求解高维波动力方程的半离散方法

本用半离散方法将高维波动方程离散为一耦合波动方程组。中给出了离散的收性及一维耦合波动方程组的适定性结果。     

求解二维波动方程正演反演问题的半离散方法

本文用半离散方法将二维波动方程离散为一维耦合波动方程组．给出了离散的收敛性及波动方程组的适定性．利用这种方法可以求解波动方程系数及演问题．     

波动方程的上行波和下行波的耦合方程组

所描述的波场p中上行波和下行波之间的耦合关系,导出了它们的耦合方程组.对于一维波动方程     

一维热弹性问题的Galerkin方法

本文研究了由一维热弹性问题提出的双曲——抛物偶合偏微方程组的Galerkin方法,导出了半离散和全离散Galerkin逼近的L~2估计。     

从离散速度模型到矩方法

为了求解动理学方程,我们通过研究一维情形下的离散速度模型,发现通过对离散速度点使用自适应技术可以直接得到Grad矩方程组.作为一个统一的认识,矩方程组可以看作是对离散速度点自适应的离散速度模型,而离散速度模型可以看作是取特别形式的"矩"的矩方程组.这使得我们可以在一致的框架下来理解离散速度模型和矩方法,而不是将它们对立起来.为了建立这样的一致框架,最近在[2]中发展的正则化理论是根本性的.     

流固耦合方程组间断Galerkin方法的探索

主要通过对复杂接触表面问题以及流固耦合方程组中边界间断问题的分析,探讨其间断Galerkin方法的有限元计算.保留有限元线性离散的计算优势,有效地弱化了边界间断对流场中速度的影响,得到流固耦合方程组的空间半离散有限元格式,为数值计算提供了有力的理论支撑.     

分数阶Burgers方程的有限元计算(英文)

建立了一维和二维分数阶Burgers方程的有限元格式.时间分数阶导数使用L1方法离散,空间方向使用有限元方法离散.通过选择合适的基函数,将离散后的方程转化成一个非线性代数方程组,并应用牛顿迭代方法求解.数值实验显示出了方法的有效性.     

环形空腔内自然对流问题的Galerkin方法

本文讨论了环形空腔内自然对流问题所满足的Boussinesq方程组——关于涡度ζ、流函数φ及温度θ的椭圆-抛物非线性耦合方程组 用Galerkin方法对其进行了数值分析,得到了Galerkin逼近(含半离散和全离散)的最优先验误差估计。     

耦合Schrdinger-KdV方程组Cauchy问题的适定性

本文研究了耦合Schrodinger－KdV方程组的Cauchy问题，此耦合方程组刻化了一维Langmuir和离子声波相互作用的非线性动力学行为．本文建立了此问题在Hk×Hk中的整体适定性理论（k∈Z+）．     

环形空腔内自然对流问题的的Galerkin方法

本文讨论了环形空腔内自然对流问题所满足的Ｂｏｕｓｓｉｎｅｓｑ方程组－关于涡度ζ、流函数ψ及温度θ的椭圆－抛物非线性耦合方程组用Ｇａｌｅｒｋｉｎ方法对其进行了数值分析，得到了Ｇａｌｅｒｋｉｎ逼近（含半离散和全离散）的最优先验误差估计。     

The exterior Dirichlet problem for the Helmholtz equation

The exterior Dirichlet problem for the reduced wave equation is reformulated as a new integral equation. It is shown that the normal derivative of the total field may be expressed as a Neumann series in terms of the known incident field. The convergence of the infinite series is established for arbitrary smooth surfaces and for small values of the wave number. An example is given that illustrates the method.     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

Developing weak Galerkin finite element methods for the wave equation

In this article, we extend the recently developed weak Galerkin method to solve the second‐order hyperbolic wave equation. Many nice features of the weak Galerkin method have been demonstrated for elliptic, parabolic, and a few other model problems. This is the initial exploration of the weak Galerkin method for solving the wave equation. Here we successfully developed and established the stability and convergence analysis for the weak Galerkin method for solving the wave equation. Numerical experiments further support the theoretical analysis. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 868–884, 2017     

The combination of collocation,finite difference,and multigrid methods for solution of the two‐dimensional wave equation

In this article, we apply compact finite difference approximations of orders two and four for discretizing spatial derivatives of wave equation and collocation method for the time component. The resulting method is unconditionally stable and solves the wave equation with high accuracy. The solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. We employ the multigrid method for solving the resulted linear system. Multigrid method is an iterative method which has grid independently convergence and solves the linear system of equations in small amount of computer time. Numerical results show that the compact finite difference approximation of fourth order, collocation and multigrid methods produce a very efficient method for solving the wave equation. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

波动方程外区域问题基于自然边界归化的区域分解算法(英文)

本文以二维波动方程为例 ,研究基于自然边界归化的一种区域分解算法 .首先将控制方程对时间进行离散化 ,得到关于时间步长离散化格式 ,对每一时间步长求解一椭圆型外问题 ;然后引入两条人工边界 ,提出了 Schwarz交替算法 ,给出了算法的收敛性 ,并对圆外区域研究了压缩因子     

A Numerical Method of Local Energy Decay for the Boundary Controllability of Time-Reversible Distributed Parameter Systems

This paper deals with the numerical computation of the boundary controls of linear, time-reversible, second-order evolution systems. Based on a method introduced by Russell ( Stud. Appl. Math. LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.     

A priori estimates for two multiscale finite element methods using multiple global fields to wave equations

We consider a scalar wave equation with nonseparable spatial scales. If the solution of the wave equation smoothly depends on some global fields, then we can utilize the global fields to construct multiscale finite element basis functions. We present two finite element approaches using the global fields: partition of unity method and mixed multiscale finite element method. We derive a priori error estimates for the two approaches and theoretically investigate the relation between the smoothness of the global fields and convergence rates of the approximations for the wave equation. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

求解粘性系数的迭代方法及其收敛性

求解粘性系数的迭代方法及其收敛性丛文相（黑龙江大学，哈尔滨１５００８０）１９９１年８月３０日收到．１９９２年８月２５日收到第一次修改稿．１９９２年１２月４日收到第二次修改稿．一、引言研究地震正、反问题时，一般把地球假设为完全弹性体，而实际地球介质并非...     

非线性不适定算子方程算子与右端项皆有扰动的Landweber迭代法

考虑非线性算子方程 F（x）=y（1）其中 F:D（F）　 X→Y,X,Y为 Hilbert空间.F是 Frechet可微的。 这里考虑算子方程的解x+不连续依赖于右端数据的情况。由于不稳定性,并且在实际问题中只有近似数据yδ满足 ‖yδ-y‖≤δ（2）可以得到,方程（1）必须正则化.