uystn

this document contain some demonstrations in mathematics , it can bee very helpful for beginners

求解一维热传导方程，格式包括FTCS、BTCS、CNCS三种差分格式(solve one dimension heat transfer equation. )

说明：  数学建模 马尔科夫链的详细讲解 马尔科夫链的详细讲解 数学建模(A detailed explanation of markov chains for mathematical modeling)

在fortran环境下编写ductile_fracture子程序，可以通过MARC来调用，实现板材成形中破裂过程的可视化(Written in fortran environment ductile_fracture subroutines can be invoked by MARC, realized in sheet metal forming rupture process visualization)

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)

FFT with fix point 2*N

采用有限元离散计算一维声子、光子能带，参数见文件源码内(Calculated using the finite element discrete one-dimensional phonon, photon energy band, within the parameters see document source)

有限元法利用铁摩辛柯梁计算转轴质量刚度阻尼矩阵(Finite element method using the Timoshenko beam to calculate the stiffness and damping matrix of the shaft quality)

程序是关于计算两相黎曼问题的一个求解器。可以直接设置。(The code is a solver about the two-phase Riemann problem. the user can use it directly.)

五点差分法(matlab)解椭圆型偏微分方程方程,分法,偏分,五点差分,椭圆型,偏微分方程(Five-point difference method (matlab) solutions of elliptic partial differential equations, sub-law, partial points, five-point difference, elliptic partial differential equations)