A Higher-order Explicit Marching-on-in-time for Analysis of Transient Acoustic Scattering from Rigid Objects

An explicit marching-on-in-time (MOT) scheme for solving the time domain Kirchhoff (surface) integral equation (TDKIE) to analyze acoustic scattering from a rigid scatterer is presented. The unknown velocity potential induced on the scatterer surface is approximated using nodal interpolation functions in space and shifted Lagrange polynomials in time. Inserting this expansion into the TDKIE and testing the resulting equation at the interpolation points (i.e., Nyström method in space) yield a system of ordinary differential equations (ODEs). This ODE system is integrated in time using a PE(CE)m-type linear multistep scheme to yield unknown expansion coefficients. Numerical results demonstrate that the explicit MOT scheme uses the same time step as its implicit counterpart without sacrificing from accuracy or stability and is faster under low frequency excitation (i.e., for large time step).