首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 140 毫秒
1.
In this follow up paper to our previous study in Bayona et al. (2011) [2], we present a new technique to compute the solution of PDEs with the multiquadric based RBF finite difference method (RBF-FD) using an optimal node dependent variable value of the shape parameter. This optimal value is chosen so that, to leading order, the local approximation error of the RBF-FD formulas is zero. In our previous paper (Bayona et al., 2011) [2] we considered the case of an optimal (constant) value of the shape parameter for all the nodes. Our new results show that, if one allows the shape parameter to be different at each grid point of the domain, one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique. We analyze the same examples studied in Bayona et al. (2011) [2], both with structured and unstructured grids, and compare our new results with those obtained previously. We also find that, if there are a significant number of nodes for which no optimal value of the shape parameter exists, then the improvement in accuracy deteriorates significantly. In those cases, we use generalized multiquadrics as RBFs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter.  相似文献   

2.
Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.  相似文献   

3.
Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD) methods can offer significant savings in computer resources (time and memory). This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation.  相似文献   

4.
In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming (SQP) algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.  相似文献   

5.
The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm. In this paper, we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm. This is answered in the specific case of the Helmholtz equation with L2-norm as the energy norm. We obtain uniform stability with respect to the wave number. We illustrate the method with a number of 1D numerical experiments, using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally. A 1D theoretical stability analysis is also developed.  相似文献   

6.
In the error analysis of 3D trilateration localization, we constructed a new tetrahedron shape measurement method based on the condition number of the tetrahedron. This method uses algebraic operations, which is simpler than the previous methods based on complex geometric operations, and is also suitable for the shape measurement of triangle. For the trilateration localization problem in 3D space, based on tetrahedron shape measurement (TSM), we designed an algorithm of selecting anchor nodes on the hollow sphere centered at the unknown node. Extensive simulation experiments show that the tetrahedron shape measurement method proposed in this paper is effective. The anchor node selection algorithm based on tetrahedron shape measurement (TSM) can effectively suppress the iterative error problem in trilateration localization. Furthermore, the calculation of the tetrahedron condition number can be used for the deployment of anchor nodes in trilateration localization.  相似文献   

7.
The local RBF is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter. We derive exact formulas for the first and second derivatives in one dimension, and for the Laplacian in two dimensions. Using these formulas we compute Taylor expansions for the error. From this analysis, we find that there is an optimal value of the shape parameter for which the error is minimum. This optimal parameter is independent of the nodal distance. Our theoretical results are corroborated by numerical experiments.  相似文献   

8.
防护林是我国荒漠绿洲区主要植被类型,可为该地区防风固沙、水盐调控、水热平衡提供有力保障,调查防护林空间分布信息十分重要。然而荒漠绿洲防护林条带较窄、斑块面积小、分布广且零散,不易大尺度准确提取。为解决此难点,以磴口县荒漠绿洲为研究区,基于GF-2号遥感影像,采用面向对象分类技术提取防护林空间分布信息。分类前,首先基于局部方差(LV)和LV变化率(ROC)曲线,选取分割防护林的最优分割尺度。然后采用随机森林(RF)算法的袋外误差率(OOB error)及基尼系数(Gini)对包含光谱、形状和纹理的分类特征进行重要性评估并筛选特征、优化模型参数;最后,基于随机森林、CART决策树、支持向量机(SVM)、K近邻(KNN)四种分类器提取防护林空间分布信息并对比验证。结果表明:(1)采用ROC-LV曲线方法相比于遍历分割参数,可更客观更高效地筛选最优分割参数的可能值;(2)基于RF算法计算的袋外误分率和基尼系数可以有效筛除冗余特征,配合分类器参数优化,在保证分类精度的同时,有效提高分类器性能,大幅提升数据处理速度;(3)基于实测数据集对分类结果进行验证,结果显示基于随机森林算法的特征优化结合SVM分类器提取的防护林空间分布信息精度最高,生产者精度达到97.14%,总体防护林面积为208.99 km2,与实际210 km2接近,在小区块中,SVM分类器的分类效果优于其他三种分类器;(4)因GF-2影像分辨率高,并且含有近红外波段,通过波段合成得到亚米级信息,故基于面向对象的方法能够以单条林带为基本单位研究防护林林网属性,例如提取断带信息等林网结构特征。研究结论可为荒漠绿洲区带状防护林提取提供重要技术支撑。  相似文献   

9.
针对大规模多输入多输出(multiple input multiple output, MIMO)系统信道估计中的导频设计问题,在压缩感知理论框架下,提出了一种基于信道重构错误率最小化的自适应自相关矩阵缩减参数导频优化算法.首先以信道重构错误率最小化为目标,推导了正交匹配追踪(orthogonal matching pursuit, OMP)算法下信道重构错误率与导频矩阵列相关性之间的关系,并得出优化导频矩阵的两点准则,即导频矩阵列相关性期望和方差最小化;然后研究了优化导频矩阵的方法,并提出相应的自适应自相关矩阵缩减参数导频矩阵优化算法,即在每次迭代过程中,以待优化矩阵平均列相关程度是否减小作为判断条件,调整自相关矩阵缩减参数值,使参数不断趋近于理论最优.仿真结果表明,与采用Gaussian矩阵、Elad方法、低幂平均列相关方法得到的导频矩阵相比,本文所提方法具有更好的列相关性,且具有更低的信道重构错误率.  相似文献   

10.
We present a method to maximize the separation of two adjacent eigenfrequencies in structures with two material components. The method is based on finite element analysis and topology optimization in which an iterative algorithm is used to find the optimal distribution of the materials. Results are presented for eigenvalue problems based on the 1D and 2D scalar wave equations. Two different objectives are used in the optimization, the difference between two adjacent eigenfrequencies and the ratio between the squared eigenfrequencies. In the 1D case, we use simple interpolation of material parameters but in the 2D case the use of a more involved interpolation is needed, and results obtained with a new interpolation function are shown. In the 2D case, the objective is reformulated into a double-bound formulation due to the complication from multiple eigenfrequencies. It is shown that some general conclusions can be drawn that relate the material parameters to the obtainable objective values and the optimized designs.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号