lbm2d

说明：  CZT和FFT的C语言实现代码，能有效滤除谐波，噪声。获得信号的频率，是一种良好的频率测量算法。(CZT and FFT of the C language code, can effectively filter out harmonics and noise. Access to the signal frequency, is a good algorithm for frequency measurement.)

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)

通过C++头文件实现的有限元形状函数计算程序(finite element shape function)

进行结构响应分析的Wilson法，是直接积分的基本算法之一，相信进行有限元动力分析编程的诸位都能用上(structural response analysis of Wilson, which is direct integration one of the basic algorithm, believe that the dynamic finite element analysis program you can use)

对于给定的一组轨迹点，用优化方法实现铰链四杆机构轨迹复演。优化方法为共轭梯度法。(For a set of track points,we use a optimization method to optimize the track of Hinge four-bar mechanism. The optimization method is conjugate gradient.)

矩量法仿真电磁辐射和散射的源代码（c++） (Moment Method Simulation of electromagnetic radiation and scattering of the source code (c++))

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.)

随机数的产生，枚举嵌套算法求解一元多次方程。按批量处理。(The generation of random Numbers, nested enumeration algorithm monadic equation according to the batch processing for many times)

用mfc实现计算器的基本操作，支持键盘输入，并保留xp风格,可计算平方，幂，时间显示等操作(With mfc achieve the basic operation of the calculator, support for keyboard input, and retain xp style, calculates the square, power, time display and other operations)

之前找不到合适精度的log2x函数的定点化源码，经过实现并验证后，发上来大家一起学习(fixed version for log2x)