problem defined in the cross-section, which in turn, depends upon the boundary data. Illustration of the method through demonstration of transmission loss of acoustic energy through two-dimensional dissipative mufflers is presented and solutions of a three-dimensional elliptical duct problem are shown.