A time-space decomposition method for calculating the nearfield pressure generated by a pulsed circular piston

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control ferroelectrics, and frequency control, 2006-06, Vol.53 (6), p.1150-1159
• Main Authors: Kelly, J.F., McGough, R.J.
• Format: Article
• Language: English
• Subjects: Acoustics; Computational modeling; Computer errors; Computer Simulation; Computer-Aided Design; Decomposition; Equipment Design; Equipment Failure Analysis; Error analysis; Errors; Exact sciences and technology; Fundamental areas of phenomenology (including applications); General equipment and techniques; Image Interpretation, Computer-Assisted - instrumentation; Image Interpretation, Computer-Assisted - methods; Impulse response; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Integrals; Mathematical analysis; Mathematical models; Memory management; Models, Theoretical; Physics; Pistons; Pulse generation; Quantum computing; Reproducibility of Results; Sensitivity and Specificity; Shape; Solid modeling; Studies; Time Factors; Transducers; Transient analysis; Ultrasonic imaging; Ultrasonics, quantum acoustics, and physical effects of sound; Ultrasonography - instrumentation; Ultrasonography - methods
• ISSN: 0885-3010; 1525-8955
• DOI: 10.1109/TUFFC.2006.1642513

A time-space decomposition approach is derived for numerical calculations of the transient nearfield pressure generated by a circular piston. Time-space decomposition analytically separates the temporal and spatial components of a rapidly converging single integral expression, thereby converting transient nearfield pressure calculations into the superposition of a small number of fast-converging spatial integrals that are weighted by time-dependent factors. Results indicate that, for the same peak error value, time-space decomposition is at least one or two orders of magnitude faster than the Rayleigh-Sommerfeld integral, the Schoch integral, the Field II program, and the DREAM program. Time-space decomposition is also faster than methods that directly calculate the impulse response by at least a factor of 3 for a 10% peak error and by a factor of 17 for a 1% peak error. The results show that, for a specified maximum error value, time-space decomposition is significantly faster than the impulse response and other analytical integrals evaluated for computations of transient nearfield pressures generated by circular pistons.