一类三阶微分方程正解的存在性

利用锥压缩拉伸不动点定理,讨论了一类非线性奇异的三阶微分方程三点边值问题,得出了正解的存在性.     

三阶伪抛物半线性微分方程边值问题解的存在性

Hilbert空间方法被用于一类三阶伪抛物型边值问题并得出了某些条件下的解的存在性．     

一维土柱试验的数学模型

主要讨论了一维土柱试验模型及其反问题.考虑到溶质在土壤及地下水中迁移的非线性行为,认为通常模型中的阻滞因子应改为与溶质浓度相关的泛函,而零阶产出项应为与时间、空间及溶质浓度相关的非线性项,进而提出了一类新的描述一维土柱试验的非线性数学模型.对于模型参数的识别问题,给出了两类典型的确定阻滞因子与源(汇)项系数的土柱试验反问题.最后,以淄博张店孝妇河-张冉原状土柱试验为例,应用所建立的数学模型对试验结果做了初步的阐释.     

Spectral Analysis for HSS Preconditioners

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.     

基于改进模拟退火算法的推动式生产-配送协调优化

为减小物资生产与配送不协调造成的成本及生产资源浪费,建立了考虑推动式生产调度的物资配送优化模型,并针对标准模拟退火算法受随机因素影响易陷入局部最优的缺点,设计带有回火与缓冷操作的改进模拟退火算法对模型求解,确定了优化的车辆配送路线以及物资生产计划。对比实验结果表明：相对于单纯的物资配送优化模型,考虑推动式生产调度的配送优化模型,能够有效减小物资滞留时间以及配送延误成本;相较于标准模拟退火算法,改进算法搜索到了更优解,且计算结果的标准差减小了93.42%,稳定性更好;同时,改进模拟退火算法具有较低的偏差率,在中小规模算例中求解质量较高,平均偏差率在0.5%以内。     

酸性气体作用下服役结构的时变可靠度

鉴于现阶段酸性气体作用对受力混凝土工作性能影响研究的匮乏,采用数值计算与实例相结合的方法分析了酸性侵蚀气体对服役钢筋混凝土结构可靠度的影响,给出了混凝土中和高度、混凝土损伤高度和截面尺寸的时变规律及其与时变可靠度指标的关系。并与一般大气环境条件对比,得到了酸性侵蚀介质对受力混凝土结构产生加剧腐蚀的定量结论。对侵蚀介质环境下的建筑结构可靠性设计提供了建设性理论指导。     

神经网络量子态及其应用

神经网络量子态是由人工神经网络所表示的量子态。得益于机器学习,尤其是深度学习近年来取得的突破性进展,神经网络量子态的研究得到了广泛的关注,成为当前的热点前沿方向。文章将介绍不同的神经网络量子态,其物理性质与典型应用场景,最新进展,以及面临的挑战。     

Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.     

A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

Some Open Problems in Parameterized Complexity Related to the Work of Jianer Chen

This short paper highlights some open problems related to the work of Jianer Chen in the area of parameterized/multivariate algorithmics.