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A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons
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10.1121/1.2950081
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Affiliations:
1 Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824
a) Electronic mail: chenduo@msu.edu
b) Electronic mail: mcgough@egr.msu.edu
J. Acoust. Soc. Am. 124, 1526 (2008)
/content/asa/journal/jasa/124/3/10.1121/1.2950081
http://aip.metastore.ingenta.com/content/asa/journal/jasa/124/3/10.1121/1.2950081

## Figures

FIG. 1.

(Color online) Orientation of the computational grid relative to the rectangular source. The rectangular source, which has width and height , lies in the plane. The dashed lines define the extent of the computational grid in the plane. The extent of the computational grid is by in the and directions, respectively.

FIG. 2.

The decomposition of an apodized rectangular source into smaller rectangles, where each small rectangle is wide and high. The apodization function is defined as constant over each small rectangle.

FIG. 3.

The apodization function evaluated on the face of a square piston. The maximum value of the apodization function is achieved when and .

FIG. 4.

Simulated reference pressure field generated by an apodized rectangular source with each side equal to four wavelengths. The results are evaluated in the plane for a time-harmonic excitation.

FIG. 5.

The normalized error distribution describes the difference between the reference pressure field and the computed pressure field for an apodized source. The error distribution is plotted for (a) the apodized FNM evaluated with 16-point Gauss quadrature in each direction, (b) the apodized Rayleigh integral evaluated with 16-point Gauss quadrature in each direction, and (c) the FIELD II program evaluated with and 30 subdivisions in each direction.

FIG. 6.

Normalized root mean square error (NRMSE) plotted as a function of the computation time for time-harmonic calculations with the apodized FNM, the apodized Rayleigh–Sommerfeld integral, and the FIELD II program. This figure demonstrates that the apodized FNM achieves the smallest errors for a given computation time and that the apodized FNM requires the smallest amount of time to achieve a given error value.

FIG. 7.

Simulated reference transient field for an apodized square source excited by the Hanning-weighted pulse in Eq. (18) with and . The sides of the square source are equal to , where the wavelength is defined with respect to the center frequency . The apodization function is given by Eq. (17). The transient reference pressure, evaluated in the plane, is computed with abscissas in each direction using the Rayleigh integral. The results are plotted at (a) and (b) .

FIG. 8.

Normalized root mean square error (NRMSE) plotted as a function of the computation time for transient pressure calculations evaluated with the apodized FNM, the apodized Rayleigh–Sommerfeld integral, and the FIELD II program. For the same computation time, the apodized FNM achieves the smallest errors. For the same error, the apodized FNM requires the least amount of time.

## Tables

TABLE I.

Terms that define the time space decomposition of the Hanning-weighted pulse for transient apodized FNM calculations.

TABLE II.

Terms that define the time space decomposition of the derivative of a Hanning-weighted pulse for transient calculations with the apodized Rayleigh–Sommerfeld integral.

TABLE III.

Simulation parameters for time-harmonic calculations that achieve normalized root mean square error (NRMSE) values of 0.1 and 0.01. The parameters listed include the number of Gauss abscissas or the corresponding FIELD II parameters, the resulting computation time, and the ratio of the computation time relative to the apodized FNM for the Rayleigh integral and the FIELD II program.

TABLE IV.

Simulation parameters for transient calculations that achieve normalized root mean square error (NRMSE) values of 0.1 and 0.01. The parameters listed include the number of Gauss abscissas or the corresponding FIELD II parameters, the resulting computation time, and the ratio of the computation time relative to the apodized FNM for the Rayleigh integral and the FIELD II program.

/content/asa/journal/jasa/124/3/10.1121/1.2950081
2008-09-01
2014-04-23

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