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Simplified reproducing kernel method for impulsive delay differential equations

APPLIED MATHEMATICS LETTERS 2018年 83卷 123-129页

作者： Mei, Liangcai Jia, Yuntao Lin, Yingzhen Beijing Inst Technol Zhuhai Campus Zhuhai 519088 Peoples R China

In this paper, a new algorithm is presented to solve the impulsive delay initial value problems. This is the first time to propose the simplified reproducing kernel method (SRKM for short) to solve the impulsive delay differential equations. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and is not less than second order convergence. The algorithm is employed successfully in some numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Impulsive delay differential equation Simplified reproducing kernel method Convergence order numerical algorithm

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On the recurrent computation of fractional operator with Mittag-Leffler kernel

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APPLIED numerical MATHEMATICS 2021年 162卷 137-149页

作者： Bohaienko, Vsevolod NAS Ukraine VM Glushkov Inst Cybernet Glushkov Ave 40 Kiev Ukraine

The paper considers the problem of computing the values of the Atangana-Baleanu derivative in Caputo sense which arises while solving fractional partial differential equations. In such case the values of the derivative are needed to be calculated in recurrent manner with increasing value of time or space variable. We consider series expansion and integral representations of the Mittag-Leffler function that is an integral kernel in the Atangana-Baleanu derivative. Expanding into series the argument of the Mittag-Leffler function and applying a variable separation technique we obtain an efficient recurrent computational algorithm when the value of argument increases. The proposed algorithm has close-to-constant computational complexity comparing to linear complexity of the algorithms that perform direct numerical integration while computing the values of the Atangana-Baleanu derivative. For the proposed algorithm we present accuracy and performance estimates checking them computing integrals of the Mittag-Leffler function and solving time-fractional convection-diffusion equation using some finite-difference scheme. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Fractional derivative Atangana-Baleanu derivative Mittag-Leffler function numerical algorithm Convection-diffusion equation Finite-difference method

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Highly accurate and numerically stable computations of double-layer coaxial waveguides

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ENGINEERING COMPUTATIONS 2019年第4期36卷 1384-1399页

作者： Kubiczek, Krzysztof Kampik, Marian Silesian Tech Univ Fac Elect Engn Dept Measurement Sci Elect & Control Zabrze Poland

Purpose The purpose of this study is to develop and investigate a fast and accurate algorithm for the modeling of characteristic impedance of double-layer coaxial waveguides. Design/methodology/approach This paper presents the newly developed numerically stable analytical formula for calculation of the characteristic impedance of double-layer coaxial conductor and its elements such as resistance, inductance, capacitance and conductance per unit length. The formula contains modified scaled Bessel functions. The results of the developed analytical formula were compared with results obtained from the axis-symmetric 2D and 3D finite element method (FEM) simulations, using three different solvers. Findings The proposed method shows a good agreement between results obtained with the new fast and stable analytical model and particular FEM models, selected depending on frequency range. The relative difference between characteristic impedance calculated using the new analytical method and obtained from chosen FEM method for discussed frequency range is less than 0.1 per cent which proves the correctness of the new analytical formula. Noteworthy is the fact that the relative difference of the resistance computed using the developed analytical method and obtained with Maxwell FEM solver for the frequency in range from 1 Hz to 10 MHz is less than 0.01 per cent. The presented work shows that when the calculations are performed over wide frequency range, it is necessary to use more than one solver, especially when the wavelength is comparable with dimensions of the conductor. The computation time of the new analytical model is much shorter than the computation time of FEM. Originality/value An efficient, numerically stable algorithm for computation of characteristic impedance of a double-layer coaxial conductor (waveguide).

