Frequency domain Time-Space Decomposition for efficient near field pressure computations

Time-Space Decomposition is one of the most efficient transient near-field pressure simulation schemes available for piston transducers, but suffers from two drawbacks. Every signal has to be individually programmed, and not all signals can be rewritten into the desired decomposition. In this work, an extension of the above method is presented in which the excitation signal is first transformed into the frequency domain and each of the frequency components is used as separate excitation signal. Spectral clipping is applied to reduce the number of terms and hence the computation time. By removing energy from the problem, the efficiency increases at the cost of accuracy. The achieved accuracy in the transient pressure field is known a priori and thus can be set prior to the actual simulation. Pressure fields obtained with the proposed method are compared to those obtained with Field II and with reference solutions obtained with an impulse response method. The proposed method reaches relative errors in the transient pressure field as low as 10^-6 and is significantly more accurate than Field II which has difficulties reaching errors below 10^-3. The time to reach an error of 10^-2 using the proposed method is more than 100× shorter than the time required by Field II to reach that same error.