Decoupled two‐grid finite element method for the time‐dependent natural convection problem I: Spatial discretization

In this article, a decoupled two grid finite element method (FEM) is proposed and analyzed for the nonsteady natural convection problem using the coarse grid numerical solutions to decouple the nonlinear coupled terms, and the corresponding optimal error estimates are derived. Compared with the standard Galerkin FEM and the usual two‐grid FEM, our algorithm not only keeps good accuracy but also saves a lot of computational cost. Some numerical examples are provided to verify the performances of the decoupled two‐grid FEM. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled two‐grid FEM for the nonsteady natural convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2135–2168, 2015     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

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.     

字符串匹配算法在DNA序列比对中的应用

高通量测序技术的飞速发展让生物信息领域迎来了大数据时代。新技术在提供海量生物遗传信息的同时,也给分析这些数据带来了新的挑战。DNA序列比对是信息分析流程中的关键步骤,为后续的变异检测提供序列比对信息。2015“深圳杯”数学建模夏令营B题以DNA序列比对为研究课题,希望参赛学生给出序列快速比对的最佳方案。本文简要点评了各参赛队伍的解答情况,然后介绍了现有DNA序列比对软件中用到的算法和数据结构。     

汽车租赁调度多目标优化模型

本文考虑一个周期的汽车租赁调度问题,在直接调运的前提下,首先以汽车租赁公司的总收益最大和总短缺损失最小为目标,建立多目标优化模型;然后提出了基于启发式的双层排序综合择优算法;最后对汽车租赁案例进行了实证研究。     

A conformal mapping approach for investigating the free-boundary seepage from symmetric channels

We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.     

基于遗传算法的自动驾驶仪测试性分析

为了提高自动驾驶仪故障测试与诊断的快速性与准确性,提出了一种基于遗传算法的自动驾驶仪测试性分析方法;此方法解决了遗传算法应用于测试项目选择的难点,构建了最优的故障测试策略,能以最短时间完成测试并满足测试覆盖性的要求;利用故障测试获得的知识,简化故障与测试间的相关性矩阵,加快了故障诊断的速度;最终获得了故障测试与诊断一体化的方法;实验结果表明,此方法有效提高了故障测试与诊断的速度,并且易于实现。     

基于多模差分融合的高速车辆定位算法

针对车辆高速运动下定位延时大、精度低、稳定性差的问题,发挥GPS、RSSI和INS三种定位模式的各自优势,将GPS差分校准算法与RSSI测距相结合求解横坐标,将RSSI测距与INS惯导迭代算法相结合求解纵坐标,提出了一种适合高速运动车辆的多模差分融合精确定位算法。以四车道的高速路为场景进行了仿真实验,当车速为70km/h时,跟踪误差<1m,定位延时<0.2s。实验结果表明,该算法可实现车身级和车道级定位,在精确交通诱导、车辆防撞等智能交通领域具有应用前景和推广价值。