An efficient meshless boundary point interpolation method for acoustic radiation and scattering

Abstract

An efficient application of the boundary point interpolation method (BPIM) to acoustic radiation and scattering is presented. With the aid of a combined field integral equation, the BPIM is effective and robust to produce unique solutions at all frequencies. Using a Lagrange point interpolation method to form shape functions in explicit form, the inversion of the interpolation matrix in the traditional point interpolation method is removed and then the computational efficiency of the BPIM is enhanced. A power series expansion method is presented to direct compute the troublesome strongly singular and hypersingular integrals in a unified way. Several benchmark examples demonstrate the efficiency and accuracy of the present meshless BPIM for acoustic radiation and scattering problems at all frequencies.