fatigue-analysis-using-XFEM

说明：  二分法算法文件，龙格库塔法，高斯法，数值计算二分法求解，适用于初学数值计算人群(Dichotomy algorithm file)

对格朗日、分段线性、三次样条插值方法的运用。(Grange, piecewise linear, cubic spline interpolation method to use.)

用于研究粒子在晶体材料内输运性质，计算扩散系数的动力学蒙特卡洛程序( Kinetic Monte Carlo program is used to study particle transport properties in crystalline materials, the calculation of the diffusion coefficient Kinetic Monte Carlo program is used to study particle transport properties in crystalline materials, the calculation of the diffusion coefficient)

分别对beta估计值模拟分析、非中心对称分布、卡方拟合优度检验、筛选抽样随机数抽取、有限样本性质模拟这5个内容进行了编程说明(The five contents of beta estimation simulation analysis, non-centrosymmetric distribution, chi-square goodness-of-fit test, random number extraction of screening sampling and Simulation of finite sample properties are explained by programming.)

用追赶法来求解三对角线性方程组，解决数值分析问题，与大家共同学习。并且提供黄金分割法、高斯赛德尔迭代法求解数值分析问题(The catch-up method is used to solve tridiagonal linear equations, to solve numerical analysis problems, and to learn from you. The Golden Section Method and Gauss Seidel Iteration Method are also provided to solve numerical analysis problems.)

非线性算法合集，包括牛顿拉夫逊法，Broyden拟牛顿法，弧长法，割线法。每种算法都包含有线性搜索迭代改进。(Nonlinear algorithm collection, including Newton Raphson, Broyden quasi-Newton method, arc-length method, secant method. Each contains a linear search algorithms for iterative improvement.)

代码为偏最小二乘法计算过程的代码，主要部分都有中文解释(Code for the calculation process of partial least squares method)

说明：  用相场法模拟晶粒的长大的一个程序，用c++编写的，(a program simulation the grain growth by Phase field written using c++)

说明：  拓扑优化MMA算法从空间的一个初始设计点出发，沿着某个搜索方向以适当步长的迭代格式 ，实现对设计变量的修改，以获得的值。(Starting from an initial design point in space, the topology optimization MMA algorithm modifies the design variables in an appropriate iterative format along a certain search direction to obtain the optimal value)

说明：  16点基4—FFT算法编程。输入16点的序列，采用基4-fft方法计算其快速傅里叶变换。(16 points-based 4-FFT algorithm for programming. Enter the 16-point sequence, with the base 4-fft method for calculating the fast Fourier transform.)