A fast and accurate algorithm for a Galerkin boundary integral method

A fast and accurate algorithm is presented to increase the computational efficiency of a Galerkin boundary integral method for solving two-dimensional elastostatics problems involving numerous straight cracks and circular inhomogeneities. The efficiency is improved by computing the combined influences of groups, or blocks, of elements—with each element being an inclusion, a hole, or a crack—using asymptotic expansions, multiple shifts, and Taylor series expansions. The coefficients in the asymptotic and Taylor series expansions are computed analytically. Implementation of this algorithm involves a single- or multi-level grid, a clustering technique, and a tree data structure. An iterative procedure is adopted to solve the coefficients in the series expansions of boundary unknowns block by block. The elastic fields in each block are calculated by superposition of the direct influences from the nearby elements and the grouped far-field influences from all the other elements. This fast multipole algorithm is considerably more efficient for large-scale practical problems than the conventional approach.     

Experimental study of the effect of digitizing parameters on digitizing uncertainty with a CMM

Planning of an automated digitization or inspection process takes time and requires experience. The accuracy of digitization and inspection depends directly on the planning of digitization strategies. This paper uses the fractional factorial experimentation approach to investigate the relationship between digitizing (inspection) uncertainty and digitizing (inspection) parameters with a coordinate-measuring machine (CMM). The parameters include travel speeds, pitch, probe angles (part orientations), probe sizes and feature sizes. Robust digitization (inspection) strategies are identified given the part geometry, dimensions and accuracy. Finally, future research directions are highlighted.     

Fast and accurate modeling of waveguide grating couplers

A boundary variation method for the analysis of both infinite periodic and finite aperiodic waveguide grating couplers in two dimensions is introduced. Based on a previously introduced boundary variation method for the analysis of metallic and transmission gratings [J. Opt. Soc. Am. A 10, 2307, 2551 (1993)], a numerical algorithm suitable for waveguide grating couplers is derived. Examples of the analysis of purely periodic grating couplers are given that illustrate the convergence of the scheme. An analysis of the use of the proposed method for focusing waveguide grating couplers is given, and a comparison with a highly accurate spectral collocation method yields excellent agreement and illustrates the attractiveness of the proposed boundary variation method in terms of speed and achievable accuracy.     

An accurate and fast regularization approach to thermodynamic topology optimization

In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii.     

Dynamic windowing algorithm for the fast and accurate determination of luminescence lifetimes

An algorithm for the accurate calculation of luminescence lifetimes in near-real-time is described. The dynamic rapid lifetime determination (DRLD) method uses a window-summing technique and dynamically selects the appropriate window width for each lifetime decay such that a large range of lifetimes can be accurately calculated. The selection of window width is based on an optimal range of window-sum ratios. The algorithm was compared to alternative approaches for rapid lifetime determination as well as nonlinear least-squares (NLLS) fitting in both simulated and real experimental conditions. A palladium porphyrin was used as a model luminophore to quantitatively evaluate the algorithm in a dynamic situation, where oxygen concentration was modulated to induce a change in lifetime. Unlike other window-summing techniques, the new algorithm calculates lifetimes that are not significantly different than the slower, traditional NLLS. In addition, the computation time required to calculate the lifetime is 4 orders of magnitude less than NLLS and 2 orders less than other iterative methods. This advance will improve the accuracy of real-time measurements that must be made on samples that are expected to exhibit widely varying lifetimes, such as sensors and biosensors.     

Towards an accurate performance modeling of parallel sparse factorization

We present a simulation-based performance model to analyze a parallel sparse LU factorization algorithm on modern cached-based, high-end parallel architectures. We consider supernodal right-looking parallel factorization on a bi-dimensional grid of processors, that uses static pivoting. Our model characterizes the algorithmic behavior by taking into account the underlying processor speed, memory system performance, as well as the interconnect speed. The model is validated using the implementation in the SuperLU_DIST linear system solver, the sparse matrices from real application, and an IBM POWER3 parallel machine. Our modeling methodology can be adapted to study performance of other types of sparse factorizations, such as Cholesky or QR, and on different parallel machines.     