关键词： Characteristic impedance Coaxial waveguide Double-layer cylindrical conductor Engineering computations FEM simulations numerical algorithm

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CONFORMING DELAUNAY TRIANGULATION OF STOCHASTICALLY GENERATED THREE DIMENSIONAL DISCRETE FRACTURE NETWORKS: A FEATURE REJECTION algorithm FOR MESHING STRATEGY

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2014年第4期36卷 A1871-A1894页

作者： Hyman, Jeffrey D. Gable, Carl W. Painter, Scott L. Makedonska, Nataliia Los Alamos Natl Lab Computat Earth Sci EES 16 Los Alamos NM 87544 USA

We introduce the feature rejection algorithm for meshing (FRAM) to generate a high quality conforming Delaunay triangulation of a three-dimensional discrete fracture network (DFN). The geometric features (fractures, fracture intersections, spaces between fracture intersections, etc.) that must be resolved in a stochastically generated DFN typically span a wide range of spatial scales and make the efficient automated generation of high-quality meshes a challenge. To deal with these challenges, many previous approaches often deformed the DFN to align its features with a mesh through various techniques including redefining lines of intersection as stair step functions and distorting the fracture edges. In contrast, FRAM generates networks on which high-quality meshes occur automatically by constraining the generation of the network. The cornerstone of FRAM is prescribing a minimum length scale and then restricting the generation of the network to only create features of that size and larger. The process is fully automated, meaning no adjustments of the mesh are performed, and the meshing of the individual fractures has been parallelized. Reported mesh statistics show that the computational meshes generated using FRAM are of high quality. Furthermore, the method does not require solving additional systems of linear equations which is needed if a nonconforming mesh is used. Details of the FRAM approach are provided, including its mathematical underpinnings and an algorithm for its implementation. We demonstrate the method's applicability by generating a DFN with similar statistics as the fractured granite at the Forsmark site in Sweden containing 6 700 fractures, and also solve the fully saturated Darcy flow equations to show the quality of the flow solutions which result from computation on the mesh.

关键词： Darcy flow Delaunay triangulation discrete fracture network (DFN) fractured media mesh generation numerical algorithm

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Extension of Newman's method to electrochemical reaction-diffusion in a fuel cell catalyst layer

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JOURNAL OF POWER SOURCES 2002年第1期107卷 24-33页

作者： Duan, TP Weidner, JW White, RE Univ S Carolina Ctr Electrochem Engn Dept Chem Engn Columbia SC 29208 USA

A numerical technique is developed for solving coupled electrochemical reaction-diffusion equations. Through analyzing the nonlinearity of the problem, a trial and error iterating procedure is constructed. The coefficient matrix is arranged as a tridiagonal form with elements of block matrix and is decomposed to LU form. A compact forward and backward substitution algorithm based on the shift of inversing block matrix by Gauss-Jordan full pivoting is developed. A large number of node points is required to converge the calculation, Computation experiences show that the iteration converges very quickly. The effects of inner diffusion on the electrochemical reaction are analyzed by numerical solutions. (C) 2002 Published by Elsevier Science B.V.

关键词： electrochemical reaction-diffusion non-linear analysis numerical algorithm convergence thiele modulus

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algorithms for bounded-influence estimation

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2007年第5期51卷 2531-2541页

作者： Bellio, Ruggero Univ Udine Dept Stat I-33100 Udine Italy

Bounded-influence estimation is a well developed and useful theory. It provides fairly efficient estimators which are robust to outliers and local model departures. However, its use has been limited thus far, mainly because of computational difficulties. A careful implementation in modern statistical software can effectively overcome the numerical problems of bounded-influence estimators. The proposed approach is based on general methods for solving estimating equations, together with suitable methods developed in the statistical literature, such as the delta algorithm and nested iterations. The focus is on Mallows estimation in generalized linear models and on optimal bias-robust estimation in models for independent data, such as regression models with asymmetrically distributed errors. (c) 2006 Elsevier B.V. All rights reserved.

