A fast near-field method for calculations of time-harmonic and transient pressures produced by triangular pistons

Analytical expressions are demonstrated for fast calculations of time-harmonic and transient near-field pressures generated by triangular pistons. These fast expressions remove singularities from the impulse response, thereby reducing the computation time and the peak numerical error with a general formula that describes the near-field pressure produced by any triangular piston geometry. The time-domain expressions are further accelerated by a time-space decomposition approach that analytically separates the spatial and temporal components of the numerically computed transient pressure. Applied to a Hanning-weighted input pulse, time-space decomposition converts each spatio-temporal integral into six spatial integral evaluations at each field point. Time-harmonic and transient calculations are evaluated for an equilateral triangle with sides equal to four wavelengths, and the resulting errors are compared to pressures obtained with exact and approximate implementations of the impulse response method. The results show that the fast near-field method achieves smaller maximum errors and is consistently faster than the impulse response and methods that approximate the impulse response.