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Solution of lossy dielectric moving waveguides using numerical method (Davidenko's approach)

ELECTROMAGNETICS 2002年第8期22卷 659-666页

作者： Shabat, MM Madi, YS Jäger, D Islamic Univ Gaza Dept Phys Gaza Israel Coll Educ Dept Math Gaza Israel Gerhard Mercator Univ Zentrum Halbleitertech & Optoelekt Duisburg Germany

This paper presents a numerical method called Davidenko's method to search the complex roots of the dispersion relation of a lossy asymmetric moving waveguide. The propagation characteristics of the guided TE waves are examined. The effects of variation of the mode, the core thickness, the dielectric constant of the substrate, and the velocity of waveguide on the attenuation of the waves are also calculated.

关键词： numerical algorithm dispersion equation complex roots moving waveguides

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A framework for numerical integration of crystal elasto-plastic constitutive equations compatible with explicit finite element codes

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INTERNATIONAL JOURNAL OF PLASTICITY 2007年第10-11期23卷 1918-1937页

作者： Amirkhizi, Alireza V. Nemat-Nasser, Sia Univ Calif San Diego Dept Mech & Aerosp Engn Ctr Excellence Adv Mat La Jolla CA 92093 USA

In this paper we summarize the elements of a numerical integration scheme for elasto-plastic response of single crystals. This is intended to be compatible with large-scale explicit finite element codes and therefore can be used for problems involving multiple crystals and also overall behavior of polycrystalline materials. The steps described here are general for anisotropic elastic and plastic response of crystals. The crystallographic axes of the lattice are explicitly stored and updated at each time step. A plastic predict or-elastic corrector scheme is used to calculate the plastic strain rates on all active slip systems based on a rate-dependent physics-based constitutive model without the need of further auxiliary assumptions. Finally we present the results of numerous calculations using a physics-based rate- and temperature-dependent model of copper and the effect of elastic unloading, elastic crystal anisotropy, and deformation-induced lattice rotation are emphasized. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： phvsics-based modeling crystal plasticity elastoplastic anisotropy numerical algorithm

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On numerical study of constrained coupled shape optimization problems based on a new shape derivative method

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numerical METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2023年第3期39卷 2018-2059页

作者： Boulkhemair, Abdesslam Chakib, Abdelkrim Sadik, Azeddine UFR Sci & Tech Nantes Lab Math Jean Leray UMR6629 CNRS Nantes France Univ Sultan Moulay Slimane Fac Sci Tech Lab Math & Applicat BP 523 Beni Mellal Morocco

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach.

关键词： boundary element convex domain coupled problem numerical algorithm shape derivative shape optimization support function

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Detection of the singularities of a complex function by numerical approximations of its Laurent coefficients

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numerical algorithmS 2018年第4期77卷 955-982页

作者： Rizzardi, Mariarosaria Univ Napoli Parthenope Ctr Direz Napoli DiST Dipartimento Sci & Tecnol Is C4 I-80143 Naples Italy

For several applications, it is important to know the location of the singularities of a complex function: just for example, the rightmost singularity of a Laplace Transform is related to the exponential order of its inverse function. We discuss a numerical method to approximate, within an input accuracy tolerance, a finite sequence of Laurent coefficients of a function by means of the Discrete Fourier Transform (DFT) of its samples along an input circle. The circle may also enclose some singularities, since the method works with the Laurent expansion. The DFT is computed by the FFT algorithm so that, from a computational point of view, the efficiency is guaranteed. The function samples may be obtained by solving a numerical problem such as, for example, a differential problem. We derive, as consequences of the method, some new outcomes able to detect those singularities which are close to the circle and to discover if the singularities are all external or internal to the circle so that the Laurent expansion reduces to its regular or singular part, respectively. Other singularities may be located by means of a repeated application of the method, as well as an analytic continuation. Some examples and results, obtained by a first implementation, are reported.

