基于加权ENO的图像放大算法

E.Arandiga的图像自适应插值方法在图像边界区域使用了ENO方法进行插值。通过比较差商的绝对值的大小自适应地选择模板,尽量避免所选择的模板中包含间断,有效地抑制了Gibbs振荡,但仍有很多不足。为弥补ENO方法的缺点,提高插值方法的精确度,提出基于加权ENO的图像放大方法。基本思想是将图像的离散化形式看成图像在单元网格上的平均值,先判断每个单元中是否存在图像边界,在图像边界区域使用加权ENO方法插值图像,在光滑区域使用线性平均插值。该放大方法能得到比FArandiga的图像自适应插值方法更高阶的精度。     

A numerical study of the convergence properties of ENO schemes

We report numerical results obtained with finite difference ENO schemes for the model problem of the linear convection equation with periodic boundary conditions. For the test function sin(x), the spatial and temporal errors decrease at the rate expected from the order of local truncation errors as the discretization is refined. If we take sin⁴(x) as our test function, however, we find that the numerical solution does not converge uniformly and that an improved discretization can result in larger errors. This difficulty is traced back to the linear stability characteristics of the individual stencils employed by the ENO algorithm. If we modify the algorithm to prevent the use of linearly unstable stencils, the proper rate of convergence is reestablished. The way toward recovering the correct order of accuracy of ENO schemes appears to involve a combination of fixed stencils in smooth regions and ENO stencils in regions of strong gradients —a concept that is developed in detail in a companion paper by Shu (this issue, 1990).     

Radial Basis Function ENO and WENO Finite Difference Methods Based on the Optimization of Shape Parameters

We present adaptive finite difference ENO/WENO methods with infinitely smooth radial basis functions (RBFs). These methods slightly perturb the polynomial reconstruction coefficients with RBFs as the reconstruction basis and enhance accuracy in the smooth region by locally optimizing the shape parameters. Compared to the classical ENO/WENO methods, the RBF-ENO/WENO methods provide more accurate reconstructions and sharper solution profiles near the jump discontinuity. Furthermore the RBF-ENO/WENO methods are easy to implement in the existing classical ENO/WENO code. The numerical results in 1D and 2D presented in this paper show that the proposed finite difference RBF-ENO/WENO methods perform better than the classical ENO/WENO methods.     

一种径向基函数插值的ENO格式

将ENO格式和径向基函数插值相结合,提出了求解双曲型偏微分方程的径向基函数插值的ENO方法。该方法依据ENO思想建立自适应模板,在选定的模板上利用径向基函数进行逼近,能够很好地处理具有间断解的问题,消除间断点处数值振荡现象。以一维双曲型偏微分方程为例,对该方法进行了验证,并通过与多项式ENO格式比较,表明该方法更具有优势。     

二维非结构网格Hamilton-Jacobi方程的一种简化的加权ENO格式

考虑标量Hamilton-Jacobi方程,对二维非结构网格给出了一种简化的三阶精度加权ENO格式.方法的主要思想是时间和空间分开处理,时间离散用三阶TVD Runge-Kutta 方法.对空间,在每一个三角形单元上构造一个三次多项式,该多项式是一些三次多项式的加权,并给出了加权因子的构造方法.最后用该格式对一些典型算例进行了数值试验,并分析了方法的精度,结果表明该格式是成功的.     

一阶迎风和二阶ENO Local Lax-Friedrich格式的修正系数研究

针对一阶迎风格式和二阶ENO Local Lax-Friedrich格式,通过"修正系数"方法对它们进行修正,在不增加模板节点数的情况下,将逼近精度提高一阶,分别称为MCupwind格式和MCENOLLF格式. 理论与数值模拟实验表明,修正后的格式保持了原有格式的所有优点,在最坏的情况下自动降为原格式,"修正系数"方法能在间断或激波附近引入间断解思想将会有更好的发展前景.     

Convex ENO Schemes for Hamilton–Jacobi Equations

In one dimension, viscosity solutions of Hamilton–Jacobi (HJ) equations can be thought as primitives of entropy solutions for conservation laws. Based on this idea, both theoretical and numerical concepts used for conservation laws can be passed to HJ equations even in several dimensions. In this paper, we construct convex ENO (CENO) schemes for HJ equations. This construction is a generalization from the work by Liu and Osher on CENO schemes for conservation laws. Several numerical experiments are performed. L ¹ and L ^∞ error and convergence rate are calculated as well.     

