Applying wavelet analysis theory to comparing effects of different orders of wavelet spectral method on acoustic calculations

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, second, fourth and eighth order wavelets respectively to calculate acoustic radiation and acoustic scattering. Figs. 2 (a) through (d) compare the effects of different wavelet orders on calculation precision; (a) is for sphere, (b) is for regular cone, (c) is for regular cylinder and (d) is for irregular structure. Similarly, 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.