A Study on Fourier Spectral and Fourier-Hankel Spectral Field Variable Approximations in BEM for 2D Interior Helmholtz Problems

In this work the numerical modeling of the time harmonic problems in acoustics using boundary element method (BEM) is studied. The different computational techniques and methods for the solution of acoustic problems are reviewed. The formulation of some of the conventional BEM techniques is presented. The mathematical formulation and numerical implementation of Fourier Spectral BEM (FSBEM) and Fourier-Hankel Spectral BEM (FHSBEM) is presented for 2D problems. The numerical implementation of the conventional C-1 and linear C0 BEM formulations and FSBEM/FHSBEM is carried out by developing MATLAB codes. The verification of the numerical implementation of C-1 and linear C0 BEM formulations is carried out by comparing with analytical solutions and FEM. The comparison of FSBEM and FHSBEM is carried out with C-1 and linear C0 BEM formulations.