关键词： estimating equation numerical algorithm optimal bias-robust estimator regression model robustness

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The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments

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IMA JOURNAL OF numerical ANALYSIS 2009年第3期29卷 467-485页

作者： Golub, Gene Uhlig, Frank Stanford Univ Stanford CA 94305 USA Auburn Univ Dept Math & Stat Auburn AL 36849 USA

Fifty years after the invention of the QR algorithm by John Francis and Vera Kublanovskaya we reconstruct the ideas and the influences that led to its genesis from the originators' own recollections and their sour... 详细信息

关键词： QR algorithm numerical algorithm matrix computation matrix eigenvalue matrix eigenvector Francis Implicit Q Theorem John Francis Vera Kublanovskaya history of math history of computation

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A true 3D frictional hardening elastoplastic constitutive model of concrete based on a unified hardening/softening function

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2018年 119卷 250-273页

作者： Wang, Guosheng Lu, Dechun Du, Xiuli Zhou, Xin Cao, Shengtao Beijing Univ Technol Inst Geotech & Underground Engn Beijing 100124 Peoples R China China Acad Bldg Res Beijing 100013 Peoples R China

This paper discusses three hardening modes of a shear-type yield surface and proposes a true three-dimensional (3D) frictional hardening method using the transformed stress. The proposed method reasonably reflects the stress-induced anisotropy of concrete for a wide range of hydrostatic pressures. A unified hardening/softening function is proposed based on the uniaxial compressive stress-strain relationship. The plastic potential function is obtained by studying the influence of linear and nonlinear plastic potential function on the dilatancy, and the relationship between the yield surface and plastic potential surface is analyzed. The loading-unloading criterion suitable for the softening behavior is obtained by transforming the yield function expressed by stress into the one expressed by strain. Furthermore, a true 3D frictional hardening elastoplastic constitutive model is established. The explicit stress integral algorithm and semi-implicit stress integral algorithm are used to implement the numerical computation. Finally, five sets of biaxial and triaxial test results of high-strength and normal-strength concrete are used to verify the established constitutive model. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Concrete True 3D frictional hardening Unified hardening/softening function Stress-induced anisotropy numerical algorithm

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A proportional differential control method for a time-delay system using the Taylor expansion approximation

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APPLIED MATHEMATICS AND COMPUTATION 2014年 236卷 391-399页

作者： Xu, Ling Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China Wuxi Inst Commerce Sch Internet Things Technol Wuxi 214153 Peoples R China

In this paper, a proportional differential control algorithm is studied. According to the system performance indices, we uses the first-order Taylor expansion to approximate the time-delay, present an algorithm to determine the controller parameters so that the desired dynamic performance can be achieved. The numerical examples are provided to show the advantages of the proposed algorithm for small time-delay. (c) 2014 Elsevier Inc. All rights reserved.

关键词： numerical algorithm Proportional differential controller Taylor approximation Dynamic performance index

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Automation of LCF material model parameters' identification

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COMPUTATIONAL MATERIALS SCIENCE 2010年第3期48卷 529-536页

作者： Franulovic, Marina Basan, Robert Kunc, Robert Prebil, Ivan Univ Rijeka Fac Engn HR-51000 Rijeka Croatia Univ Ljubljana Fac Mech Engn SI-1000 Ljubljana Slovenia

Modeling of of material behaviour has significant influence on design and optimization of mechanical structures and consequently calculation of their lifetime. When using complex constitutive material model that describes elastic-plastic behaviour of the cyclically loaded material and takes into account damage occurrence and accumulation, the process of parameter identification from experimental data is very complex and time-consuming. In this paper the damage occurrence and accumulation within the material are described by means of models of Bauschinger effect, kinematic and isotropic hardening (or softening) according to Chaboche material model and mean stress relaxation according to Ohno-Wang material model. Since the material model is highly non-linear, its parameter identification requires complex numerical procedures, carefully chosen algorithms and numerical operators, followed by software solution development. The developed automated system for material model parameter identification is validated by comparing the calculated with experimental response of the material. Its usage can make material behaviour modeling for numerous materials accurate, fast and user-friendly. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Fatigue Constitutive behaviour Elastic-plastic material Finite element numerical algorithm

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