Compact modeling and fast simulation of on-chip interconnect lines

An efficient methodology to extract compact models for microstrip lines on lossy silicon substrate is presented. The transversal magnetic field equations are solved by dual finite integration technique (dFIT), a numerical method which allows the accuracy control of the computed frequency dependent line parameters. Several techniques are used to accelerate the process of p.u.l. parameters extraction, such as minimal virtual boundary, minimal mesh and minimal frequency samples set. The solution of the transmission line equations with frequency dependent parameters is then approximated by a rational function of appropriate degree in order to extract the compact model and its SPICE equivalent circuit. The behavior of the obtained compact model of order 10 shows good agreement with respect to the measured data.     

A fast and accurate analysis of the interacting cracks in linear elastic solids

This paper presents a fast and accurate solution for crack interaction problems in infinite- and half- plane solids. The new solution is based on the method of complex potentials developed by Muskhelishvili for the analysis of plane linear elasticity, and it is formulated through three steps. First, the problem is decomposed into a set of basic problems, and for each sub-problem, there is only one crack in the solid. Next, after a crack-dependent conformal mapping, the modified complex potentials associated with the sub-problems are expanded into Laurent’s series with unknown coefficients, which in turn provides a mechanism to exactly implement in the form of Fourier series the boundary condition in each sub-problem. Finally, taking into account the crack interaction via a perturbation approach, an iterative algorithm based on fast Fourier transforms (FFT) is developed to solve the unknown Fourier coefficients, and the solution of the whole problem is readily obtained with the superposition of the complex potentials in each sub-problem. The performance of the proposed method is fully investigated by comparing with benchmark results in the literatures, and superb accuracy and efficiency is observed in all situations including patterns where cracks are closely spaced. Also, the new method is able to cope with interactions among a large number of cracks, and this capability is demonstrated by a calculation of effective moduli of an elastic solid with thousands of randomly-spaced cracks.     

MRI断层层厚测量方法研究

探讨客观、快速、准确测量二维磁共振图像断层层厚的方法。扫描有层厚测试功能的体模获得相应图像,利用传统测试方法(方法 1:调节窗宽、窗位测量目标物的方法;方法 2:单条层面灵敏度剖面线的方法)与改进的多条灵敏度剖面线平均(方法 3A)及一阶导处理自动搜寻目标物边缘的方法(方法 3B)测量层厚。标称层厚为5 mm,当图像均匀性较好时(98.97%),得到各个方法的层厚均值和标准偏差,方法1、2、3A、3B结果分别为4.96 mm/0.03 mm,4.97 mm/0.06 mm,4.98 mm/0.02 mm,4.97 mm/0.01 mm,单因素方差分析F值为0.48;当图像均匀性较差时(95.35%),方法1、2、3A、3B结果分别为4.82 mm/0.41 mm,4.80 mm/0.46 mm,4.84 mm/0.15 mm,4.85 mm/0.11 mm,F值为0.46。F值结果显示4种层厚测试方法有效,但是标准偏差的差异意味着测试结果的不确定度变化较大。方法 1标准偏差最大,方法3B的标准偏差最小。4种测试方法的结果表明:传统测试方法主观性强,误差大,不确定度大,稳定性欠佳;改进后的方法客观、快速,准确度高。特别是当图像均匀性欠佳时,改进的层厚测试方法抗干扰性强。     

A fast convergent and accurate temperature model for phase‐change heat conduction

This work proposes a temperature‐based finite element model for transient heat conduction involving phase‐change. Like preceding temperature‐based models, it is characterized by the discontinuous spatial integration over the elements affected by the phase‐change. Using linear triangles or tetrahedrals, integration can be performed in a closed analytical way, assuring an exact evaluation of the discrete balance equation. Because of its unconditional stability, an Euler‐backward time‐stepping scheme is implemented. A crucial fact is the computation of the exact tangent matrices for the Newton–Raphson solution of the non‐linear system of discretized equations. Efficiency of the model is tested by means of the results obtained for the Neumann problem and the solidification of a steel ingot. Copyright © 1999 John Wiley & Sons, Ltd.     

