Characterizing PSPACE with pointers

This paper gives an implicit characterization of the class of functions computable in polynomial space by deterministic Turing machines – PSPACE. It gives an inductive characterization of PSPACE with no ad‐hoc initial functions and with only one recursion scheme. The main novelty of this characterization is the use of pointers (also called path information) to reach PSPACE. The presence of the pointers in the recursion on notation scheme is the main difference between this characterization of PSPACE and the well‐known Bellantoni‐Cook characterization of the polytime functions – PTIME. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Accelerating molecular dynamic simulation on graphics processing units

We describe a complete implementation of all‐atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

渐近φ伪压缩映象有限族的迭代程序的强收敛(英文)

Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl.     

平面叶栅跨音流场气动特性的数值研究

通过对模型方程的分析，给出了一种新的隐格式构造思想。将它运用到关通量分裂格式中，可得到无近似因子分解、无矩阵运算的高效二阶精度隐式矢通量分裂差分格式，并用来直接求解时间平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组。数值计算标明：该方法具有精度高、稳定性好、计算量少、收敛快等优点，在平面叶栅跨音流场的计算中，较好地捕获了激波，与实验比较，结果令人满意。     

An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions

Presented here is a method, the hierarchical charge partitioning (HCP) approximation, for speeding up computation of pairwise electrostatic interactions in biomolecular systems. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of its constituent structural components. The charge distribution in each component is systematically approximated by a small number of point charges, which, for the highest level component, are much fewer than the number of atoms in the component. For short distances from the point of interest, the HCP uses the full set of atomic charges available. For long‐distance interactions, the approximate charge distributions with smaller sets of charges are used instead. For a structure consisting of N charges, the computational cost of computing the pairwise interactions via the HCP scales as O(N log N), under assumptions about the structural organization of biomolecular structures generally consistent with reality. A proof‐of‐concept implementation of the HCP shows that for large structures it can lead to speed‐up factors of up to several orders of magnitude relative to the exact pairwise O(N²) all‐atom computation used as a reference. For structures with more than 2000–3000 atoms the relative accuracy of the HCP (relative root‐mean‐square force error per atom), approaches the accuracy of the particle mesh Ewald (PME) method with parameter settings typical for biomolecular simulations. When averaged over a set of 600 representative biomolecular structures, the relative accuracies of the two methods are roughly equal. The HCP is also significantly more accurate than the spherical cutoff method. The HCP has been implemented in the freely available nucleic acids builder (NAB) molecular dynamics (MD) package in Amber tools. A 10 ns simulation of a small protein indicates that the HCP based MD simulation is stable, and that it can be faster than the spherical cutoff method. A critical benefit of the HCP approximation is that it is algorithmically very simple, and unlike the PME, the HCP is straightforward to use with implicit solvent models. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Assessment of linear finite‐difference Poisson–Boltzmann solvers

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson–Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite‐difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson–Boltzmann equation. It turns out that the time‐limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson–Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation

The Poisson‐Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson‐Boltzmann equation. We expose the flux directly through a first‐order system form of the equation. Using this formulation, we propose a system that yields a tractable least‐squares finite element formulation and establish theory to support this approach. The least‐squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

The energy conserving particle-in-cell method

A new particle-in-cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell’s equations are differenced implicitly in time by the midpoint rule and solved concurrently by a Jacobian-free Newton Krylov (JFNK) solver. Several tests show that the finite grid instability is eliminated in energy conserving PIC simulations, and the method correctly describes the two-stream and Weibel instabilities, conserving exactly the total energy. The computational time of the energy conserving PIC method increases linearly with the number of particles, and it is rather insensitive to the number of grid points and time step. The kinetic enslavement technique can be effectively used to reduce the problem matrix size and the number of JFNK solver iterations.     

变循环发动机模型的求解算法研究

采用部件法建立了变循环发动机的多维非线性隐式方程组模型,模型具有隐式性,因而求解过程复杂,收敛困难.针对上述问题,采用遗传算法和牛顿-拉夫逊法进行模型求解,提出了算法的有效性评价指标:初值敏感性、收敛性和稳定性.对两种算法进行有效性评价.针对发动机工作性能最优化问题,建立了多目标模型,用遗传算法进行求解,并分析了相关变量随马赫数变化的规律.结果可为变循环发动机模型求解算法的选择与设计提供参考.     

一类求解单调变分不等式的隐式方法

1．引言变分不等式是一个非常有趣。非常困难的数学问题［"］．它具有广泛的应用（例如，数学规划中的许多基本问题都可以归结为一个变分不等式问题），因而得到深入的研究并有了不少算法［1，2，5－8，17－21］．对线性单调变分不等式，我们最近提出了一系列投影收缩算法Ig－13］．本文考虑求解单调变分不等式其中0CW是一闭凸集，F是从正p到自身的一个单调算子，一即有我们用比（·）表示到0上的投影．求解单调变分不等式的一个简单方法是基本投影法［1，6］，它的迭代式为然而，如果F不是仿射函数，只有当F一致强单调且LIPSChitZ连续…