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Plane Wave Finite Element method for the Dynamic Response of the Periodic Pile-Type Composite Ground Under a Harmonic Concentrated Load

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2024年第0期

作者： Liu, Yang Lu, Jian-Fei Jiangsu Univ Dept Civil Engn Zhenjiang 212013 Jiangsu Peoples R China

In this study, a simplified model for the pile-type composite ground, namely, the periodic pile-type composite ground (PPCG) model is proposed. The PPCG in this study is assumed to be periodic in the horizontal directions and finite in the vertical direction. For investigation of the dynamic response of the PPCG to a harmonic concentrated load, a plane wave finite element (PWFE) method for the PPCG under the load is developed in this study. To develop the method, the concentrated load is decomposed into its wavenumber domain components by the 2D Fourier transform first. The response of the PPCG to a wavenumber domain load component is represented by a set of plane waves, and the variables associated with each plane wave are discretized via the FEM along the vertical direction of the PPCG. The finite element equations for each plane wave of the PPCG are developed via the virtual work principle. To obtain the overall dynamic response of the PPCG to the concentrated load by synthesizing the responses due to all load components effectively, the mode superposition method is used to construct the response of the PPCG to the load component, and the polar coordinate system-based inverse Fourier transform method is developed for the inversion of the 2D Fourier transform with respect to the wavenumber. With the developed method, some numerical results about the dynamic response of the PPCG to the concentrated load are presented.

关键词： The periodic pile-type composite ground plane wave expansion plane wave finite element method the fundamental solution contour integration method

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Comparison of Vector Fitting and contour integration methods for Pole-Zero Analysis of Microwave Filters

Comparison of Vector Fitting and Contour Integration Methods...

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IEEE Asia-Pacific Microwave Conference (APMC)

作者： Tan, Eng Leong Heh, Ding Yu Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

ISBN: (纸本)9781728169620

This paper presents the comparison of vector fitting and contour integration methods for pole-zero analysis of microwave filters. Two cases of microwave filters are considered, which include an all-pole classical coupled line filter and a linear phase filter with complex zeros. The poles and zeros obtained using vector fitting method with different chosen number of poles and fitting bandwidth are analyzed. It is found that the poles and zeros may be inconsistent depending on the chosen number of poles and bandwidth. Furthermore, the method may introduce spurious complex zeros that do not satisfy the S parameters unitary conditions, while the poles also do not maintain periodicity between frequency bands for transmission line structures. On the other hand, the poles and zeros obtained using contour integration method are consistent and certain. They also satisfy the unitary conditions and periodicity for transmission line structures.

关键词： Poles and zeros contour integration method vector fitting method microwave filters

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Local RBF method for Transformed Three Dimensional Sub-Diffusion Equations

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International Journal of Applied and Computational Mathematics 2022年第3期8卷 1-21页

作者： Kamran Ahmadian, A. Salimi, M. Salahshour, S. Department of Mathematics University of Management and Technology Khyber Pakhtoon Khwa Lahore Pakistan School of Mathematical Sciences College of Science and Technology Wenzhou-Kean University Wenzhou China Department of Mathematics Near East University Nicosia TRNC Mersin 10 Turkey Department of Mathematics and Statistics St. Francis Xavier University Antigonish NS Canada Center for Dynamics Faculty of Mathematics Technische Universität Dresden Dresden 01062 Germany Faculty of Engineering and Natural Sciences Bahcesehir University Istanbul Turkey

In this article we study the numerical solution of time fractional 3D sub-diffusion equation in Caputo sense. The time fraction sub-diffusion equation is obtained by replacing the time derivative in the standard sub-diffusion equation with time fractional derivative. Numerous physical phenomenon are modeled via sub-diffusion equation such as porous systems, polymers, and turbulent plasma etc. The local RBF method is one of most successful methods for numerical solution of integer and non-integer order PDEs, as it overcome the computational burden of the global RBF method. Our proposed numerical scheme approximates the solution in three main steps. Firstly, we use the Laplace transform to reduce the given time dependent problem to an equivalent time independent problem. Secondly, we approximate the solution of the transformed equation using the local RBF method. Finally, the solution of original problem is retrieved via inverse Laplace transform by representing it as a Bromwich integral. The Bromwich integral is then approximated using the mid point rule. The purpose of using the Laplace transform is avoiding the classical time marching procedure. One of the main benefits of local RBF method is that it only considers the nodes located in the sub-domain surrounding a local node for numerical approximation at this node. This method perform well for large scale problem and can also reduce the ill conditioning issues. The convergence and stability of the proposed numerical method are discussed. The proposed numerical method is tested against three examples. The computational results highlight the accuracy and efficiency of the method. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： 3D sub-diffusion equation Caputo’s derivative contour integration method Convergence Laplace transform Local RBFs method Mid point rule Stability Talbot’s contour

