基于差分格式的SOR-MC 高效计算

随着研究的深入，仿真的计算量爆炸式地增加，提高计算效率显得尤为重要。分析了蒙特卡洛法（MC）与差分法的逐次迭代(SOR)的优缺点后，本文提出了一种新型的混合算法SOR-MC，利用蒙特卡洛法（MC）随机游动为逐次迭代(SOR)构造一个初始迭代值，提高求解速度。并利用变网格精度进一步改进SOR-MC算法。通过多个数值试验验证了混合算法及其改进能大大减少了迭代次数，有效地提高了计算效率。

The SOR-MC Efficient Calculation Based on Possion DifferentialEquation

With the in-depth research, the amount of simulation calculation explosiving increase and improve the computationalefficiency is particularly important. Analysis of the Monte Carlo method (MC) and the difference method of successive iteration(SOR) of the advantages and disadvantages, this paper presents a new type of hybrid algorithm SOR-MC, the use of the Monte Carlomethod random walk construct an SOR initial iteration value, and improve the solution speed. And the use of variable grid to furtherimproves the accuracy of SOR-MC algorithm. Through multiple numerical experiments verify that the hybrid algorithm and itsimprovement can significantly reduce the number of iterations, thus effectively enhancing the computational efficiency.