A trust-region framework for managing the use of approximation models in optimization

This paper presents an analytically robust, globally convergent approach to managing the use of approximation models of varying fidelity in optimization. By robust global behaviour we mean the mathematical assurance that the iterates produced by the optimization algorithm, started at an arbitrary initial iterate, will converge to a stationary point or local optimizer for the original problem. The approach presented is based on the trust region idea from nonlinear programming and is shown to be provably convergent to a solution of the original high-fidelity problem. The proposed method for managing approximations in engineering optimization suggests ways to decide when the fidelity, and thus the cost, of the approximations might be fruitfully increased or decreased in the course of the optimization iterations. The approach is quite general. We make no assumptions on the structure of the original problem, in particular, no assumptions of convexity and separability, and place only mild requirements on the approximations. The approximations used in the framework can be of any nature appropriate to an application; for instance, they can be represented by analyses, simulations, or simple algebraic models. This paper introduces the approach and outlines the convergence analysis.This research was supported by the Dept. of Energy grant DEFG03-95ER25257 and Air Force Office of Scientific Research grant F49620-95-1-0210This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681, USAThis research was supported by the Air Force Office of Scientific Research grant F49620-95-1-0210 and by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681, USA     

Essentially Non-Oscillatory Adaptive Tree Methods

We develop high order essentially non-oscillatory (ENO) schemes on non-uniform meshes based on generalized binary trees. The idea is to adopt an appropriate data structure which allows to communicate information easily between unstructured data structure and virtual uniform meshes. While the generalized binary trees as an unstructured data structure can store solution information efficiently if combined with a good adaptive strategy, virtual uniform meshes allow us to take advantage of many well-developed ENO numerical methods based on uniform meshes. Therefore, the ENO adaptive tree methods proposed here can leverage the merits from both tree structures and uniform meshes. Numerical examples demonstrate that the new method is efficient and accurate. The authors were partially supported by an ONR MURI grant N00014-02-1-0720. The third author was partially supported by NSF DMS-0542174.     

Application of genetic algorithms to optimization of neuronet recognition devices

The possibilities of applying genetic algorithms to optimization of the structure of neural networks that solve problems of recognition of handwritten and printed symbols and words are considered. The results of an experimental study are given. The experiments performed demonstrate an increase in the efficiency of neural networks after optimization. Ways of improving the results obtained are discussed. These results were partially obtained due to grant U4M000 of the Soros International Scientific Fund and also due to the“Neurocomputer” project (1992-994) of the State Committee of NAS of Ukraine on Science and Engineering. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 23–32, September–October, 1999.     

Wave envelope technique for multimode wave guide problems

In this paper we propose a fast method for solving wave guide problems. In particular, we consider the guide to be inhomogeneous, and allow propagation of waves of higher-order modes. Such techniques have been handled successfully for acoustic wave propagation problems with single mode and finite length. This paper extends this concept to electromagnetic wave guides with several modes and infinite in length. The method is shown and results of computations are presented.Research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18107 while the first author was in residence at the ICASE, NASA Langley Research Center, Hampton, VA 23665-5225, and by NASA Grant No. NAG-1-624.     

A Local Extrapolation Method for Hyperbolic Conservation Laws. I. The ENO Underlying Schemes

In this paper, we introduce a local extrapolation method (LEM) for the essentially non-oscillatory (ENO) schemes solving nonlinear hyperbolic conservation laws. The method extrapolates the numerical flux of the underlying scheme so that it keeps conservativity. We use a minmod type limiter to avoid spurious oscillations. We propose a new balancing technique that preserves the symmetry of a symmetric wave that works well for a wide range of CFL numbers. We also introduce two artificial compression procedures to the LEM which yield sharp resolutions of contact discontinuities. Numerical examples are presented to illustrate the performance of the method.     

A weighted ENO-flux limiter scheme for hyperbolic conservation laws

We present a new scheme that combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws interpolants. We modify a second-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten–Osher reconstruction-evolution method limiter. Numerical experiments are done in order to compare a weighted version of the hybrid scheme to weighted essentially non-oscillatory (WENO) schemes with constant Courant–Friedrichs–Lewy number under relaxed step size restrictions. Our results show that the new scheme reduces smearing near shocks and corners, and in some cases it is more accurate near discontinuities compared with higher-order WENO schemes. The hybrid scheme avoids spurious oscillations while using a simple componentwise extension for solving hyperbolic systems. The new scheme is less damped than WENO schemes of comparable accuracy and less oscillatory than higher-order WENO schemes. Further experiments are done on multi-dimensional problems to show that our scheme remains non-oscillatory while giving good resolution of discontinuities.     

