The CGFFT method with a discontinuous FFT algorithm

In the conjugate gradient-fast Fourier transform (CGFFT) method, the FFT is used to evaluate the convolution integrals. When the function to be transf ormed has discontinuities, the accuracy of the FFT results, and thus the CG FFT results, will degrade. In this letter, an efficient FFT algorithm is de veloped for discontinuous functions with both uniform and nonuniform sample d data, with O(Np + N log N) complexity, where N is the number of sampling points and p is the interpolation order. The algorithm is incorporated into the CGFFT method. Numerical results for slabs demonstrate the efficiency a nd accuracy of the new FFT and CGFFT algorithms. (C) 2001 John Wiley & Sons , Inc.