A new fast block matching algorithm based on complexity‐distortion optimization

Most fast block matching algorithms ignore the efficiency in motion compensation within each checking step. In order to achieve better‐compensated performance, the limited computational complexity should be allocated more carefully into each block. It means that the fast block matching algorithm can be viewed as a kind of rate‐distortion optimization problem. The complexity‐distortion optimal fast block matching algorithm should find the maximized quality of the compensated image under a target computational complexity. In order to approach the optimal complexity‐distortion solution, some strategies are developed. For example, a domination‐based motion vector prediction technique is developed to set the initial motion vector for each block. A predictive complexity‐distortion benefit list is established to predict the compensated benefit for each block. Also, a three‐level pattern searching is employed to check the candidate motion vector. Experimental results show that our proposed algorithm outperforms significantly the three‐step search. For example, in “Salesman,” the average checkpoints for one block is 33 by using the three‐step search. The average checkpoint is 1.75 by using our proposal algorithm under the same average PSNR condition. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 63–67, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10012     

Gibbs sampler optimization for analysis of a granulated medium

A new variant of the method of probability density distribution recovery for solving topical modeling problems is described. Disadvantages of the Gibbs sampling algorithm are considered, and a modified variant, called the “granulated sampling method,” is proposed. Based on the results of statistical modeling, it is shown that the proposed algorithm is characterized by higher stability as compared to other variants of Gibbs sampling.     

一种基于帘线/橡胶复合材料细观力学的精确建模方法

为研究适应性底座的受压膨胀力学特性,提出了一种基于纤维帘线/橡胶复合材料细观力学的精确建模方法.该方法建立在帘线与橡胶材料参数的准确取值这一基础上,其中橡胶材料采用Mooney-Rivilin本构模型进行描述,通过拉伸试验验证了本构模型的准确性,基于束帘线拉伸试验规律对帘线拉伸模量进行了修正.通过上述方法,对适应性橡胶底座受压膨胀过程进行了数值模拟与试验研究.结果表明:这一精确建模方法能够较好地模拟底座的受压膨胀特性,能够获取底座中帘线与橡胶材料的应力、应变的分布以及二者的变化规律.研究工作为适应性底座的进一步研究和实际应用提供了技术支撑.     

Fast and accurate modeling of waveguide grating couplers. II. Three-dimensional vectorial case.

A boundary variation method for the fast and accurate modeling of three-dimensional waveguide grating couplers is presented. The algorithm is verified by detailed comparisons with the results of a rigorous spectral collocation method, showing excellent agreement. Examples of the modeling of large waveguide grating couplers are given to illustrate the applicability and versatility of the method.     

Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media*

We present uniform asymptotic solutions (UAS) for displacement discontinuities (DD) that lie within the middle layer of a three layer elastic medium. The DDs are assumed to be normal to the two parallel interfaces between the leastic media, and solutions will be presented for both 2D and 3D elastic media. Using the Fourier transform (FT) method we construct the leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three layer medium. Although a closed form solution will require an infinite series solution, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We present an explicit UAS for elements in which the DD fields are assumed to be piecewise constant throughout a line segment in 2D and a rectangular element in 3D. We demonstrate the usefulness of this UAS by providing a number of examples in which the UAS is used to solve problems in which cracks just touch or cross an interface. The accuracy and efficiency of the algorithm is demonstrated and compared with other numerical methods such as the finite element method and the boudary integral method.     

Fast and accurate solutions of electromagnetics problems involving lossy dielectric objects with the multilevel fast multipole algorithm

Fast and accurate solutions of electromagnetic scattering problems involving lossy dielectric objects are considered. Problems are formulated with two recently developed formulations, namely, the combined-tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE), and solved iteratively using the multilevel fast multipole algorithm (MLFMA). Iterative solutions and accuracy of the results are investigated in detail for diverse geometries, frequencies, and conductivity values. It is demonstrated that CTF solutions are significantly accelerated as the conductivity increases to moderate values and CTF becomes comparable to JMCFIE in terms of efficiency. Considering also the superior accuracy of this formulation, CTF becomes suitable for fast and accurate analysis of scattering problems involving lossy dielectric objects.     

A robust, fast, and accurate deconvolution algorithm for EM-field measurements around GSM and UMTS base stations with a spectrum analyzer

In this paper, we present a new robust, fast, and accurate deconvolution algorithm for correcting noise disturbed measurements and eliminating the influence of the resolution filter of a spectrum analyzer used for EM-field measurements around a GSM and UMTS base station. Our purpose is to be able to determine immediately the field values at a measurement site. Therefore the algorithm has to be fast and accurate. Furthermore, because of the presence of noise, our algorithm has to be robust. Our algorithm that uses windowing and filtering meets those demands and reduces the present noise by an additional convolution with a square wave function.