吸收边界条件和完美匹配层

证明了一个Maxwell方程的完美匹配层的的充要条件.条件的核心是吸收边界条件.这个判据可以用来检验文献中的各个模型,也可用来设计一些新的模型.最后给出了一些例子.     

吸收边界条件和完美匹配层

证明了一个Maxwell方程的完美匹配层的的充要条件.条件的核心是吸收边界条件.这个判据可以用来检验文献中的各个模型,也可用来设计一些新的模型.最后给出了一些例子.     

On Local Nonreflecting Boundary Conditions for Time Dependent Wave Propagation

The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region. At the artificial boundary a boundary condition is then needed, which allows the propagating waves to exit the computational domain without spurious reflection. In 1977, Engquist and Majda proposed the first hierarchy of absorbing boundary conditions, which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer. Their pioneering work, which initiated an entire research area, is reviewed here from a modern perspective. Recent developments such as high-order local conditions and their extension to multiple scattering are also presented. Finally, the accuracy of high-order local conditions is demonstrated through numerical experiments.     

Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

A reduced shallow water model under constant, non-zero advection in the infinite channel is considered. High-order (Givoli-Neta) non-reflecting boundary conditions are introduced in various configurations to create a finite computational space and solved using a spectral element formulation with high-order time integration. Numerical examples are used to demonstrate the synergy of using high-order spatial, time, and boundary discretization. We show that by balancing all numerical errors involved, high-order accuracy can be achieved for unbounded domain problems.     

Absorbing Boundary Conditions for Hyperbolic Systems

<正>This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.     

Improving the performance of Higdon non-reflecting boundary conditions by using weighted differencing

An improved version of the Higdon non-reflecting boundary scheme is presented, incorporating a weighting factor in the finite difference implementation. This weighting factor was mentioned briefly in the original Higdon papers but was not pursued further by Higdon or in subsequent development by later researchers. In this paper, we show analytically and by example that this weighting factor significantly improves the absorption properties of the boundary scheme, by as much as 99% over the unweighted scheme of the same order and 99.99% over the classic Sommerfeld radiation condition.     

On the Existence of Positive Solutions of Quasilinear Elliptic Equations with Mixed Boundary Conditions

In this paper, the existence of positive solutions for the mixed boundary problem of quasilinear elliptic equation {-div (|∇u|^{p-2}∇u) = |u|^{p^∗-2}u + f(x, u), \quad u > 0, \quad x ∈ Ω u|_Γ_0 = 0, \frac{∂u}{∂\overrightarrow{n}}|_Γ_1 = 0 is obtained, where Ω is a bounded smooth domain in R^N, ∂Ω = \overrightarrow{Γ}_0 ∪ \overrightarrow{Γ}_1, 2 ≤ p < N, p^∗ = \frac{Np}{N-p}, Γ_0 and Γ_1 are disjoint open subsets of ∂Ω.     

化波动方程的非齐次边界为齐次边界

在一维波动方程初边值问题中,通过构造辅助函数的方法,分类将各种非齐次边界条件转化为齐次边界条件.     

Periodic Solutions of Nonlinear Wave Equations with Dissipative Boundary Conditions

Applying Nash-Moser's implicit function theorem, the author proves the existence of periodic solution to nonlinear wave equation u_{tt} - u_{xx} + εg(t, x, u, u_t, u_x, u_{tt}, u_{tx}, u_{xx}) = 0 with a dissipative boundary condition, provided ε is sufficiently small.     

On $L^2$-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is devoted to stability analysis of the acoustic wave equation exterior to a bounded scatterer, where the unbounded computational domain is truncated by the exact time-domain circular/spherical nonreflecting boundary condition (NRBC). Different from the usual energy method, we adopt an argument that leads to $L^2$-a priori estimates with minimum regularity requirement for the initial data and source term. This needs some delicate analysis of the involved NRBC. These results play an essential role in the error analysis of the interior solvers (e.g., finite-element/spectral- element/spectral methods) for the reduced scattering problems. We also apply the technique to analyze a time-domain waveguide problem.     

拟线性方程非局部边值问题解的衰减估计

本文讨论一类源于拟静态热弹性力学和控制理论等领域的边值问题,通过构造适当的上下解得到拟线性方程解的衰减估计。     

无限域拉普拉斯方程问题的高阶边界条件及其应用

对无限域Laplace方程问题,推导出了高阶边界条件.在采用数值方法的有限域的外边界上应用高阶边界条件,可以在保证计算精度的前提下缩小数值求解域,从而减小计算工作量和少占用计算机内存.数值算例表明,一阶边界条件近似于精确边界条件,它明显地优于经典边界条件和二阶边界条件.     

On Boundary Stability of Wave Equations with Variable Coefficients

In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.     

阻尼边界条件散射问题的数值解法

该文研究了光滑区域上二维Helmholtz方程阻尼边界条件外问题的数值解法, 应用单双层位势组合来逼近散射场, 因此积分方程中含有超奇异算子. 给出了超奇异算子的离散化方法, 在Holder空间中给出了误差估计和解析边界的收敛性分析. 最后针对该方法给出数值实例, 以表明该方法的有效性.     

A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations

Abstract In this paper, a new kind of discrete non-reflecting boundary conditions is developed.It can be usedfor a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic waveequations and the equations for wave propagation in multi-phase media and so on.In this kind of boundaryconditions,the composition of all artifical reflected waves,but not the individual reflected ones,is consideredand eliminated.Thus, it has a uniform formula for different wave equations.The velocity C_A of the composedreflected wave is determined in the way to make the reflection coefficients minimal,the value of which depends onequations.In this psper,the construction of the boundary conditions illustrated and C_A is found,numericalresults are presented to illustrate the effectiveness of the boundary conditions.     

Exact Boundary Controllability for the Spatial Vibration of String with Dynamical Boundary Conditions

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact boundary controllability of this system by means of a constructive method with modular structure.     

常型Sturm-Liouville问题的左定边值条件

本文刻画了常型Sturm-Liouville问题的左定边值条件．通过Sturm-Liouville微分算式的系数、区间端点以及边值条件给出了其左定性的充要条件．应用自伴边值条件分类,确切地给出了所有可能的左定边值条件．     

Variational Method to the Fractional Impulsive Equation with Neumann Boundary Conditions

We study the multiplicity of solutions for a class of fractional differential equations influenced by both instantaneous and non-instantaneous impulses, subject to Neumann boundary conditions. A key contribution of this paper is that we have established a new variational structure and successfully applied critical point theory to investigate the impulsive fractional Neumann boundary value problem. By using the critical point theorem, we give some new criteria to guarantee that the impulsive problem has at least three solutions. An example is also given to illustrate the main results.     

具有特征参数多项式边界条件的Sturm-Liouville 方程的逆结点问题

逆结点问题是通过特征函数的零点重构算子. 本文主要讨论具有特征参数多项式边界条件的 Sturm-Liouville 方程的逆结点问题. 20世纪50年代以后,人们发现在许多工程领域, Sturm-Liouville 问题的谱参数不仅出现在方程中, 而且也出现在边界条件中,因此带参数边界条件的逆结点问题对数学物理方面的研究有重要意义. 本文讨论区间 $[0,1]$ 上边界条件为参数多项式的 Sturm-Liouville 方程的逆结点问题, 并证明在 $[0,b]$ \big($ b\in \big(\frac{1}{2},1\big]$\big) 上结点的稠密子集可唯一确定 $[0,1]$ 上的势函数和边界条件中多项式的未知系数.