Статті в журналах: "Numerical computation and mathematical software"

1

Prasetya, Dwi Sabda Budi, and Indira Puteri Kinasih. "KAJIAN GELOMBANG SATU DIMENSI BERDASARKAN HASIL KOMPUTASI NUMERIK." Lensa : Jurnal Kependidikan Fisika 2, no. 2 (December 24, 2014): 217. http://dx.doi.org/10.33394/j-lkf.v2i2.314.

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One-dimensional wave problem research has been done based on numerical computation reviews. The one-dimensional wave equation has been completed using the finite difference method. Results of completion based on the results of numerical computation reviews are simulated using MATLAB programming software. The simulation suggests that numerical computation is reliable for solving mathematical equations.

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2

Matos, José A. O., and Paulo B. Vasconcelos. "Effectiveness of Floating-Point Precision on the Numerical Approximation by Spectral Methods." Mathematical and Computational Applications 26, no. 2 (May 26, 2021): 42. http://dx.doi.org/10.3390/mca26020042.

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With the fast advances in computational sciences, there is a need for more accurate computations, especially in large-scale solutions of differential problems and long-term simulations. Amid the many numerical approaches to solving differential problems, including both local and global methods, spectral methods can offer greater accuracy. The downside is that spectral methods often require high-order polynomial approximations, which brings numerical instability issues to the problem resolution. In particular, large condition numbers associated with the large operational matrices, prevent stable algorithms from working within machine precision. Software-based solutions that implement arbitrary precision arithmetic are available and should be explored to obtain higher accuracy when needed, even with the higher computing time cost associated. In this work, experimental results on the computation of approximate solutions of differential problems via spectral methods are detailed with recourse to quadruple precision arithmetic. Variable precision arithmetic was used in Tau Toolbox, a mathematical software package to solve integro-differential problems via the spectral Tau method.

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3

Cheng, Yumin. "Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”." Mathematics 10, no. 13 (June 29, 2022): 2267. http://dx.doi.org/10.3390/math10132267.

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4

Gaidamauskaitė, E., and R. Baronas. "A Comparison of Finite Difference Schemes for Computational Modelling of Biosensors." Nonlinear Analysis: Modelling and Control 12, no. 3 (July 25, 2007): 359–69. http://dx.doi.org/10.15388/na.2007.12.3.14697.

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This paper presents a one-dimensional-in-space mathematical model of an amperometric biosensor. The model is based on the reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The stated problem is solved numerically by applying the finite difference method. Several types of finite difference schemes are used. The numerical results for the schemes and couple mathematical software packages are compared and verified against known analytical solutions. Calculation results are compared in terms of the precision and computation time.

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5

Sofroniou, Mark, and Giulia Spaletta. "Precise numerical computation." Journal of Logic and Algebraic Programming 64, no. 1 (July 2005): 113–34. http://dx.doi.org/10.1016/j.jlap.2004.07.007.

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6

Lundin, L. K., V. A. Barker, and J. N. Sørensen. "PARALLEL COMPUTATION OF ROTATING FLOWS." Mathematical Modelling and Analysis 4, no. 1 (December 15, 1999): 124–34. http://dx.doi.org/10.3846/13926292.1999.9637117.

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This paper deals with the simulation of 3‐D rotating flows based on the velocity‐vorticity formulation of the Navier‐Stokes equations in cylindrical coordinates. The governing equations are discretized by a finite difference method. The solution is advanced to a new time level by a two‐step process. In the first step, the vorticity at the new time level is computed using the velocity at the previous time level. In the second step, the velocity at the new time level is computed using the new vorticity. We discuss here the second part which is by far the most time‐consuming. The numerical problem is that of solving a singular, large, sparse, over‐determined linear system of equations, and the iterative method CGLS is applied for this purpose. We discuss some of the mathematical and numerical aspects of this procedure and report on the performance of our software on a wide range of parallel computers.

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7

Viklund, Lars, and Peter Fritzson. "ObjectMath – An Object-Oriented Language and Environment for Symbolic and Numerical Processing in Scientific Computing." Scientific Programming 4, no. 4 (1995): 229–50. http://dx.doi.org/10.1155/1995/829697.

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ObjectMath is a language for scientific computing that integrates object-oriented constructs with features for symbolic and numerical computation. Using ObjectMath, complex mathematical models may be implemented in a natural way. The ObjectMath programming environment provides tools for generating efficient numerical code from such models. Symbolic computation is used to rewrite and simplify equations before code is generated. One novelty of the ObjectMath approach is that it provides a comman language and an integrated environment for this kind of mixed symbolic/numerical computation. The motivation for this work is the current low-level state of the art in programming for scientific computing. Much numerical software is still being developed the traditional way in Fortran. This is especially true in application areas such as machine elements analysis, where complex nonlinear problems are the norm. We believe that tools like ObjectMath can increase productivity and quality, thus enabling users to solve problems that are too complex to handle with traditional tools.

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Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Numerical Investigation of Brusselator Chemical Model by Residual Function Using Mathematica Software." Journal of Computational and Theoretical Nanoscience 17, no. 7 (July 1, 2020): 2947–54. http://dx.doi.org/10.1166/jctn.2020.9324.

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In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathematica software includes Adams method, Backward differential formula (BDF) and Implicit Runge-Kutta method which works well on stiff systems. The graphical results are on interval of 0 ≤ t ≤ 30.

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9

Javanbakht, Masoumeh, and Tomas Sauer. "Numerical computation of H-bases." BIT Numerical Mathematics 59, no. 2 (October 6, 2018): 417–42. http://dx.doi.org/10.1007/s10543-018-0733-x.

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10

Sabin, Malcolm. "Numerical geometry of surfaces." Acta Numerica 3 (January 1994): 411–66. http://dx.doi.org/10.1017/s0962492900002476.

