specsim: A Fortran-77 program for conditional spectral simulation in 3D

A Fortran 77 program, specsim, is presented for conditional spectral simulation in 3D domains. The traditional Fourier integral method allows generating random fields with a given covariance spectrum. Conditioning to local data is achieved by an iterative identification of the conditional phase information. A flowchart of the program is given to illustrate the implementation procedures of the program. A 3D case study is presented to demonstrate application of the program. A comparison with the traditional sequential Gaussian simulation algorithm emphasizes the advantages and drawbacks of the proposed algorithm.     

The boundary element-free method for 2D interior and exterior Helmholtz problems

The boundary element-free method (BEFM) is developed in this paper for numerical solutions of 2D interior and exterior Helmholtz problems with mixed boundary conditions of Dirichlet and Neumann types. A unified boundary integral equation is established for both interior and exterior problems. By using the improved interpolating moving least squares method to form meshless shape functions, mixed boundary conditions in the BEFM can be satisfied directly and easily. Detailed computational formulas are derived to compute weakly and strongly singular integrals over linear and higher order integration cells. Three numerical integration procedures are developed for the computation of strongly singular integrals. Numerical examples involving acoustic scattering and radiation problems are presented to show the accuracy and efficiency of the meshless method.     

A subprogram for direct solution of Poisson equation in cylindrically symmetric geometry

A program for a direct solution of the Poisson equation in cylindrically symmetric geometry is described. It is based on the use of fast Fourier transforms for the axial solution, and an expansion in cubic B-splines for the radial solution.     

The Variable Order Fast Multipole Method for Boundary Integral Equations of the Second Kind

We discuss the variable order Fast Multipole Method (FMM) applied to piecewise constant Galerkin discretizations of boundary integral equations. In this version of the FMM low-order expansions are employed in the finest level and orders are increased in the coarser levels. Two versions will be discussed, the first version computes exact moments, the second is based on approximated moments. When applied to integral equations of the second kind, both versions retain the asymptotic error of the direct method. The complexity estimate of the first version contains a logarithmic term while the second version is O(N) where N is the number of panels.This work was supported by the NSF under contract DMS-0074553     

Time-accelerated integral equations for twodimensional transient scattering problems

Based on the Hilbert transform, this paper presents a totally new method to obtain the time-accelerated electric field, magnetic field and combined field integral equations for the two-dimensional transient scattering problems. The computational complexity of the time-accelerated integral equations is analysed, which can be reduced to O(N_s~2NtlogNt) from the conventional O(N_s~2N_t~2). Numerical results verify the computational complexity of this time-accelerated method, and show that the time-accelerated integral equations can provide accurate and stable solutions for both the open and closed objects.     

Accelerating the Fourier split operator method via graphics processing units

Current generations of graphics processing units have turned into highly parallel devices with general computing capabilities. Thus, graphics processing units may be utilized, for example, to solve time dependent partial differential equations by the Fourier split operator method. In this contribution, we demonstrate that graphics processing units are capable to calculate fast Fourier transforms much more efficiently than traditional central processing units. Thus, graphics processing units render efficient implementations of the Fourier split operator method possible. Performance gains of more than an order of magnitude as compared to implementations for traditional central processing units are reached in the solution of the time dependent Schrödinger equation and the time dependent Dirac equation.     

Ultrahigh-performance FFTs for the CRAY-2 and CRAY Y-MP supercomputers

In this paper a set of techniques for improving the performance of the fast Fourier transform (FFT) algorithm on modern vector-oriented supercomputers is presented. Single-processor FFT implementations based on these techniques are developed for the CRAY-2 and the CRAY Y-MP, and it is shown that they achieve higher performance than previously measured on these machines. The techniques include (1) using gather/scatter operations to maintain optimum length vectors throughout all stages of small-to medium-sized FFTs, (2) using efficient radix-8 and radix-16 inner loops, which allow a large number of vector loads/stores to be overlapped, and (3) prefetching twiddle factors as vectors so that on the CRAY-2 they can later be fetched from local memory in parallel with common memory accesses. Performance results for Fortran implementations using these techniques demonstrate that they are faster than Cray's library FFT routine CFFT2. The actual speedups obtained, which depend on the size of the FFT being computed and the supercomputer being used, range from about 5 to over 300%.     

