共查询到19条相似文献,搜索用时 109 毫秒
1.
用同伦方法反演非饱和土中溶质迁移参数 总被引:1,自引:1,他引:1
非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题. 将同伦方法
引入该问题的求解,通过构造线性同伦将原问题转化为求解同伦函数最小值的无约束优化问
题. 同时在分析了同伦参数正则化效应的基础上,提出一种两段同伦参数修正方法. 即在求
解的初始阶段,根据拟Sigmoid函数调整同伦参数,以追踪同伦路径,保证计算稳定地进行;
在迭代的后期,采用与残差相关的同伦参数修正方法,以抵抗观测噪声对求解的影响. 数值
算例为求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移模型参数反演问题,计算
结果表明了该方法的大范围收敛性及较强的抵抗观测噪声的能力. 相似文献
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应用并行PEST算法优化地下水模型参数 总被引:5,自引:0,他引:5
基于列文伯格-马夸尔特(Levenberg-Marquardt)算法的PEST参数优化程序具有寻优速度快、健壮性好的优点,在地下水模型参数优化研究中有许多成功的应用实例。但是,对于大尺度、高精度和高复杂性的大规模地下水模拟,使用PEST进行参数优化需要大量的计算时间,优化效率较低。本文应用OpenMP并行编程方法对PEST算法进行了并行化,使之可以在共享存储并行计算机上进行参数优化的并行计算。并将此方法应用于甘肃北山区域地下水模型的参数优化中,并行实验表明,使用并行化的PEST可以将地下水模型参数优化效率提高3.7倍。
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4.
跨音速翼型反设计的一种大范围收敛方法 总被引:2,自引:0,他引:2
求解跨音速翼型的反设计问题时,传统的梯度型方法一般均为局部收敛.
为增大求解的收敛范围,依据同伦方法的思想,通过构造不动点同伦,将原问题的求解
转化为其同伦函数的求解,并依据拟Sigmoid函数调整同伦参数以提高计算效率,进而构造
出一种具有较高计算效率的大范围收敛反设计方法. 数值算例以RAE2822翼型的表面压力分
布为拟合目标,分别采用B样条方法, PARSEC方法及正交形函数方法等3种不同的
参数化方法,并分别以NACA0012, OAF139及VR15翼型为初始翼型进行迭代计
算. 计算结果证明,该方法适用于多种参数化方法,且具有较好的计算效率,从多
个不同的初始翼型出发,经较少次数迭代后,
均能与目标翼型很好地拟合,是一种高效的大范围收敛方法. 相似文献
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二阶非定常多宗量热传导反问题的正则解 总被引:1,自引:0,他引:1
引入Bregman距离函数及其加权函数作为正则项,应用Tikhonov正则
化方法,对二阶非定常多宗量热传导反问题进行求解. 利用测量信息和计算信息构造最小二
乘函数,将多宗量反演识别问题转化为一个优化问题. 空间上采用8节点等参元进行离散,
时域上采用时域精细算法进行离散,建立了二阶非定常多宗量热传导问题的有限元正/反演数
值模型. 该模型不仅考虑了非均质和参数分布的影响,而且也便于正反演问题的敏度分析,
可对导热系数和边界条件等宗量进行有效的单一和组合识别. 给出了相关的数值验证,对信
息测量误差以及不同正则项的计算效率作了探讨. 数值结果表明,该方法能够对二阶非定常
多宗量热传导反问题进行有效的求解,并具有较高的计算精度. 相似文献
7.
弹性动力学反问题的数值反演方法 总被引:15,自引:1,他引:14
系统介绍了弹性动力学反问题中各种数值反演方法,包括各种近似下的线性化反演方法;非线性迭代反演方法;确定性和非确定性搜索的优化反演方法;大范围收敛的同伦反演方法以及多尺度反演方法。阐述了各类反演方法的原理、特点、适用范围和存在的局限性,指出了数值反演方法进一步研究的方向。 相似文献
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基于精细积分技术的非线性动力学方程的同伦摄动法 总被引:2,自引:0,他引:2
将精细积分技术(PIM)和同伦摄动方法(HPM)相结合,给出了一种求解非线性动力学方程的新的渐近数值方法。采用精细积分法求解非线性问题时,需要将非线性项对时间参数按Taylor级数展开,在展开项少时,计算精度对时间步长敏感;随着展开项的增加,计算格式会变得越来越复杂。采用同伦摄动法,则具有相对筒单的计算格式,但计算精度较差,应用范围也限于低维非线性微分方程。将这两种方法相结合得到的新的渐近数值方法则同时具备了两者的优点,既使同伦摄动方法的应用范围推广到高维非线性动力学方程的求解,又使精细积分方法在求解非线性问题时具有较简单的计算格式。数值算例表明,该方法具有较高的数值精度和计算效率。 相似文献
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S. Abbasbandy 《Nonlinear dynamics》2008,52(1-2):35-40
The homotopy analysis method (HAM) is used to find a family of solitary solutions of the Kuramoto–Sivashinsky equation. This
approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The homotopy analysis
method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable
and manageable. 相似文献
13.
I. G. AKSOY 《应用数学和力学(英文版)》2013,34(11):1349-1360
The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method (HAM). The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method (FDM). It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency. 相似文献
14.
In this paper, we have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting
micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic
field has been analyzed analytically. The governing fundamental equations are approximated by a system of nonlinear locally
similar ordinary differential equations which are solved analytically by applying homotopy analysis method (HAM). The effects
of Darcy number, heat generation parameter and inertia coefficient parameter are determined on the flow. Convergence of the
obtained series solution is discussed. The homotopy analysis method provides us with a new way to obtain series solutions
of such problems. This method contains the auxiliary parameter which provides us with a simple way to adjust and control the
convergence region of series solution. By suitable choice of the auxiliary parameter, we can obtain reasonable solutions for
large modulus. 相似文献
15.
This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting
fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption. The analytical solutions
for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free
stream velocity and stretching velocity, heat source parameter, Prandtl number, thermal radiation parameter, the suction and
injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy
analysis method (HAM). Convergence of the series is explicitly discussed. In addition, shear stress and heat flux at the surface
are calculated. 相似文献
16.
带源参数的二维热传导反问题的无网格方法 总被引:1,自引:1,他引:1
利用无网格有限点法求解带源参数的二维热传导反问题,推导了相应的离散方程. 与
其它基于网格的方法相比,有限点法采用移动最小二乘法构造形函数,只需要节点信息,不
需要划分网格,用配点法离散控制方程,可以直接施加边界条件,不需要在区域内部求积分.
用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点.
最后通过算例验证了该方法的有效性. 相似文献
17.
A homotopy analysis method(HAM)is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar'e method and the incremental harmonic balance method. 相似文献
18.
The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method. 相似文献
19.
Zhang Kaipeng Wu Daihua 《Acta Mechanica Solida Sinica》2005,18(3):278-282
I. INTRODUCTIONStructural damages due to the loss of sti?ness such as crack, localization bulking have remarkablein?uences on the physical properties of structure such as deformation, stress, frequency and modelshape. So the change of these properties can be used to identify the damage location and degree ofstructures. The damage identification techniques based on these properties’ changes have attractedmuch attention in recent years, and many approaches have been developed[1??5].Nowaday… 相似文献