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The mathematical techniques used within Computer Aided Design software for the representation and calculation of surfaces of objects are described. First the main techniques for dealing with surfaces as computational objects are described, and then the methods for enquiring of such surfaces the properties required for their assessment and manufacture.

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11

Ozerkin, Denis V. "Computation of the temperature field of multilayer load-bearing structures by numerical methods." Analysis and data processing systems, no. 2 (June 28, 2022): 105–20. http://dx.doi.org/10.17212/2782-2001-2022-2-105-120.

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Modern approaches to the electronic means design include modeling of thermophysical processes occurring in the apparatus being developed. At the same time, a common task in thermophysical modeling is the problem of determining the temperature field of the supporting structure of an electronic device (board, substrate). Knowledge of the quantitative indicators of the supporting structure temperature field directly affects the prediction of the entire electronic device reliability. The load-bearing structures of electronic devices are increasingly made in the form of multilayer structures where conductive, insulating and semiconductor layers can be present. These features impose new requirements on the development of mathematical models, algorithms, application software packages for calculating the temperature fields of the supporting structures of electronic means. The article considers the process of modeling the temperature field for the supporting structures of electronic means using common software systems MathCAD and SolidWorks. The whole variety of supporting structures of electronic means is divided into three categories: conditionally one-dimensional, conditionally two-dimensional and three-dimensional. It is shown that the temperature fields of conditionally one-dimensional (rods) and conditionally two-dimensional (single-layer boards and substrates) structures should be calculated by the finite difference method in the MathCAD software package. Temperature fields of three-dimensional load-bearing structures, including complex geometric configurations, should be calculated using the finite element method in the SolidWorks software package. The developed algorithms for calculating temperature fields are verified by solving a test problem. Comparative analysis has shown that the discrepancy between the calculation results relative to the test problem does not exceed 0.8%. The developed algorithms for calculating the temperature field can be practically useful in the engineering activities of the developer of electronic equipment.

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12

Ito, Shin-ichi, Takeru Matsuda, and Yuto Miyatake. "Adjoint-based exact Hessian computation." BIT Numerical Mathematics 61, no. 2 (February 17, 2021): 503–22. http://dx.doi.org/10.1007/s10543-020-00833-0.

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AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the Hessian and a given vector. One of the ways to obtain an approximation of such Hessian-vector multiplication is to integrate the so-called second-order adjoint system numerically. However, the error in the approximation could be significant even if the numerical integration to the second-order adjoint system is sufficiently accurate. This paper presents a novel algorithm that computes the intended Hessian-vector multiplication exactly and efficiently. For this aim, we give a new concise derivation of the second-order adjoint system and show that the intended multiplication can be computed exactly by applying a particular numerical method to the second-order adjoint system. In the discussion, symplectic partitioned Runge–Kutta methods play an essential role.

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13

Borisov, Milen, Neli Dimitrova, and Ivan Simeonov. "Mathematical Modeling and Stability Analysis of a Two-Phase Biosystem." Processes 8, no. 7 (July 6, 2020): 791. http://dx.doi.org/10.3390/pr8070791.

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We propose a new mathematical model describing a biotechnological process of simultaneous production of hydrogen and methane by anaerobic digestion. The process is carried out in two connected continuously stirred bioreactors. The proposed model is developed by adapting and reducing the well known Anaerobic Digester Model No 1 (ADM1). Mathematical analysis of the model is carried out, involving existence and uniqueness of positive and uniformly bounded solutions, computation of equilibrium points, investigation of their local stability with respect to practically important input parameters. Existence of maxima of the input–output static characteristics with respect to hydrogen and methane is established. Numerical simulations using a specially elaborated web-based software environment are presented to demonstrate the dynamic behavior of the model solutions.

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14

Hoe, Ho Kok, Kanesan Muthusamy, and Harikrishnan Kanthen. "An Intelligent Process Model for Manufacturing System Optimization." Advanced Materials Research 383-390 (November 2011): 6674–78. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.6674.

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The paper aims to develop an intelligent modeling system using Microsoft Excel spreadsheet interface through mathematical language, mathematical reasoning and algorithms flow chart technique for manufacturing system optimization without human involvement. The paper begins to search for a mathematical theorem which is arithmetic series to represent a dynamic manufacturing system in a production floor using production time variable through numerical analysis and is validated using software simulation. The mathematical theorem is modeled with Industrial Engineering (IE) variables into spreadsheet to perform intelligent decision making. The model sets inventory target variable to be achieved with automated computation through the data input from users. Manual analysis from human can be transposed to mathematical language in order automate the system intelligently. The building of intelligent modeling system into spreadsheet using mathematical language sets a new platform for researchers to promote the next generation of modeling technique in the manufacturing field.

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15

Krämer, Walter. "Computer-Assisted Proofs and Symbolic Computations." Serdica Journal of Computing 4, no. 1 (March 31, 2010): 73–84. http://dx.doi.org/10.55630/sjc.2010.4.73-84.

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We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

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16

Islam, Saeed, Haroon Ur Rasheed, Kottakkaran Sooppy Nisar, Nawal A. Alshehri, and Mohammed Zakarya. "Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness." Coatings 11, no. 6 (June 6, 2021): 684. http://dx.doi.org/10.3390/coatings11060684.

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The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

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17

FEUDEL, ULRIKE, and WOLFGANG JANSEN. "CANDYS/QA—A SOFTWARE SYSTEM FOR QUALITATIVE ANALYSIS OF NONLINEAR DYNAMICAL SYSTEMS." International Journal of Bifurcation and Chaos 02, no. 04 (December 1992): 773–94. http://dx.doi.org/10.1142/s0218127492000434.

