An iterative technique for fitting exponentials

An interative method to fit the function \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[y = \sum\nolimits_i^n { = 1} a_i e^{lix}\] $\end{document} to data is considered. The technique used is that of inversion of a linear differential operator with constant coefficients. This method reproduces the parameters for mathematically precise data and gives satisfactory results when the data are affected by random errors.     

An optimization technique for iterative frequency-domaindeconvolution

A technique for the optimization of the iteration (design) parameter of filters used in frequency-domain iterative deconvolution methods is presented. The technique allows the filter optimization to be performed in the frequency-domain instead of the time domain, which translates into tremendous saving of computation time. The technique provides a quantitative measure of the performance of the filter regarding noise reduction and filtration error. Illustrative examples using computer simulation as well as experimental data are given. The demonstrations show that the technique yields reliable results for the deconvolution of signals in the presence of noise     

Fast computation of static capacitance for periodic SAW transducers

An efficient algorithm to compute the static capacitance of periodic SAW (surface acoustic wave) interdigital transducers is proposed. The method is based on a new formulation of the well-known relationship giving the capacitance as a linear combination of the charges induced on an infinite transducer for one-electrode excitation. Besides computational efficiency, an interesting physical interpretation of static capacitance results. The algorithm itself is also tailored to split-finger transducers.     

Fast multipole method for micromagnetic simulation of periodic systems

We have developed a new method for computing the magnetostatic field of an infinite array of images of an arbitrary system of charges or multipoles. The result takes the form of a Taylor expansion of the potential of a "cored array" of distant images, as is required by the fast multipole method, the most efficient method known for calculating magnetostatic fields in very large systems. The new method is much faster and simpler to implement than the usual Ewald summation or fast Fourier transform, and does not require a regular grid inside the central cell.     

Fast and robust Delaunay tessellation in periodic domains

An algorithm is presented for constructing three‐dimensional Delaunay tessellations in periodic domains. Applications include mesh generation for periodic transport problems and geometric decomposition for modelling particulate structures. The algorithm is a point insertion technique, and although the general framework is similar to point insertion in a convex hull, a number of new issues are introduced by periodicity. These issues are discussed in detail in the context of the computational algorithm. Examples are given for the tessellation of random points and random sphere packings. Performance data for the algorithm are also presented. These data show an empirical scaling of the computation time with size of O(N^1.11) and tessellation rates of 7000–14000 tetrahedrons per second for the problems studied (up to 10⁵ points). A breakdown of the performance is given, which shows the computational load is shared most heavily by two specific parts of the point‐insertion procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

Fast,precise, and full extraction of the COM parameters for multielectrode-type gratings by periodic Green's function method

It is very important to extract all four coupling-of-modes (COM) parameters of the electrode cells for the simulation and optimal design of a low loss surface acoustic wave (SAW) filter. A new approach for fast and full extraction of the COM parameters for a multielectrode-type grating is proposed. The field distribution of the wave under the periodic shorted grating is calculated by the periodic Green's function method. The phase of the reflection is determined from the positions of the standing wave node. The transduction coefficient and its phase are determined by the charge distribution at low frequency. The COM parameters of the commonly used electrode width controlled (EWC) single phase unidirectional transducer (SPUDT) is computed. It shows that this is a simple and direct way to extract all the COM parameters for SPUDT and, accordingly, is a powerful tool for the optimization of the filter structure.     

A selective relaxation iterative solution technique for nonlinear structural analysis problems

A series of algorithms, to solve the nonlinear algebraic equations resulting from nonlinear finite element models, are proposed. These algorithms involve a selective relaxation of the corrections defined by the modified Newton method. The resulting techniques accelerate the convergence of the modified Newton method. The improved convergence rate is obtained at the expense of a small increase in storage requirements. The results of numerical experiments, on certain nonlinear elasticity problems, are presented to verify the developed techniques.     

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.     

GA/FDTD technique for the design and optimisation of periodic metamaterials

An efficient and powerful full-wave electromagnetic technique is presented to characterise and design periodic metamaterial structures. First, the spectral finite-difference time-domain (FDTD) method with periodic boundary conditions and uniaxial perfect matched layer is employed to predict the performance of a mushroom-like artificial magnetic conductor (AMC) surface and further extended to characterise a negative-refractive-index material consisting of lumped and distributed transmission-line elements. Then, a new computational technique is developed to design and optimise periodic metamaterial structures by integrating the spectral FDTD method with a genetic algorithm (GA), namely the micro-genetic algorithm. This computational technique is successfully applied to design and optimise single-band and dual-band AMC structures consisting of a frequency-selective surface and a ground plane. It is demonstrated that the GA/FDTD technique is a very effective approach for the design and optimisation of periodic metamaterial structures consisting of dielectrics and conductors of arbitrary configurations     

A fast convergence method with simultaneous iterative reconstruction technique for computerized tomography

Considering a system of simultaneous iterative reconstruction technique (SIRT) for X-ray computerized tomography (CT) as a discrete dynamical system, the reconstruction process can be reduced to a procedure of finding a fixed point of the dynamical system. We examine a numerical method for solving fixed points of dynamical systems derived from the algebraic reconstruction technique (ART) and the expectation maximization (EM) formulation, giving rise to the very first convergence for CT reconstruction. Because the proposed method is based on the SIRT, it has an advantage for reducing metal artifact against the filtered backprojection procedure. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 432–436, 1999     

Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy

A numerical reconstruction method believed to be new is proposed for hybrid holographic microscopy in which the hologram of a microscopic object is recorded by an image sensor and is then reconstructed by a computer. Because the Fresnel-Kirchhoff integral must be used for numerical reconstruction to achieve high resolution, we propose an approximation technique for reducing the calculation time. This approximation technique is suitable for microscopic application. The numerical reconstruction of 1-mum-sized objects was demonstrated with a He-Ne laser (lambda = 0.6328 mum).     

