Level-Set Minimization of Potential Controlled Hadwiger Valuations for Molecular Solvation.
Level-Set Minimization of Potential Controlled Hadwiger Valuations for Molecular Solvation.
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DOI：
10.1016/j.jcp.2010.07.032
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发表时间：
2010-11-01
影响因子：
4.1
通讯作者：
Wang, Zhongming
中科院分区：
文献类型：
--
作者：
Cheng, Li-Tien;Li, Bo;Wang, Zhongming
关键词：
提出了一种求解三维物体上一类具有位势的Had-wiger赋值的数值极小化问题的水平集方法。这种估值是体积、表面积和平均曲率的表面积分的线性组合。当物体缩小到超过临界尺寸时，电势迅速增加。Hadwiger赋值和势的组合是最近发展的变分隐式溶剂模型中非极性分子溶剂化的平均场自由能泛函。这种功能的表面是最小化的水平集的自由能的最陡的下降演变。这个表面演化的正常速度由平均曲率和高斯曲率，以及一个较低的顺序，“强迫”项所产生的潜在的。采用前向欧拉法离散时间导数，动态时间步长满足CFL条件。法向速度被分解为两部分。第一部分由平均曲率项和高斯曲率项组成。它是一种带参数修正的抛物型方程，用中心差分法离散。第二部分包含所有低阶项。它是双曲型的，并离散的迎风格式。发展了局部水平集方法和数值积分等新技术。数值试验证明了该方法的二阶收敛性。应用程序的分子溶剂化建模的例子。
A level-set method is developed for the numerical minimization of a class of Had-wiger valuations with a potential on a set of three-dimensional bodies. Such valuations are linear combinations of the volume, surface area, and surface integral of mean curvature. The potential increases rapidly as the body shrinks beyond a critical size. The combination of the Hadwiger valuation and the potential is the mean-field free-energy functional of the solvation of non-polar molecules in the recently developed variational implicit-solvent model. This functional of surfaces is minimized by the level-set evolution in the steepest decent of the free energy. The normal velocity of this surface evolution consists of both the mean and Gaussian curvatures, and a lower-order, “forcing” term arising from the potential. The forward Euler method is used to discretize the time derivative with a dynamic time stepping that satisfies a CFL condition. The normal velocity is decomposed into two parts. The first part consists of both the mean and Gaussian curvature terms. It is of parabolic type with parameter correction, and is discretized by central differencing. The second part has all the lower-order terms. It is of hyperbolic type, and is discretized by an upwinding scheme. New techniques of local level-set method and numerical integration are developed. Numerical tests demonstrate a second-order convergence of the method. Examples of application to the modeling of molecular solvation are presented.
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影响因子：
5.5
作者：
Cheng, Li-Tien;Xie, Yang;Dzubiella, Joachim;McCammon, J. Andrew;Che, Jianwei;Li, Bo
通讯作者：
Li, Bo
影响因子：
4.1
作者：
Beale, J. Thomas
通讯作者：
Beale, J. Thomas
影响因子：
4.1
作者：
Smereka, P
通讯作者：
Smereka, P
影响因子：
4.4
作者：
Cheng, Li-Tien;Wang, Zhongming;McCammon, J. Andrew
通讯作者：
McCammon, J. Andrew
影响因子：
4.4
作者：
Dzubiella, J;Swanson, JMJ;McCammon, JA
通讯作者：
McCammon, JA