基于遗传算法和Python多处理器并行计算的二阶热传导方程初边值问题数值解法

Numerical Solution for a Kind of Second Order Heat Conduction Equation with Initial-boundary Value Problems Based on Genetic Algorithm and Python Multiprocessor Parallel Computing

针对二阶热传导非线性偏微分方程初边值问题,对求解矩形区域进行离散网格化处理,构造差分格式的极小化目标函数,将当前计算结点作为目标函数的参数,把遗传算法参数寻优的结果作为当前结点的函数值.同时,使用了Python中的多处理器模块进行并行计算,以提高计算速度.实验结果表明,该方法可以获得较高的计算精度,且稳定有效.

For second-order nonlinear heat conduction equation with initial-boundary value problems,it first the solution of rectangular region is discretized and meshed,and the objective function of minimization of difference scheme is constructed.Then the current calculation node is taken as the parameter of the objective function,and the result of optimization of genetic algorithm is taken as the function value of current node.At the same time,the multiprocessor module in Python is used for parallel computing to improve the computing speed.The experimental results show that the method can obtain high accuracy and is stable and effective.