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Qianlong Liu 《Journal of computational physics》2011,230(22):8256-8274
Prosperetti’s seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest. 相似文献
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聚焦评价函数和极点搜索策略是自动聚焦的重要模块,直接影响聚焦的效果.为同时满足自动聚焦速度和精度上的要求,提出了一种新的自动聚焦算法.该算法综合了快速改进的灰度差分法和高精度小波变换法的优点,根据各阶段聚焦评价函数的梯度选择合适的评价函数和镜头移动步长,并且实现了从大步长快速粗扫到小步长精确细调的过渡.实验表明,与传统... 相似文献
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An efficient unsplit perfectly matched layer for numerical simulation of electromagnetic waves in unbounded domains is derived via a complex change of variables. In order to surround a Cartesian grid with the PML, the time-dependent PML requires only one (scalar) auxiliary variable in two space dimensions and six (scalar) auxiliary variables in three space dimensions. It is therefore cheap and straightforward to implement. We use Fourier and energy methods to prove the stability of the PML. We extend the stability result to a semi-discrete PML approximated by central finite differences of arbitrary order of accuracy and to a fully discrete problem for the ‘Leap-Frog’ schemes. This makes precise the usefulness of the derived PML model for longtime simulations. Numerical experiments are presented, illustrating the accuracy and stability of the PML. 相似文献
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考虑Beta函数偏导数的计算以及与此相关的广义积分的高精度快速计算问题.首先将Beta函数B(x,y)的定义扩展到整个复平面上,并建立了在整个复平面上Beta函数B(x,y)的偏导数的递推公式.对许多广义积分我们给出Beta函数偏导数的表示形式,因而利用Beta函数的偏导数计算这些广义积分.数值计算表明,算法无论从计算精度还是计算速度,远好于数值积分.另外,得到了B_(p,q)(x,y)存在闭形式的条件,并给出一些广义积分的闭形式. 相似文献
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自Pawlak提出粗糙集概念以来,人们就一直对粗糙集的近似精度很感兴趣,出现了不少有关近似精度的文献.在粗糙集理论中,精度是量化由粗糙集边界引起的不精确性的一种重要数字特征.在分析传统精度和基于等价关系图的过剩熵的近似精度的基础上,提出了一种新的精度定义.比较发现,新定义的精度更具有合理性.同时把这个新定义的精度运用到了属性约简上,通过实例比较发现,本文提出的属性约简更具有可行性. 相似文献
78.
主要研究稳定计算近似函数的高阶导数的积分逼近方法,方法因由Lanczos提出故也称为Lanczos算法.利用Legendre多项式的正交性,提出了一类逼近近似函数高阶导数的高精度积分方法,即构造出一系列积分算子Dn,h(m)去逼近噪声函数的高阶导数,且这些积分算子具有O(δ(2n+2)/(2n+m+2))的收敛速度,其中δ为近似函数的噪声水平.数值模拟结果表明提出的方法是稳定而有效的. 相似文献
79.
A multicriteria Boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality “from Condorcet to Pareto”, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an optimal alternative preserves its optimality are calculated. To illustrate the way how the stability and accuracy functions can be used as efficient tools for post-optimal analysis, an application from the voting theory is considered. 相似文献
80.