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Numerical methods are often needed if bifurcation phenomena in nonlinear dynamical systems are studied. In this paper the software system CANDYS/QA for numerical qualitative analysis is presented. A wide class of problems is treated: computation of invariant sets (e.g., steady-states and periodic orbits), path-following (continuation) of such sets, and the related bifurcation phenomena. The following bifurcation situations are detected and the corresponding critical points are calculated during path-following: turning, bifurcation, Hopf bifurcation, period-doubling, torus bifurcation points (one-parameter problems) as well as cusp and Takens-Bogdanov points (two-parameter problems). A number of newly developed methods (e.g., for computation of the Poincaré map) as well as algorithms from the literature are described to demonstrate the whole procedure of a qualitative analysis by numerical means. An illustrative example analyzed by CANDYS/QA is included.

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18

Yang, Hong, and J. Michael Orszag. "Numerical computation of H? optimal performance." Journal of Scientific Computing 7, no. 4 (December 1992): 289–311. http://dx.doi.org/10.1007/bf01108034.

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Deuflhard, Peter, Anton Schiela, and Martin Weiser. "Mathematical cancer therapy planning in deep regional hyperthermia." Acta Numerica 21 (April 19, 2012): 307–78. http://dx.doi.org/10.1017/s0962492912000049.

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This paper surveys the mathematics required for a typically challenging problem from computational medicine: cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem has given rise to many subtle mathematical problems, some of which were unsolved when the project started. Efficiency of numerical algorithms, i.e., computational speed and monitored reliability, plays a decisive role in the medical treatment. Off-the-shelf software had turned out to be insufficient to meet the requirements of medicine. Instead, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, i.e., a ‘virtual lab’, including three-dimensional geometry processing of individual virtual patients, had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analysed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the treatment of individual patients and on the construction of an improved hyperthermia applicator.

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20

Gautschi, Walter. "Orthogonal polynomials: applications and computation." Acta Numerica 5 (January 1996): 45–119. http://dx.doi.org/10.1017/s0962492900002622.

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We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done by methods relying either on moment information or on discretization procedures. The effect on the recurrence coefficients of multiplying the weight function by a rational function is also discussed. Similar methods are applicable to computing Sobolev orthogonal polynomials, although their recurrence relations are more complicated. The paper concludes with a brief account of available software.

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21

Liu, Cai Xia. "Running Simulation System of Distillation Columns Based on MATLAB." Advanced Materials Research 143-144 (October 2010): 444–47. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.444.

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Establish the mathematical model for distillation columns running system, and calculate configurable and performance parameter. Using MATLAB to simulate and analyze dynamic external load such as wind load and earthquake load, do the curve fitting. That provides theoretic results and simulating curve for designing and modifying column structure. New dynamic continuous computation in external load is substituted for the traditional subsection computation for the first time. Numerical superposition and curve fitting of load along the entire tower is completed. That avoids discontinuous stress in the junction point generated by subsection computer with deviation value to the full. Bending moment calculated can infinitely close to the ground beyond section numbers, and describes the external load more truly and reliably. Simulation results of an actual system demonstrate that precision of continuous computation is obviously higher than that of subsection computation. Simulation software based on MATLAB has high efficiency, good stability, which is convenient to checkout columns strength, rigidity and stability under dynamic external load.

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22

Sauvey, Christophe. "Mathematical Modeling of Electrical Circuits and Practical Works of Increasing Difficulty with Classical Spreadsheet Software." Modelling 3, no. 4 (November 17, 2022): 445–63. http://dx.doi.org/10.3390/modelling3040029.

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This paper presents a modeling practical works project of electrical engineering, proposed to the first-year students of the University Institute of Technology in France, during the COVID-19 pandemic. The objective of this paper is twofold. The first objective is to present to the students the opportunities of modeling and calculation development of a spreadsheet software in their professional lives. The second objective is to create a file that automatically calculates all the current and voltage values at each point of any alternative electrical circuit. The aim of this paper, geared toward students, is to bring them to build their own numerical remote lab, autonomously. Therefore, pedagogical keys are given along the reading of this document to help them to progress, both on electrical circuits conceptual understanding with series and parallel RLC circuits and on their computation in a spreadsheet software. As a conclusion, this paper can be used as a base to develop remote modeling practical works of many and different devices, as well as a database starting point of such analytical models.

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Mihaljevic, Nikola, Slobodan Jovanovic, and Aleksandar Dlabac. "A generalized mathematical model for efficiency calibration of gamma detectors: Application to practical cases." Nuclear Technology and Radiation Protection 34, no. 1 (2019): 34–46. http://dx.doi.org/10.2298/ntrp181031006m.

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Efficiency calibration, i. e. determination of detection efficiency, ?p, is a crucial issue in gamma spectrometry (quantification of gamma spectroscopic measurements) with semiconductor and scintillation detectors. Comparing three possible ways to addressing the problem ? relative, absolute and semi empirical ? advantages of the latter are emphasized. Among semi empirical models, efficiency transfer using effective solid angles, ??, is sorted out and briefly elaborated. This approach reduces the problem of efficiency calibration to the determination of ??. It proved reliable and has been broadly used in practice, mainly in the form of the long existing ANGLE software. Progressing further, a generalized mathematical formula for calcu- lations is developed ? first of the kind ? offering an opportunity for advanced applications of gamma spectrometry. The formula enables unlimited flexibility in application, as it conveniently separates the source data from the detector data during the integration procedures ?? calculations). Its practicality is demonstrated for a number of typically encountered counting arrangements, as well as for some exotic ones. The relevant formulae are used in PC calculations and numerical testing is further performed so as to check the validity of the mathematical method and the computer code. Care was taken of the optimization of complex numerical procedures employed (involving fivefold numerical integration), so as to keep computation times as low as possible (in order of minutes or even seconds on ordinary PC). Results obtained are affirmative for both the method and the code. The model will be gradually incorporated into ANGLE software, thus making it readily available for routine use by gamma spectrometry community.