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Numerical modelling of advection diffusion equation using Chebyshev spectral collocation method and Laplace transform

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RESULTS IN APPLIED MATHEMATICS 2024年 21卷

作者： Shah, Farman Ali Kamran Shah, Kamal Abdeljawad, Thabet Islamia Coll Peshawar Dept Math Peshawar 25120 Khyber Pakhtunk Pakistan Prince Sultan Univ Dept Math & Sci Riyadh 11586 Saudi Arabia Univ Malakand Dept Math Chakdara Kpk Pakistan

In this article a numerical method for numerical modelling of advection diffusion equation is developed. The proposed method is based on Laplace transform (LT) and Chebyshev spectral collocation method (CSCM). The LT is used for time-discretization and the CSCM is used for discretization of spatial derivatives. The LT is used to transform the time variable and avoid the finite difference time stepping method. In time stepping technique the accuracy is achieved for very small time step which results in a very high computational time. The spatial operators are discretized using CSCM to achieve high accuracy as compared to other methods. The method is composed of three primary stages: firstly the given problem is transformed into a corresponding inhomogeneous elliptic problem by using the LT;secondly the CSCM used to solve the transformed problem in LT domain;finally the solution obtained in LT domain is converted to time domain via numerical inverse LT. The inversion of LT is generally an ill-posed problem and due to this reason various numerical inversion methods have been developed. In this article we have utilized the contour integration method which is one of the most efficient methods. The most important feature of this approach is that it handles the time derivative with the Laplace transform rather than the finite difference time stepping approach, avoiding the untoward impact of time steps on stability and accuracy of the method. Five test problems are used to validate the efficiency and accuracy of the proposed numerical scheme.

关键词： Laplace transform Numerical inverse Laplace transform Advection diffusion problems Spectral collocation method contour integration method Trapezoidal rule

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Efficient and accurate quadrature methods of Fourier integrals with a special oscillator and weak singularities

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APPLIED MATHEMATICS AND COMPUTATION 2023年 440卷

作者： Kang, Hongchao Wang, Ruoxia Zhang, Meijuan Xiang, Chunzhi Hangzhou Dianzi Univ Sch Sci Dept Math Hangzhou 310018 Zhejiang Peoples R China

The recent article (J. Math. Anal. Appl. 494 (2021), Article number: 124 4 48) presented an asymptotic Filon-type method for computing the oscillatory integral with a special oscilla-tor and weak singularities, f0b x alpha (b - x)fi f (x)eiwxrdx, -1 < alpha , fi < 0 , 0 < b < + 00 , w E R , r E N +. In this article, we propose and analyze two different efficient and accurate quadrature methods for this singularly oscillatory integral. First, we give a two-point Taylor interpo-lation method by using a two-point Taylor polynomial instead of f (x ) . In addition, we propose a more efficient contour integration method. By exploiting the Taylor polynomial of the function f at x = 0 , and then based on the additivity of the integration interval, we change the considered integral into two integrals. One integral can be efficiently com-puted by the contour integration method based on Cauchy Residue Theorem and gener-alized Gaussian-Laguerre quadrature rule. The other integral can be explicitly calculated by special functions. Specifically, we perform the rigorous error analysis of the proposed methods and obtain asymptotic error estimates in inverse powers of the frequency param-eter w. Ultimately, the proposed methods are compared with the asymptotic Filon-type method given in this work (J. Math. Anal. Appl. 494 (2021), Article number: 124 4 48) and the modified Filon-type method. At the same computational cost, the two-point Taylor in-terpolation method and the asymptotic Filon-type method have a very close accuracy level. Their accuracy is higher than that of the modified Filon-type method, and the precision of the contour integration method is much higher than that of the asymptotic Filon-type method, the modified Filon-type method, and the two-point Taylor interpolation method. We verify error analyses of the proposed methods by experimental results. Numerical ex-periments can also verify the efficiency and precision of the proposed methods. (c) 2022 Elsevier Inc. All

