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EFFICIENT numerical METHOD FOR SOLUTION OF BOUNDARY VALUE PROBLEMS WITH ADDITIONAL CONDITIONS

BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING 2017年第3期34卷 873-883页

作者： Szukiewicz, Miroslaw K. Rzeszow Univ Technol Dept Chem & Proc Engn Al Powstancow Warszawy 6 PL-35959 Rzeszow Poland

An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking "the proper shot" allows one to satisfy "additional" boundary conditions. General considerations are illustrated by a real example. The computational example concerns the "dead zone" regime for the non-linear diffusion-reaction equation in heterogeneous catalysis. Accuracy and efficiency of the presented method confirm results obtained for a wide range of changes of process parameters, including the vicinity of a critical point. Calculations were performed with the use of the Maple (R) program.

关键词： numerical algorithm BVP with additional conditions dead zone CAS-type programs

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The Problem of the Optimal Packing of the Equal Circles for Special Non-Euclidean Metric 5th

The Problem of the Optimal Packing of the Equal Circles for ...

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5th International Conference on Analysis of Images, Social Networks, and Texts (AIST)

作者： Kazakov, Alexander L. Lempert, Anna A. Nguyen, Huy L. Matrosov Inst Syst Dynam & Control Theory SB RAS Irkutsk Russia Irkutsk Natl Res Tech Univ Irkutsk Russia

ISBN: (纸本)9783319529202;9783319529196

The optimal packing problem of equal circles (2-D spheres) in a bounded set P in a two-dimensional metric space is considered. The sphere packing problem is to find an arrangement in which the spheres fill as large proportion of the space as possible. In the case where the space is Euclidean this problem is well known, but the case of non-Euclidean metrics is studied much worse. However there are some applied problems, which lead us to use other special non-Euclidean metrics. For instance such statements appear in the logistics when we need to locate a given number of commercial facilities and to maximize the overall service area. Notice, that we consider the optimal packing problem in the case, where P is a multiply-connected domain. The special algorithm based on optical-geometric approach is suggested and implemented. The results of numerical experiment are presented and discussed.

关键词： Optimal packing problem Equal circles Non-Euclidean space Multiply-connected domain numerical algorithm Computational experiment

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Generating Families of Practical Fast Matrix Multiplication algorithms 31

Generating Families of Practical Fast Matrix Multiplication ...

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31st IEEE International Parallel and Distributed Processing Symposium (IPDPS)

作者： Huang, Jianyu Rice, Leslie Matthews, Devin A. van de Geijnt, Robert A. Univ Texas Austin Dept Comp Sci Austin TX 78712 USA Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA

ISBN: (纸本)9781538639146

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due to the increased cost of memory movement, which is particularly noticeable for non-square matrices. Such implementations also require considerable workspace and modifications to the standard BLAS interface. We propose a code generator framework to automatically implement a large family of FMM algorithms suitable for multiplications of arbitrary matrix sizes and shapes. By representing FMM with a triple of matrices [U, V, W] that capture the linear combinations of submatrices that are formed, we can use the Kronecker product to define a multi-level representation of Strassen-like algorithms. Incorporating the matrix additions that must be performed for Strassen-like algorithms into the inherent packing and micro-kernel operations inside GEMM avoids extra workspace and reduces the cost of memory movement. Adopting the same loop structures as high-performance GEMM implementations allows parallelization of all FMM algorithms with simple but efficient data parallelism without the overhead of task parallelism. We present a simple performance model for general FMM algorithms and compare actual performance of 20+ FMM algorithms to modeled predictions. Our implementations demonstrate a performance benefit over conventional GEMM on single core and multi-core systems. This study shows that Strassen-like fast matrix multiplication can be incorporated into libraries for practical use.

关键词： BLAS fast matrix multiplication GEMM linear algebra library numerical algorithm performance model Strassen

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Definition and Computation of Carson Formulas 2

Definition and Computation of Carson Formulas

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2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech)

作者： Krolo, Ivan Modric, Tonci Vujevic, Slavko Univ Split FESB Dept Elect Power Engn Split Croatia

ISBN: (纸本)9789532900712

In this paper, a new numerical algorithm for high-accurate computation of exact Carson formulas is developed. Carson formulas are used for computing of perunit-length (pul) self and mutual impedances of infinitely long parallel conductors. The proposed algorithm is based on piecewise linear approximation of kernel function and analytical integrations of piecewise-linearized kernel function multiplied by the rest of two integrands. Using proposed numerical algorithm, high-accurate results with desired n-digit accuracy can be easily obtained. Results computed by two approximation methods are compared with high-accurate results computed by proposed numerical algorithm for power frequency.

关键词： numerical algorithm Carson formulas self impedance mutual impedance piecewise linear approximation

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Atypical (Rare) Elements Detection - A Conditional Nonparametric Approach 5th

Atypical (Rare) Elements Detection - A Conditional Nonparame...

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5th International Symposium on Computational Modeling of Objects Represented in Images. Fundamentals, Methods and Applications (CompIMAGE)

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Kowalski, Piotr A. Lukasik, Szymon Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods Warsaw Poland AGH Univ Sci & Technol Div Informat Technol & Syst Res Fac Phys & Appl Comp Sci Krakow Poland Catholic Univ Lublin Inst Math & Comp Sci Fac Math Comp Sci & Landscape Lublin Poland

ISBN: (纸本)9783319546094;9783319546087

This paper presents a ready-to-use procedure for detecting atypical (rarely occurring) elements, in one-and multidimensional spaces. The issue is considered through a conditional approach. The application of nonparametric concepts frees the investigated procedure from distributions of describing and conditioning variables. Ease of interpretation and completeness of the presented material lend themselves to the use of the worked out method in a wide range of tasks in various applications of data analysis in science and practice, engineering, economy and management, environmental and social issues, biomedicine, and related fields.