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Bessonov, O. A., and N. A. Kharchenko. "Software Platform for Supercomputer Modeling of Aerothermodynamics Problems." Programmnaya Ingeneria 12, no. 6 (September 9, 2021): 302–10. http://dx.doi.org/10.17587/prin.12.302-310.

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Numerical solution of aerothermodynamics problems requires a lot of processor time, and for this reason, the numerical codes for such simulations must be efficiently parallelized. This paper presents a software platform based on a technological approach that greatly simplifies the parallelization of problems with unstructured grids. The paper formulates the principle of a unified mathematical address space of the problem for all used cluster nodes. The formalization of the presented technological approach and the implementation of its software basis in the form of data structures, exchange routines and work rules form a software platform on the basis of which parallel computational programs can be built. This approach is implemented and tested for the problem of modeling the characteristics of aircrafts, but it can be applied to other problems using unstructured grids with one-dimensional cell numbering. In this case, the physical and mathematical specifics of the problem are not important. Parallelization of the code with the new approach is carried out with minimal effort, without changing the main parts of the program. As a result, a single computational code can be created for all regimes — sequential, multi-threaded, and cluster. The performance results obtained with the new code confirm the good scalability of the parallelization method.

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Cortés-Caicedo, Brandon, Laura Sofía Avellaneda-Gómez, Oscar Danilo Montoya, Lazaro Alvarado-Barrios, and Harold R. Chamorro. "Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems." Energies 14, no. 5 (February 26, 2021): 1282. http://dx.doi.org/10.3390/en14051282.

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This article discusses the problem of minimizing power loss in unbalanced distribution systems through phase-balancing. This problem is represented by a mixed-integer nonlinear-programming mathematical model, which is solved by applying a discretely encoded Vortex Search Algorithm (DVSA). The numerical results of simulations performed in IEEE 8-, 25-, and 37-node test systems demonstrate the applicability of the proposed methodology when compared with the classical Cuh & Beasley genetic algorithm. In addition, the computation times required by the algorithm to find the optimal solution are in the order of seconds, which makes the proposed DVSA a robust, reliable, and efficient tool. All computational implementations have been developed in the MATLAB® programming environment, and all the results have been evaluated in DigSILENT© software to verify the effectiveness and the proposed three-phase unbalanced power-flow method.

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26

Kozlov, Konstantin, Alexander M. Samsonov, and Maria Samsonova. "A software for parameter optimization with Differential Evolution Entirely Parallel method." PeerJ Computer Science 2 (August 8, 2016): e74. http://dx.doi.org/10.7717/peerj-cs.74.

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Summary.Differential Evolution Entirely Parallel (DEEP) package is a software for finding unknown real and integer parameters in dynamical models of biological processes by minimizing one or even several objective functions that measure the deviation of model solution from data. Numerical solutions provided by the most efficient global optimization methods are often problem-specific and cannot be easily adapted to other tasks. In contrast, DEEP allows a user to describe both mathematical model and objective function in any programming language, such asR,OctaveorPythonand others. Being implemented in C, DEEP demonstrates as good performance as the top three methods from CEC-2014 (Competition on evolutionary computation) benchmark and was successfully applied to several biological problems.Availability.DEEP method is an open source and free software distributed under the terms of GPL licence version 3. The sources are available athttp://deepmethod.sourceforge.net/and binary packages for Fedora GNU/Linux are provided for RPM package manager athttps://build.opensuse.org/project/repositories/home:mackoel:compbio.

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Legland, David, Kiên Kiêu, and Marie-Françoise Devaux. "COMPUTATION OF MINKOWSKI MEASURES ON 2D AND 3D BINARY IMAGES." Image Analysis & Stereology 26, no. 2 (May 3, 2011): 83. http://dx.doi.org/10.5566/ias.v26.p83-92.

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Minkowski functionals encompass standard geometric parameters such as volume, area, length and the Euler-Poincaré characteristic. Software tools for computing approximations of Minkowski functionals on binary 2D or 3D images are now available based on mathematical methods due to Serra, Lang and Ohser. Minkowski functionals can not be used to describe spatial heterogeneity of structures. This description can be performed by using Minkowski measures, which are local versions of Minkowski functionals. In this paper, we discuss how to extend the computation of Minkowski functionals to the computation of Minkowski measures. Approximations of Minkowski measures are computed using fltering and look-up table transformations. The final result is represented as a grey-level image. Approximation errors are investigated based on numerical examples. Convergence and non convergence of the measure approximations are discussed. The measure of surface area is used to describe spatial heterogeneity of a synthetic structure, and of an image of tomato pericarp.

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Kirćanski, N., T. Petović, and M. Vukobratović. "Parallel computation of symbolic robot models of pipelined processor architectures." Robotica 11, no. 1 (January 1993): 37–47. http://dx.doi.org/10.1017/s0263574700015423.

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SUMMARYIncreased speed of inverse dynamics computation is essential for improving the characteristics of robot control systems. This is achieved by reducing the numerical complexity of the models and by introducing parallelism in model computation. In this paper customized symbolic models with a near minimum numerical complexity will be used as a basis for the examination of parallelism in inverse dynamic robot models. A scheduling algorithm for the distribution of computational load onto an arbitrary linear array of pipelined processors will be developed. The proposed algorithm is experimentally evaluated on a transputer network.