关键词： numerical algorithm Software suite Interactive software Complex singularities Laurent coefficients Analytic continuation

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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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numerical method research and characteristics analysis on frozen start-up process of high-temperature heat pipe

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APPLIED THERMAL ENGINEERING 2024年 257卷

作者： Wang, Weixiang Zhang, Kefan Dong, Sifan Wang, Shuai Chen, Hongli Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230026 Anhui Peoples R China Univ Sci & Technol China Deep Space Explorat Lab Hefei 230088 Anhui Peoples R China

Future space exploration technology requires a long-life and reliable power source that is not reliant on solar energy. Space micro-reactors are able to meet this need, with Heat Pipe Cooled Reactors (HPR) emerging as a notable type of space micro-reactor that has attracted widespread attention in recent years. The HPR utilizes high-temperature alkali metal heat pipes for heat transfer, which presents certain complexities due to the solid state of the alkali metals working medium at room temperature. This results in a three-phase transition during the high-temperature heat pipes start-up process, which significantly impacts the heat transfer characteristics and dynamic behavior of the HPR start-up process. Consequently, thorough research is necessary in this area. numerical simulation is a crucial tool that can effectively analyze, predict, and guide experiments. This article utilizes the Finite Volume Method (FVM) to develop a simulation code for high-temperature heat pipe frozen start-up. Various physical models are integrated to describe different components of the heat pipe: the container is represented by a two-dimensional axisymmetric heat conduction equation, the wick region utilizes a Fixed Grid Method (FGM) to depict the melting process of the medium, and the vapor channel is described through a two-dimensional axisymmetric compressible laminar flow. The wick region and vapor channel are coupled through the evaporation and condensation of the medium. For the vapor channel, numerical methods such as SIMPLE and PISO are used for solving. Adaptive time step and OpenMP acceleration are employed in the code to enhance computational efficiency. Finally, by comparing the calculated results with experimental data, the feasibility and accuracy of the code are assessed, highlighting special phenomena during the start-up process. The findings confirm that the developed code accurately predicts parameter changes during start-up, and can serve as a heat pipe analysis mo

关键词： High-temperature heat pipe numerical algorithm High-speed compressible flow

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numerical simulation of vibration of composite pipelines conveying fluids with account for lumped masses

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2020年第0期179卷 104034-000页

作者： Khudayarov, B. A. Komilova, Kh M. Turaev, F. Zh Aliyarov, J. A. Tashkent Inst Irrigat & Agr Mechanizat Engineers Dept Higher Math Str Kariniyazova 39 Tashkent 100000 Uzbekistan

Vibration problems of pipelines made of composite materials with account for lumped masses are considered in the paper. A mathematical model of motion of pipelines conveying fluid flow is developed based on the Winkler base with account for viscosity properties of the material of structures and pipeline bases, axial forces, internal pressure, resistance forces and lumped masses. To describe the strain processes in viscoelastic materials, the Boltzmann-Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov-Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations. A computational algorithm is developed based on the elimination of the features of integro-differential equations with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, lumped masses, internal pressure, Reynolds numbers and base parameters on the vibration of a viscoelastic pipeline conveying fluid flow is analyzed. It is revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in critical flow rate. It was found that an increase in the viscosity parameter, the parameters of lumped masses and internal pressure leads to a decrease in critical flow rate. It is shown that when the lumped masses are moved away from the center along the pipeline length the vibration frequency increases.

关键词： Mathematical model Viscoelasticity Pipeline numerical algorithm Vibration Lumped mass

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Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks

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JOURNAL OF COMPUTATIONAL NEUROSCIENCE 2007年第1期22卷 81-100页

作者： Rangan, Aaditya V. Cai, David NYU Courant Inst Math Sci New York NY 10012 USA

We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states;(ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step;and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models-for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in O(N) operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, hi

关键词： numerical algorithm network architecture

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A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space

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APPLIED MATHEMATICS AND COMPUTATION 2012年第14期218卷 7362-7368页

作者： Lin, Yingzhen Niu, Jing Cui, Minggen Harbin Inst Technol Dept Math Weihai 264209 Shandong Peoples R China Harbin Normal Univ Sch Math & Sci Harbin 150025 Heilongjiang Peoples R China

In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Nonlinear problems Three-point boundary value conditions numerical algorithm Reproducing kernel function

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numerical Optimal Harvesting for a Periodic Age-Structured Population Dynamics with Logistic Term

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numerical FUNCTIONAL ANALYSIS AND OPTIMIZATION 2009年第3-4期30卷 183-198页

作者： Anita, Sebastian Amautu, Viorel Stefanescu, Razvan Alexandru Ioan Cuza Univ Fac Math Iasi 700506 Romania Inst Math Octav Mayer Iasi Romania Gr T Popa Univ Med Pharm Dept Math & Comp Sci Iasi Romania

We investigate an optimal harvesting problem for age-structured population dynamics with logistic term and periodic vital rates. We use first-order necessary optimality conditions in order to derive an algorithm to ap... 详细信息

关键词： Age-structured population dynamics Logistic term numerical algorithm Optimal harvesting Optimality conditions Periodic solutions Periodic vital rates

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