High Accuracy Analysis of the Adini's Nonconforming Element

Received September 14, 2000; revised September 25, 2001     

A Hermitian Box-scheme for One-dimensional Elliptic Equations – Application to Problems with High Contrasts in the Ellipticity

We introduce a new box-scheme, called ``hermitian box-scheme' on the model of the one-dimensional Poisson problem. The scheme combines features of the box-scheme of Keller, [20], [13], with the hermitian approximation of the gradient on a compact stencil, which is characteristic of compact schemes, [9], [21]. The resulting scheme is proved to be 4th order accurate for the primitive unknown u and its gradient p. The proved convergence rate is 1.5 for (u,p) in the discrete L ² norm. The connection with a non standard mixed finite element method is given. Finally, numerical results are displayed on pertinent 1-D elliptic problems with high contrasts in the ellipticity, showing in practice convergence rates ranging from 1 to 2.5 in the discrete H ¹ norm. This work has been performed with the support of the GDR MOMAS, (ANDRA, CEA, EDF, BRGM and CNRS): Modélisation pour le stockage des déchets radioactifs. The author thanks especially A. Bourgeat for his encouragements and his interest in this work.     

Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2

A class of half-explicit methods for index 2 differential-algebraic systems in Hessenberg form is proposed, which takes advantage of the partitioned structure of such problems. For this family of methods, which we call partitioned half-explicit Runge-Kutta methods, a better choice in the parameters of the method than for previously available half-explicit Runge-Kutta methods can be made. In particular we construct a family of 6-stage methods of order 5, and determine its parameters (based on the coefficients of the successful explicit Runge-Kutta method DOPRI5) in order to optimize the local error coefficients. Numerical experiments demonstrate the efficiency of this method for the solution of constrained multi-body systems.     

Optimal estimation of parameters of dynamical systems by neural network collocation method

In this paper we propose a new method to estimate parameters of a dynamical system from observation data on the basis of a neural network collocation method. We construct an object function consisting of squared residuals of dynamical model equations at collocation points and squared deviations of the observations from their corresponding computed values. The neural network is then trained by optimizing the object function.The proposed method is demonstrated by performing several numerical experiments for the optimal estimates of parameters for two different nonlinear systems. Firstly, we consider the weakly and highly nonlinear cases of the Lorenz model and apply the method to estimate the optimum values of parameters for the two cases under various conditions. Then we apply it to estimate the parameters of one-dimensional oscillator with nonlinear damping and restoring terms representing the nonlinear ship roll motion under various conditions. Satisfactory results have been obtained for both the problems.     

水平连铸-冷轧法生产H65黄铜带工艺研究

本文主要论述采用水平连铸一冷轧工艺生产H65黄铜带的技术特点、易产生的质量问题与解决办法，以及产品的机械性能、尺寸公差及表面质量。     

An efficient algorithm for characteristic tracking on two-dimensional triangular meshes

Tracking characteristics on unstructured meshes is an important part of many numerical methods in computational fluid mechanics. In this paper, we propose an efficient algorithm for characteristic tracking on two-dimensional unstructured triangular meshes. Numerical experiments, including an example for applying this algorithm with the Eulerian-Lagrangian localized adjoint method (ELLAM) to solve a convection-dominated convection-diffusion problem, are presented to demonstrate the efficiency of this algorithm.     

Parallel integration of ODEs based on convolution algorithms

We consider parallel computing methods for ODEs based on the potential parallelism of convolution algorithms. Detailed presentations of fast convolution algorithms are provided. Implementations of our methods on signal processors and special processors are described. The main emphasis is concentrated on applications of powerful parallel signal processing facilities in ODE computations. By using convolution algorithms we show some treatments of parallel computing in finite fields. As an example of our approach we discuss integrating Lorenz's model.

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Zusammenfassung Wir behandeln parallele numerische Methoden für gewöhnliche Differentiagleichungen, die auf Parallelismus von konvolutiven Algorithmen basieren. Ausführliche Darstellungen der schnellen konvolutiven Berechnungen mit spezieller Hardware werden präsentiert. Der Schwerpunkt dieser Arbeit ist die Anwendung von leistungsfähigen parallelen Signal-Prozessoren in der Berechnung gewöhnlicher Differentialgleichungen. Unter Verwendung von Konvolutiven Algorithmen erläutern wir einige Anwendungen von parallelem Rechnen in endlichen Körpern. Als Beispiel unseres Zugangs diskutieren wir die Integration des Lorenz-Modells.

     

Effects of the International Temperature Scale of 1990 (ITS-90) on CIE Documentary Standards for Radiometry,Photometry, and Colorimetry

The differences between ITS-90 and IPTS-68 above 1235 K are described. It is shown that none of the following CIE definitions or recommendations require revision because of the introduction of the ITS-90: International Lighting Vocabulary definitions; CIE Standard Illuminants A, D₆₅, other illuminants; and sources for realizing CIE Illuminants. The effect of the ITS-90 on previously calibrated sources for realizing CIE illuminants is negligibly small.²