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VINH, PHAM NGUYEN THANH, HANH HONG NGUYEN, TAI DUONG ANH TRAN, DUC TUAN HOANG, UYEN NGOC LE, and VAN THI BICH TANG. "IMPROVEMENT OF THE PRECISION OF NUMERICAL CALCULATIONS USING “MULTIPLE PRECISION COMPUTATION” PACKAGE." Hue University Journal of Science: Natural Science 128, no. 1B (June 28, 2019): 29. http://dx.doi.org/10.26459/hueuni-jns.v128i1b.5301.

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In this work, the program so-called “Multiple Precision Computation” (MPC) proposed by D. M. Smith [Computing in Science & Engineering, 5, 88-93 (2003)] is introduced and embedded into conventional codes for considerably improving the precision of numerical calculations. The procedure is evaluated for the improvement and validated by the comparison between calculations incorporating MPC with those using regular double-precision declarations and results obtained by well-known Mathematica software, respectively. Several representatively fundamental problems are taken into account for illustration.

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30

Deliiski, N., N. Trichkov, Z. Gochev, and D. Angelski. "Modeling of the Energy Consumption for Warming up of Furniture Elements during their Unilateral Convective Heating before Lacquering." Information Technologies and Control 14, no. 4 (December 1, 2016): 11–18. http://dx.doi.org/10.1515/itc-2017-0012.

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Abstract A mathematical model and a numerical approach for the computation of the specific energy consumption, which is needed for warming up of flat furniture elements before their lacquering, have been suggested. The approach is based on the integration of the solutions of a non-linear model for the calculation of the nonstationary 1D temperature distribution along the thickness of subjected to unilateral convective heating furniture elements. With the help of a self-prepared software program, computations have been carried out for the determination of the change in the specific energy, which is consumed by oak furniture elements with an initial temperature of 20 °C, moisture content of 8 %, thickness of 16 mm, and length of 0.6 m, 1.2 m, and 1.8 m, during their 10 min unilateral convective heating by hot air with temperature of 100 °C and velocity of 5 m·s−1.

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Thong, Duong Viet, Aviv Gibali, Mathias Staudigl, and Phan Tu Vuong. "Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters." Networks and Spatial Economics 21, no. 3 (July 14, 2021): 735–68. http://dx.doi.org/10.1007/s11067-021-09548-3.

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AbstractDynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and notions of system equilibrium in one concise mathematical framework. Recently, Friesz and Han introduced an integrated framework for DUE computation on large-scale networks, featuring a basic fixed-point algorithm for the effective computation of DUE. In the same work, they present an open-source MATLAB toolbox which allows researchers to test and validate new numerical solvers. This paper builds on this seminal contribution, and extends it in several important ways. At a conceptual level, we provide new strongly convergent algorithms designed to compute a DUE directly in the infinite-dimensional space of path flows. An important feature of our algorithms is that they give provable convergence guarantees without knowledge of global parameters. In fact, the algorithms we propose are adaptive, in the sense that they do not need a priori knowledge of global parameters of the delay operator, and which are provable convergent even for delay operators which are non-monotone. We implement our numerical schemes on standard test instances, and compare them with the numerical solution strategy employed by Friesz and Han.

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Юрий Николаевич, Згода,, and Семенов, Алексей Александрович. "High performance computation of thin shell constructions with the use of parallel computations and GPUs." Вычислительные технологии, no. 6 (December 23, 2022): 45–57. http://dx.doi.org/10.25743/ict.2022.27.6.005.

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Предложен ряд высокопроизводительных алгоритмов компьютерного моделирования оболочечных конструкций (или оболочек) с использованием метода Ритца. Эти алгоритмы могут быть применены как при реализации метода Ритца в общем случае, так и при расчете напряженно-деформированного состояния (НДС) оболочечных конструкций. Описывается применение графических ускорителей в задаче расчета НДС. Предложенные алгоритмы включены в ранее разработанное авторами программное обеспечение моделирования НДС-оболочек. Для их апробации проведен вычислительный эксперимент. Исследование алгоритмов показало, что они позволяют повысить производительность расчета на несколько порядков в сравнении с неоптимизированной версией программного обеспечения. Purpose. The Ritz method often used for calculation of thin-shell structures allows performing a transition from a variational problem to the problem of multidimensional function minimization. The main disadvantage of this method is the nonlinear increase of computational complexity with the increase of terms amount in approximation functions. This fact makes it difficult or impossible to obtain results in cases where high solution accuracy is required or when a shell structure with complex geometry is investigated. At the same time, studies aimed at improving computing performance of the Ritz method, especially in problems of shell computer modelling, are rare. The purpose of this work is to develop algorithms for high-performance calculation of the stress-strain state (SSS) of thin-walled shell structures using the Ritz method. Methodology. Analysis of the current state in the field of computer modelling for shell structures was performed. Shell SSS calculation schemes are studied. Algorithms are proposed to improve computer modelling performance by using different mathematical model properties, multi-core CPUs and graphics accelerators. Findings. Described algorithms were implemented in shell SSS modelling software previously developed by the authors. Tests of the performance have shown that they improve the calculation time by several orders compared with the non-optimized version of the software. Originality/Value. New effective algorithms have been developed for modelling the SSS of thin- walled shell structures using the Ritz method. These algorithms can be applied not only to the calculation of shells, but to any other application of Ritz method to the problem of functional minimization.

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Serhii Alekseyenko, Andrii Dreus, Mykola Dron, and Olexandr Brazaluk. "Numerical Study of Aerodynamic Characteristics of a Pointed Plate of Variable Elongation in Subsonic and Supersonic Gas Flow." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 96, no. 2 (July 23, 2022): 88–97. http://dx.doi.org/10.37934/arfmts.96.2.8897.

