一类非线性二阶耦合问题的混合有限元方法

本文讨论出现于热弹性理论中的一类二阶非线性双曲-抛物耦合方程混合元方法,给出了混合元离散格式及解的存在唯一性(§1),并在适当的条件下,利用混合型的椭圆投影(§2),得到了混合元解,伴随向量函数,解对时间导数在L~2,L~∞意义下的最优误差估计(§3)。     

一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法

本文采用Modulus-based变换将非线性互补问题转化为非光滑方程组,并将一种多步自适应Levenberg-Marquardt方法推广应用于求解所得的非光滑方程组,从而得到原问题的解.在适当条件下,本文证明了算法的全局收敛性.与一种已有的参数自适应Levenberg-Marquardt方法(PSA-LMM)相比较,...     

区间自适应遗传算法优化无约束非线性规划问题

针对无约束非线性规划传统优化方法存在的问题,将区间自适应遗传算法引入无约束非线性规划优化中,算法可以利用当前进化信息,自适应移动搜索区间,找到全局最优解,故可缩短搜索区间长度,提高编码精度,降低算法计算量,解决了传统遗传算法处理优化问题时,给定区间必须包含最优解这一问题,这也是本算法有别于其他优化算法的独特优势,为某些最优解所在区间难以估计的无约束非线性规划问题的优化提供了一条有效可行的途径.系统阐述了区间自适应遗传算法的原理,给出了算法优化无约束非线性规划问题的步骤,以MatlabR2016b仿真方式对算法进行了实例测试,结果表明,方法是一种计算稳定、正确、有效、可靠实用的无约束非线性规划优化方法.     

求解非线性Black-Scholes模型的自适应小波精细积分法

针对非线性Black-Scholes方程,基于quasi-Shannon小波函数给出了一种求解非线性偏微分方程的自适应多尺度小波精细积分法.该方法首先利用插值小波理论构造了用于逼近连续函数的多尺度小波插值算子,利用该算子可以将非线性Black-Scholes方程自适应离散为非线性常微分方程组;然后将用于求解常微分方程组的精细积分法和小波变换的动态过程相结合,并利用非线性处理技术(如同伦分析技术)可有效求解非线性Black-Scholes方程.数值结果表明了该方法在数值精度和计算效率方面的优越性.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

求解非线性互补问题的一个下降算法

在[1]中,Soldov将非线性互补问题等价地转化成一个带非负约束的优化问题,基于这种转化形式,我们给出了一种求解非线性互补问题的下降算法,在映射为强单调时,证明了算法的全局收敛性。     

一类基于广义梯度的求解非线性互补问题的算法

1 引言非线性互补问题(下称NCP)的应用十分广泛,自本世纪六十年代以来,人们对这一问题解的存在唯一性、灵敏度分析、算法与应用等方面进行深入的研究,取得很大的进展。关于NCP的解法通常是将其化为序列线性互补问题,而对线性问题则有若干现成算法,如Lemke算法。但一般说来,此类方法工作量大,效果也难以令人满意。J.S.Pang于七十年代提出了B-可微算法,即将NCP转化为一个B-可微函数的零点问题。近年来提出的一些算法大多属于此类方法。 本文提出的算法也属于B-可微算法,虽同是从广义梯度出发,但不同的是,我们不是通过二次规划而是通过线性规划来获得搜寻方向。由于所涉及的线性规划问题特别的简单,我们可以很快而方便地求得其解,所以算法简易可行,速度较快。     

两个非线性耦合网络间的自适应同步

本文研究了带非线性信号连接的两个复杂网络间的同步问题,引入非线性耦合参数α来调节两个复杂网络的同步．若耦合参数不能保证网络达到外部同步,这里我们提出了一种自适应同步方式,通过此方式可以使两个复杂网络达到同步,最后通过简单的数值算例来阐述得到的理论结果,包括网络具有相同和不相同的拓扑结构两种情形．     

