A fast time-domain method for calculating the near field pressure generated by a pulsed circular piston

Abstract

A fast single-integral method has been derived for calculations of transient near field pressures generated by circular pistons. This new time-domain method outperforms other methods with respect to speed, accuracy, and ease of implementation. Unlike methods that apply the spatial impulse response, the new method inherently eliminates aliasing problems, which permits a significant reduction in the temporal sampling rate. As a result, the new method is approximately six times faster than the spatial impulse response for a 1% maximum numerical error. This new method converges exponentially with Gauss quadrature, whereas spatial impulse response methods evaluated with fast Fourier transforms only converge linearly with respect to sampling frequency. Thus, the new method achieves small numerical errors in very short times. Since the new fast method evaluates a single-integral expression that is readily computed with standard quadrature techniques, the implementation is greatly simplified relative to the spatial impulse response. The new method, which achieves smaller errors in less time with lower sampling rates, is also much more memory-efficient than the impulse response approach. Each of these advantages represents a significant improvement with respect to the impulse response method for computations of transient acoustic fields.