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This study shows a thick plate, pointed on both sides, of variable elongation under action of subsonic and supersonic air flows. The relevance of the work is driven by the development of new aircraft that change their geometry during the flight, in particular, aircraft that change the relative elongation during the flight. The aim of this work is to determine the aerodynamic fields around the pointed plate, taking into account its variable elongation, and to determine the effect of variable elongation on the drag coefficient of the plate. Numerical simulation was used as a research tool. Mathematical modeling is based on Reynolds-averaged Navier-Stokes equations. The original software was used for the analysis; the computational algorithm is based on the finite volume method. The mathematical model and algorithm of numerical computation of subsonic and supersonic air flow acting on a pointed plate are presented. A pattern of gas flow acting on the plate is obtained at zero angle of attack for Mach numbers from 0,6 to 4. The dependence of the plate drag coefficient on Mach number and relative elongation is obtained. It is established that for a thick pointed plate the drag coefficient significantly depends on the elongation for both sound and supersonic flow. As a result of numerical experiments, the anomalous behavior of the drag coefficient in the transonic area at large elongations was found. It is shown that the decrease in elongation leads to an increase in the drag coefficient of the plate, which affects the aerodynamic characteristics of the aircraft of variable elongation.

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TENG, SHANG-HUA, and CHI WAI WONG. "UNSTRUCTURED MESH GENERATION: THEORY, PRACTICE, AND PERSPECTIVES." International Journal of Computational Geometry & Applications 10, no. 03 (June 2000): 227–66. http://dx.doi.org/10.1142/s0218195900000152.

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Mesh generation is a great example of inter-disciplinary research. Its development is built upon advances in computational and combinatorial geometry, data structures, numerical analysis, and scientific applications. Its success is justified not only by mathematical proofs about the quality and the numerical relevancy of geometry-based meshing algorithms, but also by the performance of meshing software in real applications. It embraces both provably good algorithms and practical heuristics. This paper presents a brief overview of algorithms, theorems, and software in mesh generation.

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Abreu, Zita, Guillaume Cantin, and Cristiana J. Silva. "Analysis of a COVID-19 compartmental model: a mathematical and computational approach." Mathematical Biosciences and Engineering 18, no. 6 (2021): 7979–98. http://dx.doi.org/10.3934/mbe.2021396.

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<abstract>In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.</abstract>

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36

Beaudoin, N. "Tutorial/Artical didactique: A high-accuracy mathematical and numerical method for Fourier transform, integral, derivatives, and polynomial splines of any order." Canadian Journal of Physics 76, no. 9 (September 1, 1998): 659–77. http://dx.doi.org/10.1139/p98-046.

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From few simple and relatively well-known mathematical tools, an easily understandable, though powerful, method has been devised that gives many useful results about numerical functions. With mere Taylor expansions, Dirac delta functions and Fourier transform with its discrete counterpart, the DFT, we can obtain, from a digitized function, its integral between any limits, its Fourier transform without band limitations and its derivatives of any order. The same method intrinsically produces polynomial splines of any order and automatically generates the best possible end conditions. For a given digitized function, procedures to determine the optimum parameters of the method are presented. The way the method is structured makes it easy to estimate fairly accurately the error for any result obtained. Tests conducted on nontrivial numerical functions show that relative as well as absolute errors can be much smaller than 10-100, and there is no indication that even better results could not be obtained. The method works with real or complex functions as well; hence, it can be used for inverse Fourier transforms too. Implementing the method is an easy task, particularly if one uses symbolic mathematical software to establish the formulas. Once formulas are worked out, they can be efficiently implemented in a fast compiled program. The method is relatively fast; comparisons between computation time for fast Fourier transform and Fourier transform computed at different orders are presented. Accuracy increases exponentially while computation time increases quadratically with the order. So, as long as one can afford it, the trade-off is beneficial. As an example, for the fifth order, computation time is only ten times greater than that of the FFT while accuracy is 108 times better. Comparisons with other methods are presented.PACS Nos.: 02.00 and 02.60

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37

Mat Isa, Zaiton, Mohd Danial Nazri, and Amidora Idris. "Numerical Simulation of Gas Flow through a Cylindrical Grain Storage." Malaysian Journal of Fundamental and Applied Sciences 18, no. 5 (December 15, 2022): 584–91. http://dx.doi.org/10.11113/mjfas.v18n5.2619.

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This study is concerned with a process known as fumigation in the grain industry. During this process, fumigant is injected at the inlet of storage and is expected to distribute throughout the stored grain to kill the insects in it. The present research focuses on the study of the fumigant (phosphine) flow distribution based on mathematical modelling and numerical simulation through available Computational Fluid Dynamic (CFD) software. In particular, the mathematical modelling is translated into the CFD and simulation is ran to determine areas where insects might find refuge. Hence provide information for conducting more effective fumigation. Numerical simulation using CFD software, for example, FLUENT, is widely known as cost and time effective. However, the numerical simulation needs to be verified before conducting such studies. For a simple case, the analytical solution exists. Therefore, the analytic solution for a simple case, can be used for verification and serve as a basis for adopting a CFD software, FLUENT for an extended geometry and boundary conditions. The numerical results are found to agree well with the analytical results. Overall, the fumigant gas flows towards the outlet regardless of the position of the outlet.

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Yu, Li-ren, and Jun Yu. "ENVIRONMENTAL FLOW AND CONTAMINANT TRANSPORT MODELING IN THE AMAZONIAN WATER SYSTEM BY USING Q3DRM1.0 SOFTWARE." International Journal of Research -GRANTHAALAYAH 5, no. 12 (July 3, 2020): 377–91. http://dx.doi.org/10.29121/granthaalayah.v5.i12.2017.525.

