Approximate Inertial Manifold Method andMultilevel Finite Element Approximationfor the Navier-Stokes Equations

This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the every solution of Navier-Stokcs equation enters.Another part of this paper presents construction method for A.I.M. by multilevel finite clement method and give error estimates of the approximate solution of incrtial form.

Non-Rigid Image Registration Algorithm Based on B-Splines Approximation

An intensity-based non-rigid registration algorithm is discussed, which uses Gaussian smoothing to constrain the transformation to be smooth, and thus preserves the topology of images. In view of the insufficiency of the uniform Gaussian filtering of the deformation field, an automatic and accurate non-rigid image registration method based on B-splines approximation is proposed. The regularization strategy is adopted by using multi-level B-splines approximation to regularize the displacement fields in a coarse-to-fine manner. Moreover, it assigns the different weights to the estimated displacements according to their reliabilities. In this way, the level of regularity can be adapted locally. Experiments were performed on both synthetic and real medical images of brain, and the results show that the proposed method improves the registration accuracy and robustness.

B-Spline Approximation of Ship Waves on the Free Surface

We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Wavelet-Based Fractal Function Approximation

In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.

Adaptive B-snake for planar curve approximation

An adaptive B-spline active contour model for planar curve approximation is proposed. Starting with an initial B-spline curve, the finite element method is adopted to make the active B-spline curve converge towards the target curve without the need of data points parameterization. A strategy of automatic control point insertion during the B-spline active contour deformation, adaptive to the shape of the planar curve, is also given. Experimental results show that this method is efficient and accurate in planar curve approximation.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

Preservation of Linear Constraints in Approximation of Tensors

For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.

Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

基于半桥子模块构成的模块化多电平变换器研究

模块化多电平变换器(Modular multilevel converter,MMC)适用于中高压应用场合,具备损耗小、传输效率高、开关频率低、开关损耗低、输出谐波少等优点。研究以半桥子模块构成的MMC的工作原理以及其调制策略,并以MATLAB/simlink仿真软件为平台搭建仿真模型,仿真结果表明,最近电平逼近调制策略能够实现MMC输出谐波含量低的电压。

Efficient analysis of dielectric radomes using multilevel fast multipole algorithm with CRWG basis

A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.

Multilevel Characteristic Basis Function Method with ACA for Accelerated Solution of Electrically Large Scattering Problems

The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the method.

Subdivision of Uniform ωB-Spline Curves and Two Proofs of Its C^(k-2)-Continuity

ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.

The Unimodality of Initial B-Spline Approximations in Spline Fitting

Finding optimal knots is a challenging problem in spline fitting due to a lack of prior knowledge regarding optimal knots.The unimodality of initial B-spline approximations associated with given data is a promising characteristic of locating optimal knots and has been applied successfully.The initial B-spline approximations herein are required to approximate given data well enough and characterized by the unimodality if jumps from the highest-order derivatives of the approximations at some interior knots are local maxima.In this paper,we prove the unimodality of the initial B-spline approximations that are constructed under two assumptions:Data points are sampled uniformly and sufficiently from B-spline functions,and initial knots are chosen as the parameters of sampling points.Our work establishes the theoretical basis of the unimodality of initial B-spline approximations and pioneers the theoretical study of locating optimal knots.

KNOT PLACEMENT FOR B-SPLINE CURVE APPROXIMATION VIA l_(∞,1)-NORM AND DIFFERENTIAL EVOLUTION ALGORITHM

In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.

MLFMA结合最佳一致逼近快速求解目标宽带RCS

该文将多层快速多极子与最佳一致逼近结合计算了目标宽带的电磁散射特性。通过求解给定频带内的切比雪夫节点和节点处的目标表面电流,实现了频带内任意频点表面电流的快速预测,从而快速分析了目标宽带电磁散射特性。将计算结果与MLFMA逐点计算的结果进行了比较,结果表明在不影响精度的前提下,该方法大大地提高了计算效率。

NURBS自由曲面在光机设计和分析中的应用

针对光学曲面要求面形描述能力和拟合精度高以及光线追迹速度快的要求,研究了NURBS作为自由曲面的拟合、坐标空间转换和光线追迹算法。首先使用多分辨率B样条拟合方法浅度非球面,深度非球面和Peaks自由曲面进行NURBS拟合,RMS误差均小于10 nm,表现出很好的适应性。其次研究了NURBS曲面的参数空间到坐标空间的转化算法,与传统曲面求导方法相比,速度提高了3倍以上。在提出合理迭代初值计算方法的基础上,将计算每个曲面点的时间缩短至0.3 ms。最后通过NURBS曲面在自由曲面头盔系统的光机分析中和CODEV用户自定义曲面中的成功运用,证明了NURBS曲面能很好地满足光机设计、分析和加工的要求。

舰船磁特征磁矩量法的图形处理单元加速计算研究

磁矩量法(MMM)非常适合用于舰船等铁磁目标的磁场特征建模,因为这种方法不需要对空气等非铁磁区域进行网格划分,然而这种方法需要存储和处理稠密的满阵,计算时间很长,矩阵存储需要非常大的存储空间。联合采用MMM和多层自适应交叉近似(MLACA)法虽然可以显著缩减内存需求和计算时间,但对于求解精细划分网格的问题,计算时间还是太长。将具有强大并行计算能力的图形处理单元(GPU)用于加速具有天然良好并行特性的MLACA法,并给出了相应的并行计算格式,实现了舰船磁特征MMM的大规模并行加速计算。典型算例结果表明,GPU并行计算的加速比超过120倍,对于精细划分为100 000薄壳单元的舰船壳体,其计算时间也仅有约4.3 min.采用该方法的计算结果与商业有限元软件相比差别小于1%,为舰船磁场的大规模建模提供了一种快速、精确、简便的数值计算工具。

模块化多电平变换器最近电平调制研究

模块化多电平变换器(modular multilevel converter,MMC)的调制方法直接影响其运行时的整体性能。最近电平调制(nearest level modulation,NLM)由于其多电平输出时开关频率低、易于工程实现等优点在中高压大功率场合得到广泛应用。文章针对传统NLM采用电容电压排序,根据电流方向选择相应子模块触发导通的电压均衡方法,在阶梯波形成过程中引入自变量的偏差值,调整近似函数,对发波过程的算法进行修正,使得输出电平数增加一倍,显著提高交流输出电压谐波特性;同时分析比较不同调制偏差量组合情况下的输出电压谐波水平,最后仿真验证了该方法的效果。

改进的MMC子模块电压均衡策略

在传统子模块电容均压策略下,模块化多电平变流器(MMC)开关器件存在开关频率高、开关损耗大的缺点。对此,提出了一种改进的子模块电容均压策略。在原有电容电压排序法的基础上,通过设定子模块电压最大允许偏差值以及当前桥臂子模块开通数目来决定子模块的开通选择。分析了单纯依靠子模块电压偏差值确定子模块开通信号存在的问题。最后通过Matlab/Simulink软件仿真验证了该策略的有效性。