基于广角FD-BPM的PML边界处理方法

本文提出了基于三阶Padé近似广角有限差分光束传输法(FD-BPM)的简单有效的完美匹配层(PML)边界处理方法.分别给出了该方法应用于斜波导和多模干涉(MMI)数值模拟的结果,并与用完全透明边界条件处理的模拟计算结果进行了比较.本文最后对基于广角FD-BPM的PML边界处理方法进行了优化.     

On perfectly meager sets

We show that it is consistent that the product of perfectly meager sets is perfectly meager.

     

Modeling cup-burner minimum extinguishing concentration of halogenated agents

The minimum extinguishing concentration (MEC) of a fire suppression agent is usually determined by the standard cup-burner tests. Recently, a simple model based on extinction of Perfectly Stirred Reactors (PSR) was developed and validated in the prediction of the MECs for inert fire suppressants. The results show good agreement between the model predictions and the experimental data. Furthermore, the results confirmed that the MECs of inert agents are directly correlated to agent integrated heat capacities. In this paper, the model is extended to halogenated agents by adding detailed chemical kinetics of the halogenated agents to a detailed chemical mechanism of n-heptane. The consideration of reactive halogenated species as fire suppression agents increases the complexity in computing the stoichiometry, yet the use of the PSR approach simplifies interpretations relative to 1-d and 2-d simulations. Using this approach, the MEC of halogenated agents are computed and compared against experimental data. Two methods of computation were employed. In the first, “inert PSR” case, only the heptane reaction chemistry was included; so the agent acts solely as an inert and the solution provides a reference point for expected behavior if the agent acted as an inert. In the second, or “reactive PSR” case, agent-related chemistry was included. Good agreement is achieved for Halon 1301 (CF₃Br) and R-32 (CH₂F₂). The computed “inert PSR” values agreed very well with the experimental MEC data for most fluorinated agents, suggesting that chemical inhibition by these fluorinated agents is counter-balanced by the exothermic HF formation and some competing chemical reactions; thus the “net” inhibition is small. In contrast, the “reactive PSR” results show good agreement with brominated agents and are consistent with the known strong catalytic effect of such compounds. The causes for differences between experiment and predicted values are explored and discussed while strengths and limitations are considered.     

A non-uniform basis order for the discontinuous Galerkin method of the 3D dissipative wave equation with perfectly matched layer

In this study a discontinuous Galerkin method (DG) for solving the three-dimensional time-dependent dissipative wave equation is investigated. In the case of unbounded problems, the perfectly matching layer (PML) is used to truncate the computational domain. The aim of this work is to investigate a simple selection method for choosing the basis order for elements in the computational mesh in order to obtain a predetermined error level. The selection method studied here relies on the error estimates provided by Ainsworth [M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics 198(1) (2004) 106–130]. The performance of the non-uniform basis is examined using numerical experiments. In the simulated model problems, a feasible method choosing the basis order for arbitrary sized elements is achieved. In simulations, the effect of dissipation and the choices of the PML parameters on the performance of the DG method are also investigated.     

Absorbing boundary conditions for the Euler and Navier–Stokes equations with the spectral difference method

Two absorbing boundary conditions, the absorbing sponge zone and the perfectly matched layer, are developed and implemented for the spectral difference method discretizing the Euler and Navier–Stokes equations on unstructured grids. The performance of both boundary conditions is evaluated and compared with the characteristic boundary condition for a variety of benchmark problems including vortex and acoustic wave propagations. The applications of the perfectly matched layer technique in the numerical simulations of unsteady problems with complex geometries are also presented to demonstrate its capability.     

Complex frequency shifted convolution PML for FDTD modelling of elastic waves

The perfectly matched layer (PML) is nowadays considered as the best optimum absorbing boundary condition available. However, the PML with the classical stretching tensor has certain limitations. Strangely, these limitations have rarely been addressed in elastic wave modelling. For example, substantial reflections occur when strong evanescent waves are propagating parallel to the interface. To circumvent problems like this, the complex frequency shifted stretching tensor has been introduced in electromagnetic modelling. In this paper we show that the convolution PML with this stretching tensor as used in electromagnetic modelling can be adapted for elastic wave modelling. Numerical results of a model where the presence of evanescent waves is predominant show that the PML based on the complex frequency shifted stretching tensor can improve the performance of the absorbing boundary layer considerably.     

On a conjecture of Hoàng and Tu concerning perfectly orderable graphs

Hoàng and Tu [On the perfect orderability of unions of two graphs, J. Graph Theory 33 (2000) 32-43] conjectured that a weakly triangulated graph which does not contain a chordless path with six vertices is perfectly orderable. We present a counter example to this conjecture.     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.     

手性障碍电磁散射的PML有限元计算

该文建立了手性障碍电磁散射问题的二维模型, 给出问题的有限元分析, 并利用结合PML(perfectly matched layers)技术的有限元法进行数值模拟.     

Multivalued fixed point in Banach algebra using continuous selection and its application to differential inclusion

In this paper, we provide some fixed point results using continuous selection given by Poonguzali et al. [15]. Also, using the selection theorem we discusse the existence of fixed point for the product of two multivalued mappings, that is, of the form $Ax\cdot Bx.$ Using those fixed point results, we give the existence of solution for a newly developed differential inclusion.