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This paper reports a fine numerical simulation of environmental flow and contaminant transport in the Amazonian water system near the Anamã City, Brazil, solved by the Q3drm1.0 software, developed by the Authors, which can provide the different closures of three depth-integrated two-equation turbulence models. The purpose of this simulation is to refinedly debug and test the developed software, including the mathematical model, turbulence closure models, adopted algorithms, and the developed general-purpose computational codes as well as graphical user interfaces (GUI). The three turbulence models, provided by the developed software to close non-simplified quasi three-dimensional hydrodynamic fundamental governing equations, include the traditional depth-integrated two-equation turbulence model, the depth-integrated two-equation turbulence model, developed previously by the first Author of the paper, and the depth-integrated two-equation turbulence model, developed recently by the Authors of this paper. The numerical simulation of this paper is to solve the corresponding discretized equations with collocated variable arrangement on the non-orthogonal body-fitted coarse and fine two-levels’ grids. With the help of Q3drm1.0 software, the steady environmental flows and transport behaviours have been numerically investigated carefully; and the processes of contaminant inpouring as well as plume development, caused by the side-discharge from a tributary of the south bank (the right bank of the river), were also simulated and discussed in detail. Although the three turbulent closure models, used in this calculation, are all applicable to the natural rivers with strong mixing, the comparison of the computational results by using the different turbulence closure models shows that the turbulence model with larger turbulence parameter provides the possibility for improving the accuracy of the numerical computations of practical problems.

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39

Marchevsky, I. K., and V. V. Puzikova. "The Modified LS-STAG Method Application for Planar Viscoelastic Flow Computation in a 4:1 Contraction Channel." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 3 (96) (June 2021): 46–63. http://dx.doi.org/10.18698/1812-3368-2021-3-46-63.

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In this study we present the modification of the LS-STAG immersed boundary cut-cell method. This modification is designed for viscoelastic fluids. Linear and quasilinear viscoelastic fluid models of a rate type are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software is created for viscous incompressible flows simulation both by the LS-STAG method and by it developed modifications. Besides of this, the software package is designed to compute extra-stresses for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson --- Segalman fluids on the LS-STAG mesh. The construction of convective derivatives discrete analogues is described for Oldroyd, Cotter --- Rivlin, Jaumann --- Zaremba --- Noll derivatives. The centers of base LS-STAG mesh cells are the locations for shear non-Newtonian stresses computation. The corners of these cells are the positions for normal non-Newtonian stresses computation. The first order predictor--corrector scheme is the basis for time-stepping numerical algorithm. Benchmark solutions for the planar flow of Oldroyd-B fluid in a 4:1 contraction channel are presented. A critical value of Weissenberg number is defined. Computational results are in good agreement with the data known in the literature

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40

Gnegel, Fabian, Armin Fügenschuh, Michael Hagel, Sven Leyffer, and Marcus Stiemer. "A solution framework for linear PDE-constrained mixed-integer problems." Mathematical Programming 188, no. 2 (March 4, 2021): 695–728. http://dx.doi.org/10.1007/s10107-021-01626-1.

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AbstractWe present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

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41

Anuar, Nur Syazana, Norfifah Bachok, and Ioan Pop. "Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect." Mathematics 9, no. 6 (March 18, 2021): 643. http://dx.doi.org/10.3390/math9060643.

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The mathematical modeling of dusty Cu-Al2O3/water nanofluid flow driven by a permeable deformable sheet was explored numerically. Rather than no–slip conditions at the boundary, velocity slip and thermal slip were considered. To achieve the system of nonlinear ordinary differential equations (ODEs), we employed some appropriate transformations and solved them numerically using MATLAB software (built–in solver called bvp4c). The influences of relevant parameters on fluid flow and heat transfer characteristics are discussed and presented in graphs. The findings showed that double solutions appeared in the case of stretching and shrinking sheets which contributed to the analysis of stability. The stability analysis, therefore, confirmed that merely the first solution was a stable solution. The addition of nanometer-sized particles (Cu) was found to significantly strengthen the heat transfer rate of the dusty nanofluid. Meanwhile, an upsurge in the velocity and thermal slip was shown to decrease the local Nusselt number. The result also revealed that an increment of fluid particle interaction decreased the boundary layer thickness.

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42

Eminov, S. I., and S. Yu Petrova. "The Rate of Convergence of Hypersingular Equations Numerical Computation." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 11, no. 2 (2018): 139–46. http://dx.doi.org/10.14529/mmp180211.

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43

Attia, Mohamed El Hadi. "Numerical Study of the Combustion of CH4-C3H8/ Air: Application to a Combustion Chamber with Two Coaxial Jets." International Journal of Energetica 2, no. 2 (December 31, 2017): 38. http://dx.doi.org/10.47238/ijeca.v2i2.46.

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In this study, we studied numerically the non-premixed combustion provided by two coaxial methane-propane/air jets in a 3D cylindrical combustion chamber. To study this kind of phenomenon we used a special treatment of the mathematical model and we chose two models of computation PDF and LES. In order to find the aero-thermo-chemical characteristics in the burner, namely: axial velocity, temperature and mass fraction of carbon monoxide CO. Using commercial calculation software CFD Fluent The objective of this work is to research the fuel that reduces the emission of carbon monoxide CO, which is considered a gas toxic to the environment, by comparing the two fuels CH4 and C3H8. The results give methane fuel reduces carbon monoxide as a pollutant chemical species in combustion products compared to propane fuel.

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44

Borisov, V. E., E. V. Zenchenko, B. V. Kritsky, E. B. Savenkov, M. A. Trimonova, and S. B. Turuntaev. "Numerical Simulation of Laboratory Experiments on the Analysis of Filtration Flows in Poroelastic Media." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 1 (88) (February 2020): 16–31. http://dx.doi.org/10.18698/1812-3368-2020-1-16-31.

