A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems

This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conduction-convection equations by using the lowest equal-order pairs of finite elements. This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. The stability of the discrete scheme is derived under some regularity assumptions. Optimal error estimates are obtained by applying the standard Galerkin techniques. Finally, the numerical illustrations agree completely with the theoretical expectations.     

Parametric Study of Driver and Reflector of Single Axis Acoustic Levitator using Finite Element Method

Acoustical Physics - Total radiation force on a spherical levitating object, which is placed between a single axis acoustic levitator, is obtained using finite element simulation. Variation in the...     

An Inverse Finite Element Method for Pure and Binary Solidification Problems

A 2D axisymmetric formulation for the solution of a directional solidification problem using an inverse finite-element method (IFEM) is presented. An algorithm developed by A. N. Alexandrou (Int. J. Numer. Methods Eng.28, 2383, 1989) has been modified and extended to include more general boundary conditions. The latter includes the explicit presence of an ampoule (with a complex shape) that contains the solid and the melt from which it is growing. Heat transfer between the ampoule and the external environment, time-dependent thermal boundary conditions, nonmonotonic temperature distributions, and species diffusion in the melt and crystal are also taken into account. Thus, our extended formulation encompasses a wider class of solidification problems than previous IFEM methods. Numerical experiments that illustrate the suitability of the extended IFEM are presented. In particular, we present a simulation of the directional solidification of zinc cadmium telluride using boundary conditions corresponding to an actual experiment scenario.     

Fracture Analysis in Orthotropic Thermoelasticity Using Extended Finite Element Method

In this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is presented. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.     

An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations

In the paper, an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.     

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.     

Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method

In this paper, an improved singular boundary method (SBM), viewed as one kind of modified method of fundamental solution (MFS), is firstly applied for the numerical analysis of two-dimensional (2D) Stokes flow problems. The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives. The new contribution of this study is that the origin intensity factors for the velocity, traction and pressure are derived, and based on that, the SBM formulations for 2D Stokes flow problems are presented. Several examples are provided to verify the correctness and robustness of the presented method. The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.     

CR超导二极铁导线的3D有限元失超模拟

利用FEM软件ANSYS对德国GSI的FAIR项目的超导二极铁的超导线进行了失超模拟.该模拟形象地给出导线的失超过程,通过APDL编程可以得到失超传播速度,失超时导体的端电压随时间的变化.文章还进一步研究了导线的最小失超传播区域MPZ,失超段初始温度和电流对失超传播速度的影响.     

一类各项异性半线性椭圆方程自然边界元与有限元耦合法

将冯康和余德浩提出的自然边界归化方法用于研究一类半线性椭圆方程外区域问题,提出一种自然边界元与有限元的耦合算法、针对某一类半线性椭圆方程,应用变分原理,研究其弱解性及Galerkin逼近,得到有限元解的误差估计及收敛阶O(h^n),最后给出相应数值例子。     

Electronic Structure Calculations Using Self-Adaptive Multiscale Voronoi Basis Functions

The multiscale self-adaptivity of Voronoi basis functions is currently proving to be useful for the simulation of complex fluid systems involving structures on a number of distinct lengthscales. In this paper, we explore the possibility of extending the use of such multiscale basis functions to the framework of density functional theoretic electronic structure computations.     

A Mode I Crack Problem for a Thermoelastic Fibre-Reinforced Anisotropic Material Using Finite Element Method

In this article, the theory of generalized thermoelasticity with one relaxation time is used to investigate the thermoelastic fiber-reinforced anisotropic material with a finite linear crack. The crack boundary is due to a prescribed temperature and stress distribution. By using the finite element method, the numerical solutions of the components of displacement, temperature and the stress components have been obtained. Comparisons of the results in the absence and presence of reinforcement have been presented.     

A Quantum Universe and the Solution to the Cosmological Problems

We have found that the hierarchial problems appearing in cosmology are a manifestation of the quantum nature of the universe. The universe is still described by the same formulae that once hold at Planck's time. The universe is found to be governed by the Machian equation, GM = Rc ², where M and R are mass and radius of the universe. A Planck's constant xsfor different cosmic scales is provided. The status of the universe at different stages is shown to be described in terms of the fundamental constants (c, , G, , H) only. The concept of maximal (minimal) acceleration, power, temperature, etc., is introduced and justified.     

