Publications [#68084] of Qing H. Liu

Papers Published

1. Xu, X.M. and Liu, Q.H., Fast spectral-domain method for acoustic scattering problems, IEEE Trans. Ultrason. Ferroelectr. Freq. Control (USA), vol. 48 no. 2 (2001), pp. 522 - 9 [58.911735]
   (last updated on 2007/04/17)

   Abstract:
   This paper presents the application of the conjugate-gradient (CG) fast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFT (CG-NUFFT) method for the integral equation arising from acoustic scattering problems. In the conventional method of moments (MoM) for integral equations, the CPU and memory requirements are O(N³) and O(N²), respectively, where N is the number of unknowns in the problem. The CG-FFT method, which combines the iterative conjugate-gradient method with FFT, reduces these requirements to O(KN log₂N) and O(N), respectively, where K is the number of CG iterations. The CG-NUFFT method differs from the CG-FFT method in that it makes use of nonuniform FFT algorithms instead of FFT to allow a nonuniform discretization. Therefore, the CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method. These two methods are applied to solve for two-dimensional constant density acoustic scattering problems. Numerical. results demonstrate that they can solve much larger problems than the MoM

   Keywords:
   conjugate gradient methods;fast Fourier transforms;integral equations;spectral-domain analysis;ultrasonic scattering;