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1.
正则化δ函数对浸入边界法精度的影响   总被引:1,自引:0,他引:1  
浸入边界法是对流固耦合系统进行数学建模和数值模拟的有效工具,在生物力学领域的应用尤为广泛.正则化δ函数对精度的影响是研究浸入边界法本身性质的一个重要课题.采用虚拟解法对此展开分析.首先使用光滑虚拟解证明程序的正确性,然后使用压力存在跳跃的虚拟解研究浸入边界法的精度.通过分析使用4种不同的正则化δ函数时整个流场的离散误差,得到以下结论:浸入边界法只具有1阶精度;选用不同的正则化δ函数,不能提高浸入边界法的精度,但会影响整个流场的离散误差值.  相似文献   

2.
何尚琴  冯秀芳 《数学学报》1936,63(6):545-556
本文研究带有混合边界的二维Helmholtz方程不适定问题.为了获得稳定的数值解,利用基于de la ValléePoussin算子的软化正则方法,得到了正则近似解,给出正则近似解与精确解之间在先验参数选取规则之下的误差估计,并通过数值实验检验了数据有噪声扰动时方法的有效性和稳定性.  相似文献   

3.
利用最小化方法对含未知边界的不适定方程组进行正则化处理,然后依次迭代更新边界和相应的密度函数,最终得到反演的边界.给出一些数值例子以表明这种方法是有效的和可行的。  相似文献   

4.
构造了一种正则化的积分方程方法来由Cauchy数据确定一维热传导方程的移动边界.在将区域延拓至规则区域后,通过Fourier方法将问题转化为一个第一类Volterra积分方程.然后分别用Lavrentiev正则化方法以及Tikhonov正则化方法将不稳定的第一类Volterra积分方程转化为适定的第二类积分方程,并分别将积分方程转化为常微分方程组,并用Runge—Kutta方法数值求解,以及直接离散来求解.最后通过自由边界上的条件得到数值的移动边界.通过一些数值试验表明此方法是有效可行的,并且给出的方法无需迭代,数值计算较简单.  相似文献   

5.
讨论了具有Dirichlet边界控制和同位观测的Petrovsky系统的正则性,给出了相应的直接传输算子,证明了系统在G.Weiss意义下是正则的,且其直接传输算子为零.  相似文献   

6.
本文应用正则边界元方法研究了由一个电镀模型问题导出的Signorini问题的数值解,给出了近似解的误差分析,计算例子表明,用正则边界元方法求解Signorini问题是行之有效的,并具有计算简便、节省计算时间与内存等优点。  相似文献   

7.
用正则化方法求解声波散射反问题   总被引:1,自引:1,他引:0  
研究了从声波散射场的远场模式的信息来再现散射物边界形状的反问题.首先构造表达散射物特征的指示函数,然后利用该函数之特性,建立求解该类反问题的基本方程,从而确定散射物的边界形状.在这个算法中,不需预先知道散射物的边界类型和形状等知识,从T ikhonov正则化方法进行的数值计算结果表明了该方法是有效的和实用的.  相似文献   

8.
数据缺损下矩阵低秩逼近问题出现在许多数据处理分析与应用领域. 由于极高的元素缺损率,数据缺损下的矩阵低秩逼近呈现很大的不适定性, 因而寻求有效的数值算法是一个具有挑战性的课题. 本文系统完整地综述了作者近期在这方面的一些研究进展, 给出了基本模型问题的不适定性理论分析, 提出了两种新颖的正则化方法: 元素约束正则化和引导正则化, 分别适用于中等程度的数据缺损和高度元素缺损的矩阵低秩逼近. 本文同时也介绍了相应快速有效的数值算法. 在一些实际的大规模数值例子中, 这些新的正则化算法均表现出比现有其他方法都好的数值特性.  相似文献   

9.
徐应祥  关履泰 《计算数学》2013,35(3):253-270
考虑一种新的散乱数据带自然边界二元样条光顺问题.根据样条变分理论和Hilbert空间样条函数方法,构造出了显式的二元带自然边界光顺样条解,其表达式简单且系数可以由系数矩阵对称正定的线性方程组确定.证明了解的存在和唯一性,讨论了收敛性和误差估计.并由此得到一种新的基于散乱数据上的正则化二元数值微分的方法.最后,给出了一些数值例子对方法进行了验证.  相似文献   