From Kalman—Mesarovic realization to a normal-hyperbolic linear model

The principles of the methodology are formulated, which underlie the procedures of the Kalman—Mesarovic realization for dynamic systems with state equations in the class of autonomous linear differential equations in the normalized Frechet space. In this connection, the key approaches to the solution of classical problems of realization theory regarding linear dissipation models of normal-hyperbolic type are interpreted. The study was sponsored by the Russian Fund for Basic Research (grant No. 05-01-00623), the “Integration” Russian Federal Target Program (grant No. B0077), and the Program for Basic Research of the Presidium of the Russian Academy of Sciences (program No. 19, project 2.5). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 137–157, November–December 2005.     

High-order centered difference methods with sharp shock resolution

High-order centered finite difference approximations of hyperbolic conservation laws are considered. Different ways of adding artificial viscosity to obtain sharp shock resolution are proposed. For the Riemann problem simple explicit formulas for obtaining stationary one- and two-point shocks are presented. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Laxk-shock condition. Numerical experiments verify the theoretical results.This work has been sponsored by NASA under Contract No. NAS 2-13721.     

NAS存储系统性能测评方法研究

基于文件级共享存取的NAS存储系统已被广泛使用,但随着数据量的急剧增长,存储系统规模迅速扩大,其性能问题也因此日趋严重,对其评测也变得非常复杂,目前还未形成对NAS存储系统性能评测的有效标准方案.因此,用户在选购存储产品时没有参考标准和方法,极大地影响了用户的数据中心建设规划;同时,测评技术的落后也制约了存储技术的发展.为了解决这些问题,通过对NAS存储系统性能影响因素等的大量研究,制定了一套包括测评指标和测评方法等内容在内的性能测评方案,并通过测试实验展示了对NAS存储系统性能测评的方法和性能分析.本测评方案为用户提供了可行的技术参考方法,解决了目前存储测评技术发展的主要问题.     

Delay point schedules for irregular parallel computations

In irregular scientific computational problems one is periodically forced to choosea delay point where some overhead cost is suffered to ensure correctness, or to improve subsequent performance. Examples of delay points are problem remappings, and global synchronizations. One sometimes has considerable latitude in choosing the placement and frequency of delay points; we consider the problem of scheduling delay points so as to minimize the overal execution time. We illustrate the problem with two examples, a regridding method which changes the problem discretization during the course of the computation, and a method for solving sparse triangular systems of linear equations. We show that one can optimally choose delay points in polynomial time using dynamic programming. However, the cost models underlying this approach are often unknown. We consequently examine a scheduling heuristic based on maximizing performance locally, and empirically show it to be nearly optimal on both problems. We explain this phenomenon analytically by identifying underlying assumptions which imply that overall performance is maximized asymptotically if local performance is maximized.This research was supported in part by the National Aeronautics and Space Administration under NASA contract NAS1-18107 while the author consulted at ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, Virginia 23665.Supported in part by NASA contract NAS1-18107, the Office of Naval Research under Contract No. N00014-86-K-0654, and NSF Grant DCR 8106181.     

Ergonomics in Hungary

This report was made possible by a grant from the National Academy of Sciences. The NAS maintains an exchange programme with the USSR and Eastern European countries in order to stimulate the development of improved scientific relationships between East and West. The author participated in this exchange programme as an individual researcher and not as a representative of his employer, The Lockheed Missiles and Space Co.     

Approximate algorithms for partitioning problems

We consider the problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple processor system under certain restrictions on the interconnection structure of the program as well as the multiple computer system. We show that for a variety of such problems, it is possible to find if a partition of the modular program exists in which the load on any processor is whithin a certain bound. This method when combined with a binary search over a fixed range, provides an optimal solution to the partitioning problem.The specific problems we consider are partitioning of (1) a chain structured parallel program over a chain-like computer system, (2) multiple chain-like programs over a host-satellite system, and (3) a tree structured parallel program over a host-satellite system.For a problem withN modules andM processors, the complexity of our algorithm is no worse thanO(Mlog(N)log(W _T/)), whereW _T is the cost of assigning all modules to one processors, and the desired accuracy. This algorithm provides an improvement over the recently developed best known algorithm that runs inO(MNlog(N)) time.This Research was supported by a grant from the Division of Research Extension and Advisory Services, University of Engineering and Technology Lahore, Pakistan. Further support was provided by NASA Contracts NAS1-17070 and NAS1-18107 while the author was resident at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, Virginia, USA.