Four Easy Ways to a Faster FFT

The Fast Fourier Transform (FFT) was named one of the Top Ten algorithms of the 20th century , and continues to be a focus of current research. A problem with currently used FFT packages is that they require large, finely tuned, machine specific libraries, produced by highly skilled software developers. Therefore, these packages fail to perform well across a variety of architectures. Furthermore, many need to run repeated experiments in order to re-program their code to its optimal performance based on a given machine's underlying hardware. Finally, it is difficult to know which radix to use given a particular vector size and machine configuration. We propose the use of monolithic array analysis as a way to remove the constraints imposed on performance by a machine's underlying hardware, by pre-optimizing array access patterns. In doing this we arrive at a single optimized program. We have achieved up to a 99.6% increase in performance, and the ability to run vectors up to 8388608 elements larger, on our experimental platforms. Preliminary experiments indicate different radices perform better relative to a machine's underlying architecture.     

Processing of thermogram sequences to determine the rotation rate of a vortex flame

We study vortex flame radiation in laboratory conditions. A fire torch was burning from a tank, which was fixed at the axis of uprising swirl airflow. Ethanol was used as a fuel. Processing of a sequence of thermograms of a swirling torch is described. The vortex flame revolutions were calculated using FFT of time pulsations of a signal from a thermal imaging system.     

A fast algorithm for full non-linear transient waves

The transient surface wave motion is studied by a method which transfers the computational region into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analytical function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain. The project supported by National Natural Science Foundation of China     

Measurement of decay time based on FFT

Decay time is an important parameter in fluorescence temperature and pH value measurement. Many approaches are developed based on different principles. The decay acquisition and estimation method is one of them. A novel estimation method is given in this paper, based on the fast Fourier transform (FFT). The decay time can be calculated from the frequent items of the FFT. The advantages of this method include high accuracy, quick processing, independence on base offset etc. A set of experiment results is obtained based on this method.     

Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment

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Accelerating electrostatic interaction calculations with graphical processing units based on new developments of ewald method using non‐uniform fast fourier transform

We present new algorithms to improve the performance of ENUF method (F. Hedman, A. Laaksonen, Chem. Phys. Lett. 425, 2006, 142) which is essentially Ewald summation using Non‐Uniform FFT (NFFT) technique. A NearDistance algorithm is developed to extensively reduce the neighbor list size in real‐space computation. In reciprocal‐space computation, a new algorithm is developed for NFFT for the evaluations of electrostatic interaction energies and forces. Both real‐space and reciprocal‐space computations are further accelerated by using graphical processing units (GPU) with CUDA technology. Especially, the use of CUNFFT (NFFT based on CUDA) very much reduces the reciprocal‐space computation. In order to reach the best performance of this method, we propose a procedure for the selection of optimal parameters with controlled accuracies. With the choice of suitable parameters, we show that our method is a good alternative to the standard Ewald method with the same computational precision but a dramatically higher computational efficiency. © 2015 Wiley Periodicals, Inc.     

A fast algorithm for numerical solutions to Fortet's equation

A fast algorithm for computation of default times of multiple firms in a structural model is presented. The algorithm uses a multivariate extension of the Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M1 firms and N discretization points in every dimension the algorithm uses O(nlogn·M·M!·N^M(M-1)/2) operations, where n is the number of discretization points in the time domain. The algorithm is applied to firm survival probability computation and zero coupon bond pricing.     

Convex Optimization and Feasible Circulant Matrix Embeddings in Synthesis of Stationary Gaussian Fields

Circulant matrix embedding is one of the most popular and efficient methods for the exact generation of Gaussian stationary univariate series. Although the idea of circulant matrix embedding has also been used for the generation of Gaussian stationary random fields, there are many practical covariance structures of random fields where classical embedding methods break down. In this work, we propose a novel methodology that adaptively constructs feasible circulant embeddings based on convex optimization with an objective function measuring the distance of the covariance embedding to the targeted covariance structure over the domain of interest. The optimal value of the objective function will be zero if and only if there exists a feasible embedding for the a priori chosen embedding size.