Stiff_equations.pdf

Compute isotherms in quad

基于凸优化算法的矩阵填充稀疏矩阵理论的Matlab实现。(Based on convex optimization algorithm of matrix fill sparse matrix theory Matlab achieve.)

用基于主元分析的方法对被控过程进行建模，可以消除变量之间的贡献性。(Accused of process modeling method based on principal component analysis, contribution between the variables can be eliminated.)

说明：  1.5MW风力机叶片功率系数Cp计算程序示例，采用梯形法数值积分计算(1.5MW wind turbine blade power coefficient the Cp calculation program examples, numerical integration using the trapezoidal method)

求解任意区域上的二元函数的二重积分，功能强大实用方便！(Solving binary function on any area of ​ ​ the double integral, powerful practical and convenient!)

各种数值积分，龙贝格积分。反常积分。高斯积分。三重积分。(Various numerical integration Romberg integration. Improper integrals. Gaussian integral. Triple integral.)

用LBM结合非平衡外推方法实现的圆柱绕流，柱面边界以非平衡外推方法实现。(LBM combined with the extrapolation method of achieving non-equilibrium flow around a cylinder, cylinder boundary to achieve non-equilibrium extrapolation method.)

罚函数法 它将有约束最优化问题转化为求解无约束最优化问题: 其中M为足够大的正数, 起"惩罚"作用, 称之为罚因子, F(x, M )称为罚函数.(hunhefahanshufa)

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)

一个用FTT法实现相关函数的快速估计程序(A correlation function with the FTT method to achieve the rapid estimation procedures)