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The work is devoted to mathematical simulation of laboratory experiments on the single-phase fluid displacement in synthetic porous samples. The basis of the mathematical model used is the system of poroelasticity equations in terms of the Biot's model, which implies that the processes of fluid filtration and the dynamics of changes in the stress-strain state of a continuous medium are considered together in the framework of a single coupled statement. For simulation, the software package developed at the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, was used. The laboratory experiments considered in this work were performed at the Institute of Geosphere Dynamics, Russian Academy of Sciences. The mathematical model used is briefly presented; the main computational algorithms and the features of their software implementation are described. A detailed description of the laboratory set-up, laboratory experiments themselves and their results are given. A significant part of the work is devoted to the problem statement description in terms of mathematical simulation. The results of calculations are presented; the calculated and experimentally observed dependencies are compared. The possible causes of the observed deviations are analyzed.

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45

Booker, Andrew R., Andreas Strömbergsson, and Holger Then. "Bounds and algorithms for the -Bessel function of imaginary order." LMS Journal of Computation and Mathematics 16 (2013): 78–108. http://dx.doi.org/10.1112/s1461157013000028.

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AbstractUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of${K}_{ir} (x)$and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of$r$. Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of${K}_{ir} (x)$.

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46

Borisov, Vitaly Evgenyevich, Boris Viktorovich Kritskiy, and Yuri Germanovich Rykov. "MCFL-Chem software module for numerical simulation of high-speed reacting flows." Keldysh Institute Preprints, no. 21 (2022): 1–40. http://dx.doi.org/10.20948/prepr-2022-21.

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In this paper we present a computational model for high-speed multicomponent flows of reacting gases mixtures, which formed the core of the MCFL-Chem software module. The system of Navier–Stokes equations for a multicomponent reacting gas is used as a mathematical model; chemical reactions are described by a detailed kinetic scheme. The general solution algorithm is based on the splitting scheme for the types of processes under consideration: convection–diffusion–chemical reactions, an approach based on the modified method of S.K. Godunov is used. The present work continues the previous studies of the authors on numerical simulation of multicomponent gas mixtures flows, in this work we focus on the implementation of the chemical reactions module, its implementation in the general algorithm, validation and verification tests.

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47

Borisov, Vitaly Evgenyevich, Boris Viktorovich Kritskiy, and Yuri Germanovich Rykov. "MCFL-Chem software module for numerical simulation of high-speed reacting flows." Keldysh Institute Preprints, no. 21 (2022): 1–40. http://dx.doi.org/10.20948/prepr-2022-21.

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Анотація:

In this paper we present a computational model for high-speed multicomponent flows of reacting gases mixtures, which formed the core of the MCFL-Chem software module. The system of Navier–Stokes equations for a multicomponent reacting gas is used as a mathematical model; chemical reactions are described by a detailed kinetic scheme. The general solution algorithm is based on the splitting scheme for the types of processes under consideration: convection–diffusion–chemical reactions, an approach based on the modified method of S.K. Godunov is used. The present work continues the previous studies of the authors on numerical simulation of multicomponent gas mixtures flows, in this work we focus on the implementation of the chemical reactions module, its implementation in the general algorithm, validation and verification tests.

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48

Chistyakov, Alexander, Alena Filina, and Vladimir Litvinov. "NUMERICAL MODELING OF HYDRODYNAMIC PROCESSES IN THE TAGANROG BAY OF THE AZOV SEA." Computational Mathematics and Information Technologies 1, no. 2 (2020): 101–13. http://dx.doi.org/10.23947/2587-8999-2020-1-2-101-113.

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This paper covers the creation and numerical realization of proposed mathematical model of hydrodynamical processes in shallow water based on contemporary information technology and new computational methods that allow improve the prediction accuracy of the environmental situation using the example of the Taganrog Bay in the Azov Sea basin. The proposed mathematical hydrodynamics model takes into account surges, dynamically reconstructed geometry, elevation of the level and coastline, wind currents and friction against the bottom, Coriolis force, turbulent exchange, evaporation, river flow, deviation of the pressure field value from the hydrostatic approximation, the salinity and temperature impact. The discretization of the mathematical model of hydrodynamics was performed using the splitting schemes for physical processes. The constructed discrete analogs possess the properties of conservatism, stability, and convergence. Numerical algorithms are also proposed for solving the arising SLAEs that improve the accuracy of predictive modeling. The practical significance of this research is software implementation of the developed model and the determination of limits and prospects of its application. The experimental software development was based on a graphics accelerator for mathematical simulation the possible scenarios of shallow water ecosystems in consideration the environmental factors influence. The decomposition methods taking into account the CUDA architecture specifications were used at parallel implementation for computationally labors diffusion-convection problems.

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49

LUHANDJULA, M. K. "A MONTE CARLO SIMULATION BASED APPROACH FOR STOCHASTIC SEMI-INFINITE MATHEMATICAL PROGRAMMING PROBLEMS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, supp02 (April 2007): 139–57. http://dx.doi.org/10.1142/s0218488507004662.

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The paper deals with stochastic mathematical programming problems with additional difficulty brought up by the presence of infinitely many constraints. A sample average approximation (SAA) approach is proposed and properties of SAA estimators, analyzed. It is shown that for the case of deterministic constraints, SAA estimators are consistent and meet requirements to qualify the estimates as acceptable approximations of unknown values. Moreover, good error bounds of the estimate of the objective function are provided. We also discuss a Galerkin-like scheme and a tailored cutting-plane method for solving resulting semi-infinite SAA problems. The framework is then extended to the case of random constraints through Karhunen–Loève expansion or constraints approximation via sampling. A general procedure for solving stochastic semi-infinite programming problems, that lends itself better for parallel computation, is then described. Numerical examples are also included for the sake of illustration.

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50

Konkina, A. S. "Numerical Research of the Mathematical Model for Traffic Flow." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 12, no. 4 (2019): 128–34. http://dx.doi.org/10.14529/mmp190411.

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