声学计算中不同阶子波谱方法的比较

Applying Wavelet Analysis Theory to Comparing Effects of Different Orders of Wavelet Spectral Method on Acoustic Calculations

为了研究子波阶数对子波谱方法计算精度、收敛速度和压缩性能的影响,分别用不同阶子波计算了二维和三维规则结构和不规则结构的声辐射和声散射。结果表明:子波谱法的计算精度和收敛速度随着子波阶数的增加而提高;高阶子波谱法的压缩性能不如低阶子波谱法,二阶子波谱法的压缩特性总体最优。

Abstract： Aim. At the beginning of this paper, we, after considerable discussion, conclude preliminarily that the further application of the wavelet spectral method in acoustic calculations requires the solution of the bottleneck problem of the effect of wavelet order on the precision, convergence and the compression capability of wavelet spectral method. Section 1 of the full paper briefs the Helmholtz boundary integral equation in acoustics, wavelet analysis and wavelet spectral method. Section 2 uses the first, fourth and eighth order wavelets respectively to calculate acoustic radiation and acoustic scattering. （a） through （d） compare the effects of different wavelet orders on calculation precision; （a） is for （b） is for regular cone, （c） is for regular cylinder and （d） is for irregular structure. Similarly, second, Figs. 2 sphere, Figs. 3 （a） through （d） compare the effects of different wavelet orders on convergence speed and Figs. 4 （a） through （d） compare the effects of different wavelet orders on compression capability. Section 3, on the basis of the comparisons afforded by Figs. 2, 3 and 4, discusses how to select the wavelet order that is suitable for each of several different situations.