空间运动方程快速求解器设计与实现

文章基于四阶经典龙格库塔法(classical Runge-Kutta method of order four,RK-4)和四阶Adams预测校正法(fourth-order Adams predictor-corrector method,Adams-4),提出一种现场可编程逻辑门阵列(field programmable gate array,FPGA)实现的数据路径可动态配置的空间运动方程快速求解器(space motion equation fast solver,SMEFS)。SMEFS采用折叠式结构,借助高效的任务映射和精准的状态管理,通过资源复用和动态配置运算器内部连接关系实现数据路径的动态配置,快速求解空间运动方程,并有效节省硬件资源。采用某型运载火箭的相关数据对SMEFS进行大批量空间运动方程求解的性能评估,实验结果表明SMEFS能够快速可靠地求解发射坐标系下的五自由度空间运动方程,与软件求解的平均加速比为12.765,求解结果最大相对误差小于9×10^(-5,)具备较好的加速效果和较高的计算可靠性。

一类四阶非线性波动方程整体经典解的存在性

借助线性问题的衰减估计,在一适当的Banach空间,利用整体迭代法证明了一类半线性四阶波动方程Cauchy问题整体经典解的存在性.

Studying the Impact of Vaccination Strategy and Key Parameters on Infectious Disease Models

In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.

地磁偶极子场磁力线疏密可视化算法

好的磁力线可视化结果应该是空间中某点附近磁力线疏密能正确反映该点磁感应强度的大小,磁力线上任一点的切线方向和该点磁感应强度的方向一致.所以磁力线可视化需要能准确、合理地解决磁力线种子点的选取和磁力线的追踪问题.种子点是磁力线追踪的起始点,其选取原则是满足追踪得到的磁力线疏密能准确映射磁感应强度大小的要求.传统的种子点选取算法是基于实际数据的统计算法.本文提出了基于物理约束的等磁通量法和等磁通密度衰减法,并对两种方案进行了严格的数学推导,最后基于经典四阶龙格库塔法实现了磁力线追踪.实验得到了较满意的效果图.