10.
本文研究包含于RN的有Lipschitz边界的有界区域Ω上涉及到p-Laplacian算子的退化椭圆障碍问题弱解的边界正则性,得到了C1,aloc边界正则性.  相似文献   

11.
We consider in this work the boundary value problem for Stokes equations on a two dimensional domain in cases where non-standard boundary conditions are given. We study the cases where pressure and normal or tangential components of the velocity are given in different parts of the boundary and solve the problem with a minimal regularity. We introduce the problem and its variational formulation which is a mixed one. The principal unknowns are the pressure and the vorticity, the multiplier is the velocity. We present the numerical discretization which needs some stabilization. We prove the convergence and the behavior of the a priori error estimates. Some numerical tests are also presented. To cite this article: M. Amara et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 603–608.  相似文献   

12.
Summary. We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the -norm to the true solution without any additional regularity assumptions. Received May 23, 1997 / Published online December 6, 1999  相似文献   

13.
We consider a class of boundary value problems for linear multi-term fractional differential equations which involve Caputo-type fractional derivatives. Using an integral equation reformulation of the boundary value problem, some regularity properties of the exact solution are derived. Based on these properties, the numerical solution of boundary value problems by piecewise polynomial collocation methods is discussed. In particular, we study the attainable order of convergence of proposed algorithms and show how the convergence rate depends on the choice of the grid and collocation points. Theoretical results are verified by two numerical examples.  相似文献   

14.
A boundary integral method is developed for the mixed boundary value problem for the vector Helmholtz equation in R3. The obtained boundary integral equations for the unknown Cauchy data build a strong elliptic system of pseudodifferential equations which can therefore be used for numerical computations using Galerkin's procedure. We show existence, uniqueness and regularity of the solution of the integral equations. Especially we give the local "edge" behavior of the solution near the submanifold which divides the Dirichlet boundary from the Neumann boundary  相似文献   

15.
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated the boundary conditions of two-point type. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional. Finally, we present some numerical results.  相似文献   

16.
This article considers the inverse problem of identification of a time‐dependent thermal diffusivity together with the temperature in an one‐dimensional heat equation with nonlocal boundary and integral overdetermination conditions when a heat exchange takes place across boundary of the material. The well‐posedness of the problem is studied under some regularity, and consistency conditions on the data of the problem together with the nonnegativity condition on the Fourier coefficients of the initial data and source term. The inverse problem is also studied numerically by using the Crank–Nicolson finite difference scheme combined with predictor‐corrector technique. The numerical examples are presented and discussed. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 564–590, 2016  相似文献   

17.
In this paper we propose a hybrid between direct and indirect boundary integral methods to solve a transmission problem for the Helmholtz equation in Lipschitz and smooth domains. We present an exhaustive abstract study of the numerical approximation of the resulting system of boundary integral equations by means of Galerkin methods. Some particular examples of convergent schemes in the smooth case in two dimensions are given. Finally, we extend the results to a thermal scattering problem in a half plane with several obstacles and provide numerical results that illustrate the accuracy of our methods depending on the regularity of the interface.  相似文献   

18.
In this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid-like tissues. The model equations include a quasi-stationary diffusion equation for the nutrient concentration, and a Stokes equation with a source representing the proliferation density of the tumor cells, subject to a boundary condition with stress tensor effected by surface tension. This problem is a fully nonlinear problem involving nonlocal terms. Based on the employment of the functional analytic method and the theory of maximal regularity, we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity.  相似文献   

19.
The dynamic Maxwell equations with a strictly dissipative boundary condition is considered. Sharp trace regularity for the electric and the magnetic field are established for both: weak and differentiable solutions. As an application a shape optimization problem for Maxwell's equations is considered. In order to characterize the shape derivative as a solution to a boundary value problem, the aforementioned sharp regularity of the boundary traces is critical.  相似文献   

20.
In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

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