Problem1

说明：  基于OpenSEES平台的一个桥墩算例，可以供大家参考(An example of Bridge Pier Based on OPENSEES platform can be used for reference)

利用有限元理论，求一二维梁的固有频率和振型。短边固定，给定长度、横截面积，弹性模量及材料密度已知。并对比理论计算结果进行分析。各参数自己设定。(Using finite element theory, seeking a two-dimensional beam natural frequencies and modes. The short side is fixed, given the length, cross-sectional area, modulus of elasticity and density of the material is known. And compare the theoretical calculation results were analyzed. Each parameter set.)

自己写了一个二维Euler方程的间断有限元程序 上次发了一个三角形单元的程序 因为不是曲边单元 所以在圆柱后面容易形成涡 现在把程序改为曲边四边形单元了 没有涡出现 单元是8节点四边形单元 节点编号顺序是 1 5 2 6 3 7 4 8 也就是四个角点依次 是1 2 3 4 然后是边的中点编号 5 6 7 8. 时间推进采用 Runge-Kutta 方法 数值通量采用全局Lax-Friedrichs通量 仍然不能捕捉激波 因为没有做重构或者加人工粘性 等这个做出来了 再发一次。 程序没有进行优化 比如说内存的消耗没有优化 比如直边单元的边界积分仍然采 用了曲边的积分方法 增加了计算量 比如面积分、线积分都是采用的是Gauss- Legendre-Lobatto积分 积分精度会比一般的Gauss-Legendre积分精度低一阶 等 等问题。 二维的 纯属交流性质 就没有考虑这些问题 ^_^ 如果物面全部是直边 那么只要改变一个参数N 就可以获得不同的计算精度 且具 有谱精度 因为单元的节点是Gauss-Legendre-Lobatto积分点。 其实就是谱元法 （物面是曲边的情况我不清楚是不是也可以通过提高基函数的阶数 也就是增加N 来提高计算精度）(Wrote a two-dimensional Euler equations with discontinuous finite element program Last made ​ ​ a triangular element of the program, not curved edge unit is so easy to form a vortex in the cylinder behind the Program to curved edge quadrilateral element vortices appear Unit is the order of 8-node quadrilateral element node number is 15,263,748 which is the four corners of the points in turn Is 1234 and then the side of the midpoint of the number 5678. Time promote the use of Runge-Kutta method Numerical flux of the overall situation of Lax-Friedrichs, flux Still can not capture the shock wave did not do the reconstruction or artificial viscosity do it Zaifayici. The program is not optimized for example, memory consumption is not optimized such as straight-edge boundary integral of the unit is still mining Integral method to increase the amount of computation such as surface integral with a curved edge, the line integral using the Gauss- The Legendr)

偏微分方程数值解上机实习 运用古典显式差分格式求解二维扩散方程的初边值问题 运用P-R差分格式求解二维扩散方程的初边值问题

ANSYS中关于车桥耦合的接触法命令流，车辆模型为二分之一车(About the vehicle.the contact method in ANSYS command stream, with half vehicle model car)

这是四阶的龙格库塔算法和lyapunov指数稳定性。(tihs is a runge kutta method )

卡尔曼机动，加入了对机动的检测和处理，对于机动模型，滤波解更加有效(Kalman mobility, the right to join the mobile detection and processing, motor model, a more effective filtering solution)

矩阵理论：如线性空间、线性变换、内 积空间、正交投影、Jordan标准型、范数 理论等(Matrix theory: linear space, linear transformations, inner product spaces, orthogonal projection, Jordan standard norm theory, etc.)

说明：  二级转运站选址数学规划模型求解的lingo 程序(Lingo Program for Solving Mathematical Programming Model of Secondary Transfer Station Location)

Python bindings for CUDA 2.1 with numpy integration