Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems

We consider the approximation of the frequency domain three-dimensional Maxwell scattering problem using a truncated domain perfectly matched layer (PML). We also treat the time-harmonic PML approximation to the acoustic scattering problem. Following work of Lassas and Somersalo in 1998, a transitional layer based on spherical geometry is defined, which results in a constant coefficient problem outside the transition. A truncated (computational) domain is then defined, which covers the transition region. The truncated domain need only have a minimally smooth outer boundary (e.g., Lipschitz continuous). We consider the truncated PML problem which results when a perfectly conducting boundary condition is imposed on the outer boundary of the truncated domain. The existence and uniqueness of solutions to the truncated PML problem will be shown provided that the truncated domain is sufficiently large, e.g., contains a sphere of radius . We also show exponential (in the parameter ) convergence of the truncated PML solution to the solution of the original scattering problem inside the transition layer.

Our results are important in that they are the first to show that the truncated PML problem can be posed on a domain with nonsmooth outer boundary. This allows the use of approximation based on polygonal meshes. In addition, even though the transition coefficients depend on spherical geometry, they can be made arbitrarily smooth and hence the resulting problems are amenable to numerical quadrature. Approximation schemes based on our analysis are the focus of future research.

     

n-Hg_(0.80)Mg_(0.20)Te界面积累层中二维电子气的输运特性研究

通过变磁场霍耳测量研究了MBE生长的Hg0 .80 Mg0 .2 0 Te薄膜在 1 5— 2 5 0K温度范围内的输运特性 .采用迁移率谱 (MS)和多载流子拟合过程 (MCF)相结合的方法对实验数据进行了分析 ,由该方法获得的结果和ShubnikovdeHass(SdH)振荡测量的结果都证明材料中存在二维 (2D)电子和三维 (3D)电子 .其中 2D电子主要来自于Hg1-xMgxTe CdTe的界面积累层或Hg1-xMgxTe与真空界面附近的积累层 .3D电子迁移率随温度的变化关系表明了Hg1-xMgxTe中的电子散射机理与Hg1-xCdxTe中的非常相似 :在低温下电离杂质散射 (考虑了屏蔽效应 )起主导地位 ,而温度在 10 0K以上时 ,晶格散射占主导地位 .     

Resonance split of ballistic conductance peaks in electric and magnetic superlattices

Resonant peak splitting for ballistic conductance in finite electric superlattices (ES) and magnetic superlattices (MS) was investigated theoretically. It is shown that, for electron tunneling through the ES (MS) of identical n electric (magnetic) barriers, the resonance split of the conductance peak is (n–1)-fold; while for electron tunneling through the ES (MS) made of two different barriers, one resonant window of the former splits into two subwindows, within each of which the resonance split is (m–1)-fold, where m is the number of the renormalized building blocks consisting of two different barriers of the latter. Received 15 February 2000     

Superconducting and magnetic properties of Nb/Pd 1-xFex/Nb triple layers

The superconducting and magnetic properties of Nb/Pd_1-xFe_x/Nb triple layers with constant Nb layer thickness d_Nb=200 ? and different interlayer thicknesses 3 ?≤ d_PdFe ≤ ? are investigated. The thickness dependence of the magnetization and of the superconducting transition temperature shows that for small iron concentration x the Pd_1-xFe_x layer is likely to be in the paramagnetic state for very thin films whereas ferromagnetic order is established for x ≥ 0.13. The parallel critical field B_c2||(T){B_{c2||}}(T) exhibits a transition from two-dimensional (2D) behavior where the Nb films are coupled across the interlayer, towards a 2D behavior of decoupled Nb films with increasing d_PdFeand/or x. This transition allows a determination of the penetration depth x_F{\xi _F} of Cooper pairs into the Pd_1-xFe_x layer as a function of x. For samples with a ferromagnetic interlayer x_F{\xi _F} is found to be independent of x.     

CPML在空中核爆电磁脉冲三维数值模拟中的应用

在分析不同类型完全匹配层(PML,perfectl ymatched layer)特点的基础上,选用了卷积形式PML(CPML,convolutional perfectly matched layer)截断空中核爆电磁脉冲(NEMP,nuclear electromagnetic pulse)数值模拟的开放边界.从自由空间中电磁波的平面波解和分裂形式的PML出发,构造了未分裂形式的PML,应用付里叶变换的卷积定理,推导出三维旋转椭球-双曲正交坐标系下CPML介质中电磁场的迭代形式的离散方程.获得了很好的截断效果,展示了CPML在NEMP数值模拟中的应用前景.     

Singularly perturbed semilinear elliptic equation with boundary-interior layer interaction

In this paper, we consider the phenomenon of the boundary and interior layer interactions for a class of semilinear elliptic equation. Under some appropriate conditions,we get the existence of the exact solution for the problem and its high order uniformly valid expansion.     

The numbers of jump layers of boundary value problems in quasilinear differential equations

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1] is always equal to zero.     

THE NEW SOLUTION FOR THE AXIALLY SYMMETRICAL LAMINAR BOUNDARY LAYER EQUATIONS BETWEEN TWO PARALLEL SPHERICAL SURFACES

The transformations, which are similar to Mangler's transformations, are given in this paper. They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfaces into the flow of two-dimensional boundary layer, and simplify the problems. The simplified equattons can be solved by the two-dimensional boundary layer theory and numerical methods. Therefore, a new way is opened up to solve the diffusive laminar fiow in the entrance region between two parallel spherical surfaces.     

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.     

Boundary and interior layer behavior for singularly perturbed vector problem

In this paper,we consider the vector nonlinear boundary value problem:εy~v=f(x,y,z,y′,ε),y(0)=A_1,y(1)=B_1εz~v=g(x,y,z,z′,ε),z(0)=A_2,z(1)=B_2whereε>0 is a small parameter,0≤x≤1 ,f and g are continuous functions in R~4,Under appropriate assumptions,by means of the differential inequalities,we demonstratethe existence and estimation,involving boundary and interior layers,of the solutions to theabove problem.