A fast singular boundary method for 3D Helmholtz equation

This paper presents a fast singular boundary method (SBM) for three-dimensional (3D) Helmholtz equation. The SBM is a boundary-type meshless method which incorporates the advantages of the boundary element method (BEM) and the method of fundamental solutions (MFS). It is easy-to-program, and attractive to the problems with complex geometries. However, the SBM is usually limited to small-scale problems, because of the operation count of $O\left(N^3\right)$ with direct solvers or $O\left(N^2\right)$ with iterative solvers, as well as the memory requirement of $O\left(N^2\right)$. To overcome this drawback, this study makes the first attempt to employ the precorrected-FFT (PFFT) to accelerate the SBM matrix–vector multiplication at each iteration step of the GMRES for 3D Helmholtz equation. Consequently, the computational complexity can be reduced from $O\left(N^2\right)$ to $O\left(NlogN\right)$ or $O\left(N\right)$. Three numerical examples are successfully tested on a desktop computer. The results clearly demonstrate the accuracy and efficiency of the developed fast PFFT-SBM strategy.     

Mathematical modelling of cylindrical electromagnetic vibration energy harvesters

In this paper the first steps for the derivation of a mathematical model to describe the mechanical behaviour of a cylindrical electromagnetic vibration energy harvester, designed to extract energy from human gait to power biomedical implantable devices, are provided. As it is usual, in the modelling of such devices, the proposed mechanical model is also based on the solution of Newton's second law, but here a nonlinear closed-form expression is used for the resulting magnetic force of the system, unlike what has been done in previous works where, traditionally, that expression is a linear or is a nonlinear approximation of the real one. The main feature of this mechanical model is that it depends on several parameters which are related to the main characteristics of this kind of devices, which constitutes a major advantage with respect to the usual models available in the literature since these characteristics can always be changed in order to optimize the device.     

A throughput maximised parallel architecture for 2D fast Discrete Pascal Transform

In this paper, we present a fully pipelined parallel implementation of a two dimensional (2D) Discrete Pascal Transform (DPT). Our approach first makes use of the properties of the Kronecker product and the vec operation on matrices to form an alternate 2D DPT representation suitable for column parallel computation. Next, we lend ourselves to the results from Skodras’ work in 1D DPT to achieve the final architecture for fast 2D DPT. With a fully pipelined implementation, the architecture possesses an initial latency of 2(N-1) clock cycles and a maximum throughput of one complete two dimensional transform every clock cycle, given any input matrix of size N×N. To evaluate our work, our results obtained from actual FPGA implementation were benchmarked against results from other previous works.     

Computing the Fourier transform of real data on a hypercube

There are two ways, other than the standard fast Fourier transform (FFT) algorithm, of computing Fourier transforms of real data, namely, (1)the real fast Fourier transform (RFFT) algorithm, and (2) the fast Hartley transform (FHT) algorithm. On a sequential computer, it has been shown that both the RFFT and the FHT algorithms are faster than the FFT algorithm. However, it is not obvious that the same is true on a parallel machine. The communication requirements of the RFFT and the FHT algorithms, which are critical to the cost of any parallel implementation, are different from those of the FFT algorithm. In this paper we present efficient implementations of the RFFT and the FHT algorithms on a hypercube machine. Experimental results are given for the implementation of the RFFT and the FHT algorithms on the NCUBE machine.     

细节保持的曲面浅浮雕算法

为保持曲面浮雕的细节特征,改善浮雕与背景曲面的过渡效果,提出一种细节保持的曲面浮雕算法.首先采用Canny算子在梯度域定位内外轮廓,获得连续的梯度域;其次提出非线性函数,并用其压缩梯度幅值实现形状压缩;再通过双边滤波算子来保持和增强浮雕细节;最终通过求解积分方程重建曲面浮雕.该算法将背景曲面作为积分方程的优化条件,使浮雕在轮廓处向曲面光滑过渡;在重建过程中利用Fourier变换的微分性质在频域实现方程的精确求解,无需设置迭代收敛条件;通过调整参数可方便地控制浮雕整体变化范围、细节锐化程度以及浮雕与背景曲面的过渡效果.实验结果表明,文中算法参数的几何意义直观,所得曲面浮雕细节清晰,边界过渡自然.     

