New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

The configurational dependence of binding free energies: A Poisson–Boltzmann study of Neuraminidase inhibitors

The linear finite difference Poisson-Boltzmann (FDPB) equation is applied to the calculation of the electrostatic binding free energies of a group of inhibitors to the Neuraminidase enzyme. An ensemble of enzyme-inhibitor complex conformations was generated using Monte Carlo simulations and the electrostatic binding free energies of subtly different configurations of the enzyme-inhibitor complexes were calculated. It was seen that the binding free energies calculated using FDPB depend strongly on the configuration of the complex taken from the ensemble. This configurational dependence was investigated in detail in the electrostatic hydration free energies of the inhibitors. Differences in hydration energies of up to 7 kcal mol^–1 were obtained for root mean square (RMS) structural deviations of only 0.5 Å. To verify the result, the grid size and parameter dependence of the calculated hydration free energies were systematically investigated. This showed that the absolute hydration free energies calculated using the FDPB equation were very sensitive to the values of key parameters, but that the configurational dependence of the free energies was independent of the parameters chosen. Thus just as molecular mechanics energies are very sensitive to configuration, and single-structure values are not typically used to score binding free energies, single FDPB energies should be treated with the same caution.     

Molecular mechanics and dynamics of biomolecules using a solvent continuum model

An easy implementation of molecular mechanics and molecular dynamics simulation using a continuum solvent model is presented that is particularly suitable for biomolecular simulations. The computation of solvation forces is made using the linear Poisson-Boltzmann equation (polar contribution) and the solvent-accessible surface area approach (nonpolar contribution). The feasibility of the methodology is demonstrated on a small protein and a small DNA hairpin. Although the parameters employed in this model must be refined to gain reliability, the performance of the method, with a standard choice of parameters, is comparable with results obtained by explicit water simulations. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1830-1842, 2001     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

一种非定常N-S方程并行求解设计

为了解决计算流体力学(CFD)中非定常计算与越来越大的计算量,并行计算已成为一种现实有效的选择.论文首先研究了一种并行区域分解策略,该策略简单而高效,但需要算法配合.为此,采用了一种与并行完全兼容的隐式方法DP-LUR方法.通过双时间步长法,将DP-LUR方法延伸应用到非定常计算中而不改变其原有的性质.最后分析了并行编程中的主要难点,提出解决方法,即采用中间数据分离节点下标与处理,并给出了并行程序的总体结构.     

A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.     

Membrane protein native state discrimination by implicit membrane models

Four implicit membrane models [IMM1, generalized Born (GB)‐surface area‐implicit membrane (GBSAIM), GB with a simple switching (GBSW), and heterogeneous dielectric GB (HDGB)] were tested for their ability to discriminate the native conformation of five membrane proteins from 450 decoys generated by the Rosetta‐Membrane program. The energy ranking of the native state and Z‐scores were used to assess the performance of the models. The effect of membrane thickness was examined and was found to be substantial. Quite satisfactory discrimination was achieved with the all‐atom IMM1 and GBSW models at 25.4 Å thickness and with the HDGB model at 28.5 Å thickness. The energy components by themselves were not discriminative. Both van der Waals and electrostatic interactions contributed to native state discrimination, to a different extent in each model. Computational efficiency of the models decreased in the order: extended‐atom IMM1 > all‐atom IMM1 > GBSAIM > GBSW > HDGB. These results encourage the further development and use of implicit membrane models for membrane protein structure prediction. © 2012 Wiley Periodicals, Inc.     

广义sine-Gordon方程高精度隐式紧致差分方法

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.