Using Fast Fourier Transform in the 3-d Multilevel Fast Multipole Algorithm
نویسندگان
چکیده
In this paper a method is presented how to perform interpolation and anterpolation in both spherical coordinates θ and φ by trigonometric polynomials and the fast Fourier transform (FFT) in the 3-D multilevel fast multipole algorithm (MLFMA). The proposed method is exact in interpolation and anterpolation, and has the high numerical efficiency of FFT. A numerical comparison suggests that the proposed method is equally or more efficient, depending on the desired accuracy, than the method of using spherical harmonics and polynomial interpolation in interpolation and anterpolation.
منابع مشابه
Fourier-Based Fast Multipole Method for the Helmholtz Equation
The multilevel fast multipole method (MLFMM) is an algorithm that has had great success in reducing the computational time required to find the solution to the Galerkin boundary integral form of the Helmholtz equation. We present a new formulation of the MLFMM using Fourier basis functions rather than spherical harmonics in order to accelerate and simplify the time-critical stages of the algori...
متن کاملA New Algorithm for the Nonequispaced Fast Fourier Transform on the Rotation Group
We develop an approximate algorithm to efficiently calculate the discrete Fourier transform on the rotation group SO(3). Our method needs O ( L3 logL log(1/ε) + log(1/ε)3Q ) arithmetic operations for a degree-L transform at Q nodes free of choice and with desired accuracy ε. Our main contribution is a method that allows to replace finite expansions in Wigner-d functions of arbitrary orders with...
متن کاملFast Spherical Harmonic Transform Algorithm based on Generalized Fast Multipole Method
Spherical harmonic transform is the most important orthogonal function transform only except Fourier transform, and is used not only for climate simulation and signal processing but also for a base of several numerical algorithms. Fast Fourier Transform (FFT), which runs in time O(N logN) is quite well known, but, for spherical harmonic transform, there is no fast algorithm which is as simple a...
متن کاملFast Multipole Method based filtering of non-uniformly sampled data
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented with attention to data structures and error analysis.
متن کاملParticle Simulation Based on Nonequispaced Fast Fourier Transforms
The fast calculation of long-range interactions is a demanding problem in particle simulation. The main focus of our approach is the decomposition of the problem in building blocks and present efficient numerical realizations for these blocks. For that reason we recapitulate the fast Fourier transform at nonequispaced nodes and the fast summation method. We describe the application of these alg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002