关键词： Weak singularities contour integration method Two-point Taylor interpolation method Generalized Gaussian-Laguerre quadrature rule

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View factor in cone calorimeter testing

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2016年 93卷 217-227页

作者： Kang, Sungwook Choi, Sengkwan Choi, J. Yoon Univ Ulster Sch Built Environm Newtownabbey BT37 0QB Antrim North Ireland Korea Conform Labs Div Built Environm Fire Safety Team Ochang Chungchongbukdo South Korea

This work focuses on algebraic derivations of geometric view factors (i) from plane element to interior of truncated cone in parallel configuration;(ii) from plane element to segment of interior of truncated cone in perpendicular configuration, to clarify irradiance-related uncertainties generated in cone calorimeter tests on intumescent-type fire resistant systems. Since such specimens undergo moving boundaries and perimeter surface exposures in the course of the bench-scaled fire tests, it is inevitable to encounter (i) irradiance intensifications on their top boundaries and (ii) irradiance influxes on their perimeter areas, which have not been reflected in conventional approaches. These irradiance-related issues can be solved by calculating diffuse view factors. Their derivations are achieved by using the contour integration method and verified by existing literature and direct measurements. The calculations are presented by graphical representations obtained through a process of mapping. This theoretical approach enables one to clarify the exact quantity of irradiance at any position under the heater, and thus to quantitatively analyse the resultant impacts of (i) non-uniform irradiance dispersions and (ii) non-consistent thermal loads occurring during the tests, on the quantification of radiation absorption. The findings demonstrate that discrepancies between exact calculations and conventional approximations, induced by these effects, are appreciable and hence should not be neglected in such quantifications. The derived formulae can be applied in solving radiation issues arising with analogous geometries, and the particulars in terms of irradiance can also promote the subsequent assessment of thermal behaviours of any specimen experiencing geometrical changes during cone calorimeter tests. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Thermal radiation Irradiance View factor Cone calorimeter contour integration method

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Layer-resolved magneto-optical Kerr effect in semi-infinite inhomogeneous layered systems

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PHASE TRANSITIONS 2002年第1-2期75卷 167-184页

作者： Vernes, A Szunyogh, L Weinberger, P Vienna Univ Technol Ctr Computat Mat Sci A-1060 Vienna Austria Budapest Univ Technol & Econ Dept Theoret Phys H-1521 Budapest Hungary

The contour integration technique applied to calculate the optical conductivity tensor at finite temperatures in the case of inhomogeneous surface layered systems within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker band structure method is extended to arbitrary polarizations of the electric field. It is shown that besides the inter-band contribution, the contour integration technique also accounts for the intra-band contribution. Introducing a layer-resolved complex Kerr angle, the importance of the first, non-magnetic buffer layer below the ferromagnetic surface on the magneto-optical Kerr effect in the Co \ Pt-m multilayer system is shown. Increasing the thickness of the buffer Pt, the layer-resolved complex Kerr angles follow a linear dependence with respect to m only after nine Pt mono-layers.

关键词： magneto-optical Kerr effect band structure calculations contour integration method layer-resolved Kerr angles

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Experimental study and numerical simulation of preform or sheet exposed to infrared radiative heating

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JOURNAL OF MATERIALS PROCESSING TECHNOLOGY 2001年第1-3期119卷 90-97页

作者： Monteix, S Schmidt, F Le Maoult, Y Ben Yedder, R Diraddo, RW Laroche, D Natl Res Council Canada Inst Ind Mat Ottawa ON K1A 0R6 Canada

Thermoplastic processing like the injection stretch blow moulding and thermoforming processes provide the heating stage with infrared oven. This is a critical stage of the process, as the final part thickness is strongly dependent on the preform or sheet temperature distribution prior to forming. Optimisation of the infrared oven is therefore necessary. Experiments have been conducted in order to characterise the heat source of the infrared emitter and the interaction between the heaters and a semi-transparent PET sheet. An 880 LW AGEMA infrared camera has been used to determine the surface distribution of the transmitted heat flux by measuring the temperature distribution on the surface of the thermoplastic sheet. In addition, numerical simulations of the temperature distribution using control-volume method have been carried out and compared with experimental data. (C) 2001 Published by Elsevier Science B.V.

关键词： contour integration method control-volume method heating stage infrared camera stretch blow moulding thermoforming view factor computation

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