An efficient approach to solve very large dense linear systems with verified computing on clusters

Automatic result verification is an important tool to guarantee that completely inaccurate results cannot be used for decisions without getting remarked during a numerical computation. Mathematical rigor provided by verified computing allows the computation of an enclosure containing the exact solution of a given problem. Particularly, the computation of linear systems can strongly benefit from this technique in terms of reliability of results. However, in order to compute an enclosure of the exact result of a linear system, more floating‐point operations are necessary, consequently increasing the execution time. In this context, parallelism appears as a good alternative to improve the solver performance. In this paper, we present an approach to solve very large dense linear systems with verified computing on clusters. This approach enabled our parallel solver to compute huge linear systems with point or interval input matrices with dimensions up to 100,000. Numerical experiments show that the new version of our parallel solver introduced in this paper provides good relative speedups and delivers a reliable enclosure of the exact results. Copyright © 2014 John Wiley & Sons, Ltd.     

Achieving Efficient Multichannel Conductance in Through‐Space Conjugated Single‐Molecule Parallel Circuits

Constructing single‐molecule parallel circuits with multiple conduction channels is an effective strategy to improve the conductance of a single molecular junction, but rarely reported. We present a novel through‐space conjugated single‐molecule parallel circuit (f‐4Ph‐4SMe) comprised of a pair of closely parallelly aligned p‐quaterphenyl chains tethered by a vinyl bridge and end‐capped with four SMe anchoring groups. Scanning‐tunneling‐microscopy‐based break junction (STM‐BJ) and transmission calculations demonstrate that f‐4Ph‐4SMe holds multiple conductance states owing to different contact configurations. When four SMe groups are in contact with two electrodes at the same time, the through‐bond and through‐space conduction channels work synergistically, resulting in a conductance much larger than those of analogous molecules with two SMe groups or the sum of two p‐quaterphenyl chains. The system is an ideal model for understanding electron transport through parallel π‐stacked molecular systems and may serve as a key component for integrated molecular circuits with controllable conductance.     

加工时间可控和简单线性增长的平行机排序

本文研究加工时间可控并随开工时间简单线性增长的平行机排序问题.证明了该问题为NP-难问题,该问题存在满足以下性质的最优排序:每个工件的加工时间要么完全压缩,要么完全不压缩;每台机器的工件排序由一个工件参数和控制变量的函数的递增序给出.通过将问题等价转换为0-1非线性整数规划问题,给出了平行机排序问题的贪婪算法.     

芯片-系统电磁脉冲耦合的高性能全波电磁模拟

目的是研究高性能的电磁场仿真软件,对真实的芯片-系统电磁脉冲耦合过程进行高分辨率、高置信度的电磁仿真。研究重点是针对多尺度问题,突破算法的并行计算瓶颈。基于自主软件平台快速研发出仿真软件,在高性能计算平台上完成对真实复杂问题的全波电磁仿真。通过对某真实机箱内部芯片的电磁脉冲耦合仿真分析,验证了本文提出的算法的高性能、高效率的特性。     

Parallel orthogonal factorization null-space method for dynamic quadratic programming

An algorithm has been developed to solve quadratic programs that have a dynamic programming structure. It has been developed for use as part of a parallel trajectory optimization algorithm and aims to achieve significant speed without sacrificing numerical stability. the algorithm makes use of the dynamic programming problem structure and the domain decomposition approach. It parallelizes the orthogonal factorization null-space method of quadratic programming by developing a parallel orthogonal factorization and a parallel Cholesky factorization. Tests of the algorithm on a 32-node INTEL iPSC/2 hypercube demonstrate speedup factors as large as 10 in comparison to the fastest known equivalent serial algorithm.This research was supported in part by the National Aeronautics and Space Administration under Grant No. NAG-1-1009.     

A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems

A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation,and optimization problems in complex MDOF nonlinear dynamic systems.     

A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing

This work studies the build-up method for the global minimization problem for molecular conformation, especially protein folding. The problem is hard to solve for large molecules using general minimization approaches because of the enormous amount of required computation. We therefore propose a build-up process to systematically construct the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each build-up stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the Lennard-Jones microcluster conformation problem. The experiments showed that the algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation. In particular, for the 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.     

“平行板电容器的电容”演示实验探讨

分析了“平行板电容器的电容”演示实验中与静电计指针偏转变化量有关的因素。     

Representing protein and peptide structures with parallel-coordinates

Graphical representation of molecular conformations is an important tool used by chemists to gain molecular insight. In spite of today's enhanced computer graphics there are still situations, such as in multiple conformation displays, in which standard visualization techniques are limited. Parallel-coordinate (‖-coords) representation, which was originally developed for visualizing multivariant datasets in fields other than chemistry, offers an alternative basis for graphical representation of molecular structures. In parallel-coordinates, the axes are drawn parallel rather than perpendicular to each other, allowing many axes to be placed and seen. This mapping procedure has unique geometric properties and useful relationships to the original space. In this article, we apply the parallel-coordinate representation for presenting peptide and protein structural conformations. In particular, we demonstrate the usefulness of parallel-coordinates in the context of conformational analysis where this representation, combined with multiple filters, allows nontrivial clustering of data points, leading to new observations. The ‖-coords representation is also demonstrated as a tool for two-dimensional (2D) representation of protein secondary structure and for identification of disulfide-bonded pairs in protein structures. Regardless of the application, an advantage of the ‖-coords approach is that it retains its inherent simplicity and ease of use, and requires little or no software development. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1893–1902, 1997     

光学向量-矩阵乘法器教学演示实验

为了在光计算教学中提供让学生更易于形象理解光的并行计算能力和实现方式的教学环境,基于向量-矩阵乘法的基本原理,采用LED阵列、光敏管阵列、柱面透镜、薄透镜等简易的基础光学元件搭建了4×4的光学向量-矩阵乘法器教学演示实验.该演示实验展示了并行光计算系统的基本功能实现和构成要素,有助于学生对光计算有初步的形象认识和了解,认知本课程的目的和意义,有利于激发学生对课程学习的兴趣.