Local,hierarchic, and iterative reconstructors for adaptive optics

Adaptive optics systems for future large optical telescopes may require thousands of sensors and actuators. Optimal reconstruction of phase errors using relative measurements requires feedback from every sensor to each actuator, resulting in computational scaling for n actuators of n2. The optimum local reconstructor is investigated, wherein each actuator command depends only on sensor information in a neighboring region. The resulting performance degradation "global" modes is quantified analytically, and two approaches are considered for recovering global performance. Combining local and global estimators in a two-layer hierarchic architecture yields computations scaling with n(4/3); extending this approach to multiple layers yields linear scaling. An alternative approach that maintains a local structure is to allow actuator commands to depend on both local sensors and prior local estimates. This iterative approach is equivalent to a temporal low-pass filter on global information and gives a scaling of n(3/2). The algorithms are simulated by using data from the Palomar Observatory adaptive optics system. The analysis is general enough to also be applicable to active optics or other systems with many sensors and actuators.     

Fast in situ sizing technique for single levitated liquid aerosols

A fast in situ sizing technique for single levitated aerosol particles is presented. It makes use of the analysis of fast-Fourier-transformed vertically polarized Mie scattering patterns from single liquid aerosols levitated in a Paul-trap-type electrodynamic balance. The technique is shown to give reliable results for a test sphere of known physical properties. A first application to aqueous sodium chloride aerosol particles that changed size on humidity variation is presented, yielding good agreement with the full Mie theory.     

Reduced-order model technique for the analysis of anisotropic inhomogeneous media: application to liquid-crystal displays

Electromagnetic wave propagation in anisotropic inhomogeneous media is computed by a novel reduced-order model technique, which is based on the restriction of the Marcuvitz-Schwinger equations on Krylov subspaces and on the application of the singular-value decomposition. The model is derived from the standard coupled-wave method and includes both wide-angle diffraction and light scattering at dielectric interfaces. The method, currently implemented for two-dimensional problems, was applied to the analysis of different liquid-crystal test cells. Numerical results are compared with those obtained through the application of the coupled-wave method and the Jones method and with experimental microscopic measurements.     

A truly boundary-only meshfree method for inhomogeneous problems based on recursive composite multiple reciprocity technique

This study presents a novel technique called the recursive composite multiple reciprocity method (RC-MRM), to develop a truly boundary-only meshfree boundary particle method (BPM) for general inhomogeneous problems. It does not require any inner nodes to evaluate the particular solution, and thus it is a truly boundary-only numerical method. “Composite” in the RC-MRM implies that the RC-MRM employs a high-order composite differential operator rather than a high-order Laplacian operator in the standard MRM to annihilate inhomogeneous term of various types and enables the present BPM to handle a much wider variety of inhomogeneous problems, while the “recursive” algorithm in the RC-MRM significantly reduces CPU time and storage requirements of the original MRM. In addition, we also find high-order harmonic solutions of the Laplacian operator. Numerical illustrations reveals that the present BPM has rapid convergence, high accuracy and efficiency, and mathematical simplicity, through various two- and three-dimensional benchmark problems.     

A parametric study on the effectiveness of the NSM technique for the flexural strengthening of continuous RC slabs

Recent experimental research has shown that the Near Surface Mounted (NSM) technique has significant potential for increasing the load-carrying capacity of continuous reinforced concrete (RC) slabs. This flexural strengthening technique is based on the installation of rectangular cross sectional carbon fibre reinforced polymer (CFRP) laminates into thin slits that have been opened into the top concrete cover on intermediate supports as well as into the bottom concrete cover in the tensile zones.However, there are several drawbacks to the NSM technique. The linear-elastic behaviour of the CFRP laminates, combined with the possibility of premature detachment of the concrete cover that includes these laminates, can compromise the effectiveness of the flexural strengthening, the moment redistribution and the ductility performance of this type of structure.In order to evaluate the influence of concrete strength, the strengthening configuration, the percentage of CFRP on the load-carrying capacity, the moment redistribution ability and ductility performance of this type of structure, a parametric study was carried out by executing material nonlinear analysis with an FEM-based computer program, whose predictive performance was calibrated based on the results of a previous experimental program.     

快速子空间迭代法、迭代Ritz向量法与迭代Lanczos法的比较

以高效的细胞稀疏直接快速解法为核心步骤，实现了快速的固有振动广义特征值问题解法。并在相同的允许模态误差的意义下检验了三种常用的大型矩阵特征模态算法——子空间迭代法、迭代Ritz向量法和迭代Lanczos法的计算效率。迭代Ritz向量法平均最快，子空间迭代法最慢，三种解法效率相差不是太大。与ANSYS的子空间迭代和Lanczos法相比。本文的子空间迭代比ANSYS的效率高很多，Lanczos法和ANSYS的效率差不多。大量较大规模的例题显示。本文对特征值算法的改进是十分有效的。算法的健壮性，通用性都达到了高水平。     

Shear design of reinforced concrete beams, slabs and walls

The paper presents the background to the shear design provisions for reinforced concrete beams and slabs used in the Australian practice. Correlation of design equations with experimental results are given. The design provisions are illustrated by examples. The importance of shear strength in the design of structural walls is discussed. A new expression to calculate the shear strength of walls is presented.