An improved boundary point interpolation method for exterior acoustic radiation problem

In this paper, an improved boundary point interpolation method (BPIM) is developed for solving exterior acoustic radiation problems. With the help of Lagrange basis polynomials, a Lagrange point interpolation method (PIM) is presented to avoid the inversion of the moment matrix in the PIM. Then combining the acoustic double layer potential with the Lagrange PIM, the improved BPIM for exterior acoustic radiation problems is presented. Detailed and efficient computational formulas are established to compute acoustic hypersingular and nearly hypersingular integrals. Numerical results show that the current BPIM can produce efficient numerical solutions to exterior acoustic radiation problems.