Calculation of acoustic loading on transducers in the time domain

One technique that has been widely used to calculate the acoustic loading on single transducers and transducer elements of an array is the numerical solution of the Helmholtz integral equation. This technique calculates the acoustic pressure on the radiating surface in the frequency domain. When working with nonlinear devices or when employing short pulses, it is often more convenient to work in the time domain. In this paper we show how the Kirchhoff integral equation can be used to calculate the acoustic loading on a transducer in the time domain. This integral equation expresses the pressure at a given position and time in terms of past values of the pressure and its time derivative over the surface. For a given spatial discretization the numerical solution of this equation becomes unstable if the time step is too small. We present a method for stabilizing the solution as the time steps become small. Numerical results will be presented and compared with known analytic solutions and with transformed frequency-domain results.