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A systematic study on weak Galerkin finite-element method for second-order wave equation

COMPUTATIONAL & APPLIED MATHEMATICS 2022年第8期41卷 1-25页

作者： Jana, Puspendu Kumar, Naresh Deka, Bhupen Indian Inst Technol Guwahati Dept Math North Guwahati 781039 India

In this article, we present a systematic numerical study for second-order linear wave equation using weak Galerkin finite-element methods (WG-FEMs). Various degrees of polynomials are used to construct weak Galerkin finite-element spaces. Error estimates in L-2 norm as well as in discrete H-1 norm have been established for general weak Galerkin space (P-k (K), P-j (partial derivative K), [P-l (K)](2)), where k, j&l are non-negative integers with k >= 1. Time discretization for fully discrete scheme is based on second order in time Newmark scheme. Finally, we provide several numerical results to confirm theoretical findings.

关键词： Wave equation finite-element method Weak Galerkin method Semidiscrete and fully discrete schemes Optimal error estimates

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Fiber-alignment shifts in butterfly laser packaging by laser-welding technique: Measurement and finite-element method analysis

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JOURNAL OF ELECTRONIC MATERIALS 2004年第1期33卷 40-47页

作者： Hsu, YC Huang, WK Sheen, MT Cheng, WH Natl Sun Yat Sen Univ Inst Electroopt Engn Kaohsiung 80424 Taiwan

The post-weld shift (PWS)-induced fiber-alignment shifts of fiber-ferrule clip (FFC) joints in butterfly laser packaging by using laser-welding techniques and a high-magnification, video-probe camera system were studied experimentally and numerically. The measured results show that the fiber shifts of FFC joints with a 5-mum gap between the clip and ferrule exhibited shifts less than that without a gap. This suggests that the 5-mum gap design may be more suitable for FFC joints in laser packaging. The experimental measurements of fiber shifts in FFC joints were in reasonable agreement with the numerical calculations of the finite-element method (FEM) analysis. The major fiber-shift formation mechanisms of FFC joints in the laser-welding process may come from the mismatch of the thermal expansion coefficient, the solidification shrinkage, and the residual stresses within the FFC joint, but solidification shrinkage is the dominant cause. This study demonstrates that the FEM is an effective method for predicting PWS-induced fiber-alignment shifts in laser-module packaging.

关键词： fiber-alignment shift post-weld shift laser welding butterfly laser package finite-element method

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Design of trapezoidal-ridge waveguide by finite-element method

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IEE PROCEEDINGS-MICROWAVES ANTENNAS AND PROPAGATION 2004年第3期151卷 205-211页

作者： Lu, M Leonard, PJ Univ Bath Dept Elect & Elect Engn Bath BA2 7AY Avon England

Transmission characteristics of single and double trapezoidal-ridge waveguides, are analysed by the finite-element method. Design data of cutoff wavelength and single-mode bandwidth for different ridge dimensions are presented in tabulated forms. Field patterns of dominant mode and the first higher-order TE mode in both waveguides are also illustrated. Numerical results provide an extension to the existing design data of rectangular-ridge waveguides and are considered to be helpful in practical applications.

关键词： single-mode bandwidth waveguide theory cutoff wavelength Waveguides and microwave transmission lines trapezoidal-ridge waveguide design transmission characteristics finite element analysis finite element analysis Waveguide and cavity theory dominant mode field patterns first higher-order TE mode ridge waveguides finite-element method

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Investigating the Effects of Lead Forming Parameters on Intermetallic Layer Crack Using the finite-element method

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JOURNAL OF ELECTRONIC MATERIALS 2012年第4期41卷 774-781页

作者： Chin, J. W. C. Kok, C. K. Rajmohan, M. M. Yeo, V. S. H. Said, M. R. Multimedia Univ Fac Engn & Technol Bukit Beruang 75450 Melaka Malaysia Infineon Technol Malaysia Batu Berendam 75350 Melaka Malaysia Univ Teknikal Malaysia Melaka Durian Tunggal 76100 Melaka Malaysia

