共查询到20条相似文献,搜索用时 187 毫秒
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有限元后处理中超收敛计算的EEP(单元能量投影)法以及基于该法的自适应分析方法对线性ODE(常微分方程)问题的求解已经获得了全面成功,也推动了非线性ODE问题自适应求解的研究。经过研究,已经实现了一维有限元自适应分析技术从线性到非线性的跨越,该文意在对这方面的进展作一简要综述与报道。该文提出一种基于EEP法的一维非线性有限元自适应求解方法,其基本思想是通过线性化,将现有的线性问题自适应求解方法直接引入非线性问题求解,而无需单独建立非线性问题的超收敛计算公式和自适应算法,从而构成一个统一的、通用的非线性问题自适应求解算法。该文给出的数值算例表明所提出的算法高效、稳定、通用、可靠,解答可逐点按最大模度量满足用户给定的误差限,可作为先进高效的非线性ODE求解器的核心理论和算法。 相似文献
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以能量有限元方法(EFEM)建立控制方程,研究了复合材料层合梁受激励时的横向振动问题。该方法以结构中的能量密度作为变量,根据波动理论中功率流与能量密度的平衡关系建立了与傅里叶热传导方程类似的二阶偏微分方程组,通过有限元离散得到结构单元节点的能量密度矩阵形式方程。根据耦合连续平衡条件,建立耦合单元节点矩阵,从而对总矩阵方程进行组集及求解,得到结构中能量密度的分布。通过数值算例与传统有限元方法(FEM)结果做了对比,取得了较好的一致性。 相似文献
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有限元线法(FEMOL)是一种优良的半解析、半离散方法,可将其比拟为广义一维问题,进而将一维有限元中单元能量投影(EEP)法及相应的自适应求解技术引入,使FEMOL由半解析方法变为完全解析、数值精确的方法。在对二维线性问题成功地实现了自适应FEMOL分析的基础上,该文进一步报道FEMOL自适应方法在二维自由振动问题中的成功应用和最新进展。该文简要介绍了FEMOL自适应分析二维振动问题的求解策略和技术,整套方法思路清晰、算法严谨、高效可靠,可以得到满足精度要求的自振频率和按最大模度量满足用户事先给定误差限的振型,均为数值精确解。该文给出的数值算例表明所提出的算法具有高效、稳定、通用、可靠的优良特性。 相似文献
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基于新近提出的一维有限元后处理超收敛算法——单元能量投影(EEP)法,将有限元自适应求解问题转化为对超收敛解答的自适应分段多项式插值问题,一步便可获得最优的有限元网格划分,在该网格上再次进行有限元计算,即可获得满足用户给定的误差限的有限元解答。该法简单实用、快速高效,是一个颇具优势和潜力的自适应方法。文中以二阶常微分方程模型问题为例,对该法的形成思路和实施策略做一介绍,并给出有代表性的数值算例用以展示该法的优良性能和效果。 相似文献
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找形分析是膜结构设计中的关键环节,但在数学上,膜结构的极小曲面找形分析是一个高度非线性问题,一般无法求得其解析解,因此数值方法成为重要工具。近年来,基于单元能量投影法(EEP法)的一维非线性有限元的自适应分析已经取得成功,基于EEP法的二维线性有限元自适应分析也被证实是有效、可靠的。在此基础上,该文提出一种基于EEP法的二维非线性有限元自适应方法,并成功将之应用于膜结构的找形分析。其主要思想是,通过将非线性问题用Newton法线性化,引入现有的二维线性问题的自适应求解技术,进而实现二维有限元自适应分析技术从线性到非线性的跨越,将非线性有限元的自适应分析求解从一维问题拓展到二维问题。该方法兼顾求解的精度和效率,对网格自适应地进行调整,最终得到优化的网格,其解答可按最大模度量逐点满足用户设定的误差限。该文综述介绍了这一进展,并给出数值算例用以表明该方法的可行性和可靠性。 相似文献
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A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems
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Zuliang Lu Yanping Chen & Weishan Zheng 《East Asian journal on applied mathematics.》2012,2(2):108-125
A Raviart-Thomas mixed finite element discretization for general bilinear optimal
control problems is discussed. The state and co-state are approximated by lowest
order Raviart-Thomas mixed finite element spaces, and the control is discretized by
piecewise constant functions. A posteriori error estimates are derived for both the coupled
state and the control solutions, and the error estimators can be used to construct
more efficient adaptive finite element approximations for bilinear optimal control problems.