计算二维零空间的非线性分歧问题的新途径

三引言对于具有一维零空间的非线性分歧问题,数值方法相对而言比较成熟,处理各种奇异性的正则扩张系统已经构造出来用于计算这类分歧点（［3〕）．具有二维零空间的非线性分歧问题出现在许多具体问题中,例如vonKarman方程,化学反应模型中的Br。lsselator方程,非线性振动,两个空间变量的非线性椭圆型方程等等．计算二维零空间的非线性问题的有效算法正在发展之中,「l」、「Zj提出了计算这一类问题的正则扩张系统和算法．考虑如下具有二维零空间的二参数非线性问题：f（,入,的一O,门．1）其中f：R”XRXR＋R’是C‘映照,假定x…     

求解非线性互补问题的内点正算法

针对非线性互补问题,提出了与其等价的非光滑方程的内点正算法,并在一定条件下证明了该算法的收敛性定理。数值结果表明,该算法是十分有效的。     

Minimum time‐step criteria for the Galerkin finite element methods applied to one‐dimensional parabolic partial differential equations

The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

NONCONFORMING FINITE ELEMENT APPROXIMATIONS TOTHE UNILATERAL PROBLEM

1.IntroductionTherehavebeennumerousworkintheanalysisoffiniteelementmethodsfortheunilateralproblem(c.f.[4]andthereferencestherein).ItshouldbementionedthatinF.Scarpiniet.al.[6],I.Hlavaceket.al.[5]andF.Brezziet.al.[1],theconforminglinearelementapproximationtotheunilateralproblemhavebeenconsidered,andthevariouserrorboundshavebeenobtainedinthedifferentassumptionofregularityofsolutionoftheproblem.Inthispaper3weconsiderthreenonconformingfiniteelement(i.e.twoCrouzrixRaviartlinearelementsandWilsone…     

A multirate time stepping strategy for stiff ordinary differential equations

To solve ODE systems with different time scales which are localized over the components, multirate time stepping is examined. In this paper we introduce a self-adjusting multirate time stepping strategy, in which the step size for a particular component is determined by its own local temporal variation, instead of using a single step size for the whole system. We primarily consider implicit time stepping methods, suitable for stiff or mildly stiff ODEs. Numerical results with our multirate strategy are presented for several test problems. Comparisons with the corresponding single-rate schemes show that substantial gains in computational work and CPU times can be obtained. AMS subject classification (2000)  65L05, 65L06, 65L50     

A time discretization scheme for a non-linear degenerate eddy current model for ferromagnetic materials

^** Email: marian.slodicka{at}ugent.be This paper is devoted to the study of a non-linear degeneratetransient eddy current model of the type [graphic: see PDF] for some 0 < < 1 subject to homogeneous Dirichlet boundarycondition H x = 0. Here, the magnetic properties of a softferromagnet are linked by a power material law. The well-posednessof the problem is proved and a non-linear time-discrete numericalscheme for the approximation in suitable function spaces isdesigned. Convergence of the approximation to a weak solutionis proved and error estimates are derived.     

粘弹性动力问题中的一种新的时域递进算法

提出一种新的求解粘弹性动力问题的时域递进技术,在离散时段内将各物理量展开,导出有限元形式的递推计算格式。对不同的时间步长,可做自适应计算,以保证计算精度。数值验证给出了令人满意的结果。     

A MIXED FINITE ELEMENT METHOD FOR THE CONTACT PROBLEM IN ELASTICITY

Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from O（h3/4） to quasi-optimal O（h│logh│^1/4）. If stronger but reasonable regularity is available, the convergence rate can be optimal O（h）.     

On the comparison of four different implementations of a third-order ENO scheme of box type for the computation of compressible flow

Following ideas of Abgrall, four different implementations of a third-order ENO scheme on general triangulations are described and examined. Two implementations utilize implicit time stepping where the resulting linear systems are solved by means of a preconditioned GMRES method. Two other schemes are constructed using an explicit Adams method in time. Quadratic polynomial recovery is used to result in a formally third-order accurate space discretisation. While one class of implementations makes use of cell averages defined on boxes and thus is close in spirit to the finite volume idea, the second class of methods considered is completely node-based. In this second case the interpretation as a true finite volume recovery is completely lost but the recovery process is much simpler and cheaper than the original one. Although one would expect a consistency error in the finite difference type implementations no such problem ever occurred in the numerical experiments.Dedicated to Willi Törnig on the occasion of his 65th birthday     

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].