The lead trim-and-form process is important in the manufacturing of programmable logic devices, microprocessors, and memories. Normally, inspection of a chip package is performed in a lead inspection machine after the lead forming process to detect defects on the leads. One such defect is the lead intermetallic compound (IMC) crack, exhibiting itself as plating crack. In this study, IMC crack of package leads, which causes loose connection between the copper lead and the tin plating, was analyzed using the finite-element method. The simulation results were verified by matching the simulated and actual formed lead profile. Simulation results showed a strong correlation between IMC crack after forming and aging and high residual tensile strain induced during lead forming. A proposal was made to resolve the crack issue by performing design of experiment (DOE) to reduce the residual tensile strain of the lead upon forming. Three optimization parameters were chosen, namely the forming angle, the shank angle, and the pre-forming angle. It is shown that, with the optimized parameter setting, a reduction of the residual strain can be achieved, thus minimizing the risk of IMC crack.

关键词： Intermetallic layer crack lead trim-and-form tin plating residual tensile strain finite-element method

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Designing the performance of a thick-film laser power detector by means of a heat-transfer analysis using finite-element method

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SENSORS AND ACTUATORS A-PHYSICAL 1997年第3期58卷 213-218页

作者： Smetana, W Reicher, R Institut für Werkstoffe der Elektrotechnik Technische Universität Wien Gusshausstrasse 27–29 Vienna Austria

Besides the usual application of thick-film technology to produce circuits of high reliability, this technology is also attractive for the fabrication of sensors. A laser power detector has been realized utilizing the thick-film technique. A special detector configuration provides an exact laser power measurement independent of the position of beam impingement on the detector area and independent of the intensity distribution of the laser beam. The detector, which actually operates as a heat-flow meter, consists of a thermopile circularly applied on an AlN substrate. The geometrical proportions of the detector have been accommodated to an NdYAG laser with a given specification by means of thermal heat-transfer analysis using the finite-element method (FEM). Based on the FEM simulation of steady state and transient temperature distributions on the detector area induced by laser beam impingement, the performance and the operating range of the detector have been specified.

关键词： finite-element method heat-transfer analysis laser power detector thick films

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Evaluation of Through-Thickness Residual Stresses by Neutron Diffraction and finite-element method in Thick Weld Plates

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JOURNAL OF PRESSURE VESSEL TECHNOLOGY-TRANSACTIONS OF THE ASME 2017年第3期139卷 031401页

作者： Jiang, Wenchun Woo, Wanchuck Wan, Yu Luo, Yun Xie, Xuefang Tu, S. T. Korea Atom Energy Res Inst Neutron Sci Div 1045 Daedeok Daero Daejeon 305353 South Korea China Univ Petr East China Coll Chem Engn State Key Lab Heavy Oil Proc Qingdao 266580 Peoples R China East China Univ Sci & Technol Sch Mech & Power Engn Key Lab Pressure Syst & Safety MOE Shanghai 200237 Peoples R China

Through-thickness distributions of the welding residual stresses were studied in the range of 50-100mm thick plates by using finite-element modeling (FEM) and neutron diffraction measurements. In order to simulate the residual stresses through the thickness of the thick weld joints, this paper proposes a two-dimensional generalized plane strain (GPS) finite-element model coupled with the mixed work hardening model. The residual stress distributions show mostly asymmetric parabola profiles through the thickness of the welds and it is in good correlation with the neutron diffraction results. Both the heat input and plate thickness have little influence on the residual stress distributions due to the relatively large constraints of the thick specimen applied for each welding pass. A general formula has been suggested to evaluate the distributions of the through-thickness residual stresses in thick welds based on FEM and neutron diffraction experimental results.

关键词： weld residual stress finite-element method neutron diffraction measurements heat input

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A new explicit time-domain finite-element method based on element-level decomposition

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2006年第10期54卷 2990-2999页

作者： Lou, Zheng Jin, Jian-Ming Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

A new explicit time-domain finite-element method (TDFEM), which is fundamentally different from traditional explicit TDFEM formulations for solving Maxwell's equations, is introduced. This new explicit TDFEM is derived from a recently developed TDFEM domain-decomposition algorithm by extending domain decomposition to the element level. This method solves dual-field second-order wave equations and computes the electric and magnetic fields in a leapfrog fashion. With the element-level decomposition, no global system matrix has to be assembled and solved as required in the implicit TDFEM, and each element is related to its neighboring elements in an explicit manner. Hence, the computational complexity of the method is reduced to only O(N) for both computer memory and CPU time. A hybrid explicit/implicit scheme is also proposed to alleviate a major disadvantage of the proposed explicit TDFEM formulation. In addition, the convergence behavior of the corresponding higher order algorithms and the stability issues are discussed.

