Fast spectral-domain method for acoustic scattering problems

摘要

This paper presents the application of the conjugate-gradient (CG)nfast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFTn(CG-NUFFT) method for the integral equation arising from acousticnscattering problems. In the conventional method of moments (MoM) fornintegral equations, the CPU and memory requirements are O(N3)nand O(N2), respectively, where N is the number of unknowns innthe problem. The CG-FFT method, which combines the iterativenconjugate-gradient method with FFT, reduces these requirements to O(KNnlog2N) and O(N), respectively, where K is the number of CGniterations. The CG-NUFFT method differs from the CG-FFT method in thatnit makes use of nonuniform FFT algorithms instead of FFT to allow annonuniform discretization. Therefore, the CG-NUFFT method can solve thenintegral equation with both uniform and nonuniform grid while retainingnthe efficiency of the CG-FFT method. These two methods are applied tonsolve for two-dimensional constant density acoustic scattering problems.nNumerical. results demonstrate that they can solve much larger problemsnthan the MoM