Explicit Solution of Time Domain Scalar Potential Surface Integral Equations for Penetrable Scatterers

An explicit time marching scheme is developed to solve a system of time domain surface integral equations enforced on homogeneous penetrable objects for scalar potential and its normal derivative. This system is cast in the form of an ordinary differential equation (ODE) and unknowns are expanded using high-order nodal functions. Inserting these expansions into the ODE and applying point-testing (Nyström method) yield a system in time-dependent coefficients of the unknown expansions. This system is integrated in time using a predictor-corrector algorithm to yield the expansion coefficients. The resulting explicit time marching scheme uses the same time step size as its implicit counterpart without sacrificing the stability of the solution and is almost three times faster for low frequency excitations.