关键词： domain decomposition explicit methods finite-element method time-domain simulation

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Comparison of Inductance Gradient and Electromagnetic Force in Two Types of Railguns With Two Projectiles by finite-element method

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IEEE TRANSACTIONS ON PLASMA SCIENCE 2017年第8期45卷 2387-2392页

作者： Keshtkar, Asghar Khorrami, Zahra Jafari Gharib, Leila Imam Khomeini Int Univ Qazvin *** Iran

Nowadays lunching masses to faraway distances is an important issue. One of important electromagnetic launcher for this purpose is duble-projectil railgun because it can launch synchronously two separated projectiles. It has been obtained before that two-turn railgun have better inductance gradient and performance than simple railgun. Also, self-inductance gradient and mutual-inductance gradient in two-turn railgun depend on the initial position of armatures. In this paper, we want to calculate the inductance gradient of a new structure that we named it plus railgun. The plus railgun has one barrel between two-pair rails by two separated armatures and two pairs of rails are powered by one pulse power at the same time. A 3-D finite-element method is applied to the transient analysis of the magnetic field, current distribution, and the inductance gradient of railguns. Finally, we will compare the parameters of two-turn and plus railguns.

关键词： Electromagnetic force electromagnetic launcher finite-element method inductance gradient railgun

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Complementary finite-element method for finite deformation nonsmooth mechanics

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JOURNAL OF ENGINEERING MATHEMATICS 1996年第3期30卷 339-353页

作者： Gao, DY Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg U.S.A.

The complementary finite-element programming method and algorithm for solving finite deformation problems in nonsmooth mechanics are presented. This method provides a dual approach for the numerical solutions of the mixed boundary-value problem governed by nonsmooth physical laws. Application to non-smooth plastic flow is illustrated.

关键词： finite-element method finite deformation nonsmooth mechanics complementary variational method plastic limit analysis

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A split-step finite-element method for incompressible Navier-Stokes equations with high-order accuracy up-to the boundary

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JOURNAL OF COMPUTATIONAL PHYSICS 2020年 408卷

作者： Li, Longfei Univ Louisiana Lafayette Dept Math Lafayette LA 70504 USA

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on a split-step scheme in conjunction with the standard finite-element method. The split-step scheme employed for the temporal discretization of our algorithm completely separates the pressure updates from the solution of velocity variables. When the pressure equation is formed explicitly, the algorithm avoids solving a saddle-point problem;therefore, our algorithm has more flexibility in choosing finite-element spaces. In contrast, popular mixed finite-element methods that solve the INS equations in the primitive variables (or velocity-divergence formulation) lead to discrete saddle-point problems whose solution depends on the choice of finite-element spaces for velocity and pressure that is subject to the well-known Ladyzenskaja-BabuSla-Brezzi (LBB) (or inf-sup) condition. For efficiency and robustness, Lagrange (piecewise-polynomial) finite elements of equal order for both velocity and pressure are used. Accurate numerical boundary condition for the pressure equation is also investigated. Motivated by a post-processing technique that calculates derivatives of a finite element solution with super-convergent error estimates, an alternative numerical boundary condition is proposed for the pressure equation at the discrete level. The new numerical pressure boundary condition that can be regarded as a better implementation of the compatibility boundary condition improves the boundary-layer errors of the pressure solution. A normal-mode analysis is performed using a simplified model problem on a uniform mesh to demonstrate the numerical properties of our methods. Convergence studies using P-1 elements support the analytical results and demonstrates that our algorithm with the new numerical boundary condition achieves the optimal second

关键词： Navier-Stokes equations Pressure-Poisson reformulation Split-step method finite-element method Normal-mode analysis

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