An adaptive algorithm to guide the mesh refinement is also provided. Finally, we
present a numerical example to demonstrate our theoretical results. 相似文献
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Summary A new analytic finite element method (AFEM) is proposed for solving the governing equations of steady magnetohydrodynamic (MHD) duct flows. By the AFEM code one is able to calculate the flow field, the induced magnetic field, and the first partial derivatives of these fields. The process of the code generation is rather lengthy and complicated, therefore, to save space, the actual formulation is presented only for rectangular ducts. A distinguished feature of the AFEM code is the resolving capability of the high gradients near the walls without use of local mesh refinement. Results of traditional FEM, AFEM and finite difference method (FDM) are compared with analytic results demonstrating the manifest superiority of the AFEM code. The programs for the AFEM codes are implemented in GAUSS using traditional computer arithmetic and work in the range of low and moderate Hartmann numbersM<1000. 相似文献
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Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints
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A quadratic optimal control problem governed by parabolic equations with
integral constraints is considered. A fully discrete finite element scheme is constructed
for the optimal control problem, with finite elements for the spatial but the backward
Euler method for the time discretisation. Some superconvergence results of the control,
the state and the adjoint state are proved. Some numerical examples are performed to
confirm theoretical results. 相似文献
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R. A. Meric 《International journal for numerical methods in engineering》1979,14(12):1851-1863
The boundary control problem of optimal heating of an infinitely long slab with tempertue-dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods. In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co-ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization. 相似文献
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基于EEP (单元能量投影)超收敛计算的自适应有限元法,已对一系列问题取得成功,但其自适应特性尚缺乏相关研究。该文以二阶常微分方程为模型问题,同时考察基于EEP和SPR (超收敛分片恢复)超收敛解的自适应分析方法,与有限元最优网格进行了比较分析,进而提出反映自适应有限元收敛特性的估计式,并给出了自适应收敛率β的定义。该文给出的数值试验表明:采用m次单元,对于解答光滑的问题,SPR法与EEP法均可有效用于自适应求解,其位移可按最大模获得m+1的自适应收敛率;对于奇异因子为α(<1)的奇异问题,SPR法失效,而基于EEP法的自适应求解,其位移按最大模可获得m+α的自适应收敛率,远高于α的常规有限元收敛率。 相似文献
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R. A. Meric 《International journal for numerical methods in engineering》1979,14(4):624-628
A stationary variational formulation of the necessary conditions for optimality is derived for an optimal control problem governed by a parabolic equation and mixed boundary conditions. Then a mixed finite element model with elements in space and time is utilized to solve a simple numerical example whose analytical and finite difference solutions are given elsewhere. Numerical results show that the proposed method with C° continuity elements constitutes a powerful numerical technique for solution of optimal control problems of distributed parameter systems. 相似文献
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特征值问题迭代伽略金法与Rayleigh商加速 总被引:3,自引:0,他引:3
该文讨论特征值问题非协调有限元和混合有限元的加速计算方法。基于迭代伽略金法和Rayleigh商加速技巧,我们建立了特征值问题Wilson非协调有限元和Ciarlet-Raviart混合有限元的加速计算方案。这些新方案把在细网格上解一个特征值问题简化为在粗网格上解一个特征值问题和在细网格上解一个线性方程。文中证明了新方案的计算结果仍然保持了渐近最优精度阶,并用数值实验验证了理论结果。 相似文献
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For a kind of the singularly perturbed reaction-diffusion problem, the standard energy norm is too weak to measure adequately the errors of solutions computed by finite element methods. The multiplier of this problem gives an unbalanced norm whose different components have different orders of convergence. In the paper, we introduce a new stronger norm, construct the least-squares finite element method (LSFEM) in this new norm and develop a robust and stable numerical approach for more general singularly perturbed reaction-diffusion problems in 1D spaces. At last, numerical examples are presented to illustrate the proposed method and theoretical results. 相似文献