A 3D finite element spectral integral (FESI) method for acoustics

We present a novel hybrid method that integrates the spectral integral method (SIM) with finite element for pressure acoustics in an inhomogeneous medium surrounded by spherical or incomplete spherical surfaces. Our approach, called the finite element spectral integral (FESI) method, enables efficient calculations of the pressure field in near-field and far-field zones. It is more efficient than the conventional finite element method hybridized with the boundary element method (i.e., the FEBI method). Furthermore, we construct a symmetric coefficient matrix using the proposed symmetric coupling to speed up the FESI method. We demonstrate through several examples that our FESI method offers significantly improved efficiency and lower memory consumption compared to the FEM combined with the perfect matching layer method while achieving higher accuracy.