关键词： Rare element Atypical element Outlier Outlier detection Conditional approach Distribution free method numerical algorithm

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Computation of Carson Formulas Using Piecewise Quadratic Approximation 25

Computation of Carson Formulas Using Piecewise Quadratic App...

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25th International Conference on Software, Telecommunications and Computer Networks (SoftCOM)

作者： Krolo, Ivan Vujevic, Slavko Modric, Tonci Univ Split FESB Dept Elect Power Engn Split Croatia

ISBN: (纸本)9781538632123

In this paper, an existing numerical algorithm for high-accurate computation of exact Carson formulas based on piecewise linear approximation is improved. Carson formulas are used for computing of per-unit-length (pul) self and mutual impedances of infinitely long parallel conductors. The proposed algorithm is based on piecewise quadratic approximation of kernel function and analytical integrations of approximated kernel function multiplied by the rest of two integrands. Using proposed algorithm, high-accurate results with desired computer machine n-digit accuracy can be easily obtained. Total number of sample points is significantly decreased with proposed algorithm in comparison with piecewise linear approximation. Results computed by two approximation methods are compared with high-accurate results computed by proposed numerical algorithm for large frequency range.

关键词： numerical algorithm Carson formulas self impedance mutual impedance piecewise quadratic approximation

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An Operational Matrix Method for Solving a Class of Nonlinear Volterra Integro-Differential Equations by Operational Matrix Method

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International Journal of Applied and Computational Mathematics 2017年第4期3卷 3279-3294页

作者： Öztürk, Yalçın Gülsu, Mustafa Ula Ali KoÇman Vocational School Muğla Sıtkı Koçman University Muğla Turkey Department of Mathematics Faculty of Science Muğla Sıtkı Koçman University Muğla Turkey

In this paper, the improved Chebyshev operational matrix method is proposed to solve a class of nonlinear Volterra integro-differential equation. The main characteristic behind this approach is that it reduces such problems to ones of solving systems of algebraic equations. Some examples are included to demonstrate the validity and applicability of the this techinque. The only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory result. © 2017, Springer India Pvt. Ltd.

关键词： Approximation method Chebyshev polynomials Nonlinear Volterra integro-differential equations numerical algorithm Operational matrix method

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Coupled viscoelastic-viscoplastic modeling of homogeneous and isotropic polymers: numerical algorithm and analytical solutions

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2011年第47-48期200卷 3381-3394页

作者： Miled, B. Doghri, I. Delannay, L. Catholic Univ Louvain Inst Mech Mat & Civil Engn IMMC B-1348 Louvain Belgium

A coupled viscoelastic-viscoplastic (VE-VP) model is implemented and studied. The total strain is the sum of VE and VP parts, and the Cauchy stress is given by a linear YE model as a Boltzmann integral of the history of VE strains. The proposed computational algorithm features fully implicit integration, return mapping based on a two-step YE predictor/VP corrector strategy, and a consistent tangent operator. The algorithm is applied to J(2) VP coupled with VE. Very compact expressions are obtained which are form-identical to classical elasto-viscoplasticity (EVP) provided that the constant linear elastic shear and bulk moduli are replaced with incremental relaxation moduli which are appropriate functions of the time increment. Two different integration methods to obtain the incremental moduli are proposed and assessed. Closed-form solutions for uniaxial tension and simple shear are developed, based on an original solution method for integro-differential equations. The analytical results enable to illustrate the constitutive model and provide unambiguous benchmarks for numerical algorithms. Model predictions are compared with experimental data and reasonable correlation is obtained. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Viscoelasticity Viscoplasticity Isothermal numerical algorithm Analytical solutions

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numerical optimization method for packing regular convex polygons

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第8期56卷 1402-1413页

作者： Galiev, Sh. I. Lisafina, M. S. Kazan Natl Res Technol Univ Ul Karla Marksa 10 Kazan 420111 Tatarstan Russia

An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. numerical results are presented that demonstrate the effectiveness of the method.

关键词： packing problem polygon packing packing of polygons in a given domain packing of regular convex polygons linear programming problem numerical algorithm

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Variational assimilation of mean daily observation data for the problem of sea hydrothermodynamics

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RUSSIAN JOURNAL OF numerical ANALYSIS AND MATHEMATICAL MODELLING 2017年第3期32卷 187-195页

作者： Parmuzin, Eugene I. Agoshkov, Valery I. Zakharova, Natalia B. Shutyaev, Victor P. RAS Inst Numer Math Moscow 119333 Russia Moscow Inst Phys & Technol Dolgoprudnyi 141700 Moscow Region Russia

The mathematical model of hydrothermodynamics of the Baltic Sea is considered with the pole moved to a neighbourhood of St. Petersburg in order to improve the horizontal resolution in the Gulf of Finland. The problem of variational assimilation of mean daily data for sea surface temperature (SST) is formulated and studied for the given type of calculation grid of this model. A new algorithm of solution of the inverse problem for reconstruction of the heat flux on the interface of two media is proposed on the base of variational assimilation of satellite observation data. Results of numerical experiments are presented for reconstruction of heat fluxes in the problem of variational assimilation of mean daily observations of SST data.

关键词： Variational assimilation numerical algorithm determination of heat fluxes sea surface temperature

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