共查询到20条相似文献,搜索用时 875 毫秒
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相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。 相似文献
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本文给出了数值计算具有Z2对称性和双参数的非线性动力学方程二次分叉问题的具体方法,并用此方法计算了不同长宽比矩形区域内多孔介质热对流的二次分叉点和相应的流场和温度场分布。 相似文献
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研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法,按照复变函数描述,对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ,分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数,按双相介质中平面SH波的处理方法,给出介质Ⅰ和介质Ⅱ中的平面位移波,两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件,定解积分方程组,得到问题的稳态解,并给出圆孔位置和介质参数对散射的影响。 相似文献
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本文采用双重孔隙介质模型和非线性二项式渗透定律,对一维问题推导了溶洞裂缝-孔隙介质中二相驱替问题的基本方程,并采用特征线方法求得了数值解,通过和线性情况比较,揭示了非线性效应和溶洞裂缝-孔隙介质中水驱油的基本规律。 相似文献
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矩形悬臂板的非线性振动分析是板理论中的一个相当困难问题至今这个问题还没有解答。本文给出一个满足大这界条件的挠度函数及满足全部纵向边界条件的应力函数,利用伽辽金方法和广信伽辽金方法,在非线性动静态分析中,使解函数逼近相容方程平衡方程及未满足的边界条件,最后建立起求解方程。文中给出数值算例。 相似文献
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横观各向同性介质中弹性波的吸收边界条件 总被引:2,自引:0,他引:2
在数值求解固体中的弹性波动问题时,常需引入吸收边界条件来限制大范围或无边界的求解区域,使数值计算得以顺利进行。本文通过合成简单的一阶偏微分算子,给出了横观各向同性介质中弹性波的吸收边界条件,其中每个单一的算子均可完全吸收沿某一角度出射的平面波。文中还基于弹性波的势函数理论,导出了准P波和准S波在吸收边界处的反射系数公式,用以检验其吸收能力。本文所给出的吸收条件,形式简单,且算例表明吸收效果良好,因 相似文献
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空间机械臂非完整运动规划的最优控制 总被引:13,自引:1,他引:13
讨论空间机械臂系统的运动规划问题,利用系统的非完整特性,将空间机械臂动力学方程转化为非线性控制系统的状态方程,给出一种最优控制的数值自满。通过仿真计算,表明该算法的有效性。 相似文献
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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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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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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
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S. Nadeem Anwar Hussain 《应用数学和力学(英文版)》2009,30(12):1569-1578
The present paper investigates the magnetohydrodynamic(MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem is then solved by the homotopy analysis method.The pertinent parameters appearing in the problem are discussed graphically and presented in tables.It is found that the shrinking solutions exist in the presence of MHD.It is also observed from the tables that the solutions for f(0) with different values of parameters are convergent. 相似文献
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弹性动力学反问题的非线性及其迭代反演 总被引:4,自引:1,他引:3
分析了弹性动力学反问题的非线性及在迭代反演过程中表现出的复杂非线性现象。迭代反演的结果依赖于反演系统参数和迭代初值,而系统参数对应的Mandelbrot集和迭代初值对应的Julia集都是复杂的分形集。随反演系统状态参数的变化,完全确定性的反演系统却可能产生一系列无规则的,不可预测的迭代输出序列。反演迭代过程中出现的分形和混沌现象反映了表面简单的反演迭代后隐藏的复杂性,正是这种复杂性给迭代系统参数的合理选择带来困难,进而使反演迭代不总能给出满意的结果。 相似文献
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Comparison of Iterative Methods for Improved Solutions of the Fluid Flow Equation in Partially Saturated Porous Media 总被引:2,自引:0,他引:2
Abstract. The Picard and modified Picard iteration schemes are often used to numerically solve the nonlinear Richards equation governing water flow in variably saturated porous media. While these methods are easy to implement, they are only linearly convergent. Another approach to solve the Richards equation is to use Newton's iterative method. This method, also known as Newton–Raphson iteration, is quadratically convergent and requires the computation of first derivatives. We implemented Newton's scheme into the mixed form of the Richards equation. As compared to the modified Picard scheme, Newton's scheme requires two additional matrices when the mixed form of the Richards equation is used and requires three additional matrices, when the pressure head-based form is used. The modified Picard scheme may actually be viewed as a simplified Newton scheme.Two examples are used to investigate the numerical performance of different forms of the 1D vertical Richards equation and the different iterative solution schemes. In the first example, we simulate infiltration in a homogeneous dry porous medium by solving both, the h based and mixed forms of Richards equation using the modified Picard and Newton schemes. Results shows that, very small time steps are required to obtain an accurate mass balance. These small times steps make the Newton method less attractive.In a second test problem, we simulate variable inflows and outflows in a heterogeneous dry porous medium by solving the mixed form of the Richards equation, using the modified Picard and Newton schemes. Analytical computation of the Jacobian required less CPU time than its computation by perturbation. A combination of the modified Picard and Newton scheme was found to be more efficient than the modified Picard or Newton scheme. 相似文献
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流体饱和多孔隙介质波动方程多尺度反演 总被引:1,自引:0,他引:1
基于多尺度的思想,将小波多分辨分析和多尺度方法相结合,应用于流体饱和多孔隙介质孔隙率的反演。利用小波变换,将原始反问题分解为不同尺度上的一系列子反问题,并按照尺度从粗到细的顺序依次求解。在每一个尺度上,都采用稳定、收敛快的正则化高斯牛顿法求解,次一级尺度上求出的“全局最优解”作为上一级的初始解,依此类推,直到求出原始问题的真正的全局最优解。通过与传统的正则化高斯牛顿法相比较,显示了小波多尺度法是一个大范围收敛、能够有效节省计算量的方法,数值模拟的结果也表明了方法的有效性。 相似文献
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Layne T. Watson 《Nonlinear dynamics》1990,1(2):143-191
Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new globally convergent homotopy techniques have been successfully applied to solve Brouwer fixed point problems, polynomial systems of equations, constrained and unconstrained optimization problems, discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements, and finite difference, collocation, and Galerkin approximations to nonlinear partial differential equations. This paper introduces, in a tutorial fashion, the theory of globally convergent homotopy algorithms, deseribes some computer algorithms and mathematical software, and presents several nontrivial engineering applications.This work was supported in part by DOE Grant DE-FG05-88ER25068, NASA Grant NAG-1-1079, and AFOSR Grant 89-0497. 相似文献