Maximization of Acoustic Levitating Force for a Single-Axis Acoustic Levitation System Using the Finite Element Method

We investigate single-axis acoustic levitation using standing waves to levitate particles freely in a medium bounded by a driver and a reflector. The acoustic pressure at the pressure antinode of the standing wave counteracts the downward gravitational force of the levitating object. The optimal relationship between the air gap and the driving frequency leads to resonance and hence maximization of the levitating force. Slight deviation from the exact resonance condition causes a reduction in acoustic pressure at the pressure antinodes. This results in a significant reduction of the levitating force. The driving frequency is kept constant while the air gap is varied for different conditions. The optimal air gap for maximizing the levitation force is studied for first three resonance modes. Furthermore, a levitating particle is introduced between the driver and the reflector. The dependence of the resonance condition on the size of the levitating particle as well as the position of the particle between the driver and the reflector has also been studied. As the size of the levitating particle increases, the resonance condition also gets modified. Finite element results show a good agreement with the validated results available in the literature. Furthermore, the finite element approach is also used to study the variation of acoustic pressure at the pressure antinode with respect to the size of the reflector. The optimum diameter of the reflector is calculated for maximizing the levitating force for three resonance modes.     

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel, highly efficient and accurate adaptive higher-order finite element method ($hp$-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD) tool response in a borehole environment. Presented in this study are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic $hp$-adaptivity strategy. The new $hp$-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new $hp$-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive $h$-FEM. The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models, which further confirm the accuracy of the results using the Hermes library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool response in a borehole environment.     

Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems

This paper derives a higher order hybrid stress finite element method on quadrilateral meshes for linear plane elasticity problems. The method employs continuous piecewise bi-quadratic functions in local coordinates to approximate the displacement vector and a piecewise-independent 15-parameter mode to approximate the stress tensor. Error estimation shows that the method is free from Poisson-locking and has second-order accuracy in the energy norm. Numerical experiments confirm the theoretical results.     

Finite Element Time Domain Solution of Resonant Modes in Photonic Bandgap Cavities

In this paper, an efficient finite-element based time-domain propagation procedure is presented for the accurate modelling of two-dimensional photonic bandgap cavities. Through the propagation along the ‘complex’ time domain, a novel numerically efficient procedure is suggested to calculate the resonant wavelength, the quality factor and the area of the resonant mode in a very few steps of propagation. The high numerical precision of the proposed method is demonstrated through the excellent agreement of the results obtained using this method and their counterparts in the literature obtained using other numerical techniques.     

Finite State and Finite Stop Quantum Languages

We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition, the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq) and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. In this way, we establish two proper inclusion relations (fsqa) ⊂ (ftqa) and (icftq) ⊂ (vcftq), where the symbol means languages, and two infinite language hierarchies (fsqa) ⊂ (fsqa), (icftq) (icftq).     

应用径向基函数去除数字图像中的椒盐噪声

去除图像中的椒盐噪声可转化为二维曲面的重建问题。选用Multi-Quadric函数对图像中损失的信息构造插值格式,自动选择待插值点和插值参考点并求解插值方程组得到处理后的图像。实验证明,本方法可以在很少破坏图像细节的情况下去除大部分甚至全部噪声,并且在噪声密度非常大的情况下仍然可以还原相当多的图像信息。对噪声密度为50％和90％的单色Lena图像进行处理,该方法得到的信噪比比自适应中值滤波高6dB以上。     

Multi-party Quantum Private Comparison Protocol Using d-Dimensional Basis States Without Entanglement Swapping

We present a new multi-party quantum private comparison protocol based on d-dimensional basis states. Different from previous protocols, our protocol have some advantages. n parties can determine wether their private information are equal or not in one time execution of our protocol. Without using the entangled character of d-dimensional basis states, we only need to perform the local unitary operation on particles to encode the information and to get the comparison result. We also discuss that our protocol can withstand various kinds of outside attacks and participant attacks.     

Field Patterns in Double Circular-Groove Guide by Finite Element Method

The electromagnetic power coupling in symmetrical and asymmetrical double circular-groove guides have been analyzed by finite element method (FEM) in this paper. The electrical field patterns of the dominant mode and the first higher-order TE mode have been presented. The electromagnetic field of the dominant mode distributes with a concentration in the two grooves and the region between grooves as well for symmetrical double circular-groove guide, while it distributes with a concentration in the groove with larger radius for the asymmetrical double circular-groove guide. The electrical field patterns of the first higher-order TE mode in symmetrical and asymmetrical double circular-groove guide are also presented. The figures in this paper have important values in design of circular-groove guide power coupler for millimeter wave applications.