An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

Abstract

An explicit marching-on-in-time scheme for solving the Kirchhoff integral equation enforced on an acoustically rigid scatterer is proposed. The unknown velocity potential introduced on the surface of scatterer is expanded using unit pulse functions in space and Lagrange polynomial interpolation functions in time. The resulting system is cast in the form of an ordinary differential equation and then integrated numerically in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. Numerical results demonstrate that the time step size required by the proposed explicit scheme to ensure an accurate and stable solution is as large as that used by its implicit counterpart.