2-D Systolic Array architecture of CBNS based Discrete Hilbert Transform Processor

This paper proposes an optimized design of Discrete Hilbert Transform (DHT) processor using Complex Binary Number System (CBNS). The conventional implementation of DHT based on the “divide and conquer” approach involves two separate computational units for the real and imaginary parts, which requires a large silicon area and increases the path delay. In contrast, incorporation of CBNS in transformation techniques facilitates complex-valued signal processing through a single computational unit.The CBNS-DHT processor has been designed using the standard computational method of Fast Fourier Transform (FFT). The 2-D Systolic Array architecture along with a novel processing element has been proposed for CBNS based Complex-valued FFT (CFFT) and Inverse FFT (CIFFT) computations. The architecture of CBNS-CFFT/CIFFT has been extended to develop the CBNS-DHT processor on the Zynq-7000 family, XC7Z020-CLG484 FPGA platform. A comparative performance analysis of CBNS-DHT and Normal Binary Number System (NBNS)-DHT highlights the efficiency of CBNS-DHT in terms of VLSI parameters — silicon area, path-delay and memory utilization. CBNS-CFFT shows significant improvement in path delay and area consumption as compared to NBNS-CFFT for both Twiddle Factors and FFT size, which proves that CBNS based CFFT and DHT processor design is more efficient in terms of speed and area requirements.     

Approximate solution of dual integral equations using Chebyshev polynomials

The aim of the present work is to introduce solution of special dual integral equations by the orthogonal polynomials. We consider a system of dual integral equations with trigonometric kernels which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions and convert them to Cauchy-type singular integral equations. We use the Chebyshev orthogonal polynomials to construct approximate solution for Cauchy-type singular integral equations which will solve the main dual integral equations. Numerical results demonstrate effectiveness of this method.     

快速傅里叶变换在地学信息提取中的应用

对地学数据处理时,把原始数据中的干扰去掉,保留数据中的真实信息,是迫切需要解决的问题。文章引入快速傅里叶变换对地学数据进行处理,以地球化学数据为例,通过谱密度图分析对数据进行降噪,以达到优化数据,提高信息提取准确度的目的。     

Direct boundary integral equation method for electromagnetic scattering by partly coated dielectric objects

We present a new variational direct boundary integral equation approach for solving the scattering and transmission problem for dielectric objects partially coated with a PEC layer. The main idea is to use the electromagnetic Calderón projector along with transmission conditions for the electromagnetic fields. This leads to a symmetric variational formulation which lends itself to Galerkin discretization by means of divergence-conforming discrete surface currents. A wide array of numerical experiments confirms the efficacy of the new method. Dedicated to George C. Hsiao on the occasion of his 70th birthday. Communicated by: W. L. Wendland     

基于游程检测与快速傅里叶变换的加密比特流识别

为获得链路层中的加密与未加密比特流样本,首先提出了基于游程检测方法的链路层加密比特流识别方案,解决了未知网络环境下的加密与未加密比特流样本获取问题.同时,采用快速傅里叶变换分别对加密与未加密比特流样本进行处理,根据最大差异原则确定了快速傅里叶变换结果的特征点位置,并基于正态分布原理确定了特征点的取值,建立了特征模板.最后,以某无线网络链路层加密比特流为识别对象,对提出的方案的有效性进行了验证.结果表明,该方案对链路层加密与未加密比特流的识别率均可达到95％以上.     

长信号卷积的快速运算及其语音处理的应用

通过对有限长信号卷积运算的快速算法分析,根据长序列信号的结构特点及卷积运算的数学特征,提出了一种长信号引速卷积及相关的算法实现,给出了相应的C 算法程序,结合算术傅立叶变换进行了改进。并把该算法运用到实际的语音处理中,得到了较好的快速和重建效果。     

Parallel calculations on the CM-2: BBS test programs and spectral methods

The implementation of the Because Benchmark Set programs on the Connection Machine CM-2 is presented and discussed. The characteristics of this machine have been taken into account during the BBS implementations, leading to somewhat different formulations, for some of the BBS programs. These situations are detailed to outline the way algorithms work.

In a second section, the generation of a Computational Fluid Dynamics software is described; the numerical method used (spectral method) is explained, in order to understand the algorithmic solutions that are proposed. The resulting code has then been run on an example showing mixing layer instability, and then compared with similar codes running on Convex and CRAY II vector supercomputers.