并行求解抛物型方程的AGE算法在边值处的改进 The Improvements of AGE Algorithm for Parallel Solving Parabolic Equations at the Boundary

摘要

AGE方法是一种求解偏微分方程的并行算法，通过重新构造有限差分格式，把所要求解的差分方程组分裂成若干个可以独立并行求解的规模较小的方程组。但此种算法在靠近边值处误差较高，本文在靠近左右边界处对格式进行改进，得到一种在边值处改进的AGE方法。该方法在边界附近尽可能的保持较小的截断误差，从而提高了计算精度。AGE method is a parallel algorithm for solving partial differential equations, by re-construct a finite difference scheme, so the required solution of difference equations can be split into several smaller inde-pendent parallel solution of equations. However, this algorithm gets higher truncation errors near the boun-dary. In this paper, I get an improvement AGE method, by improving the format close to the left and right boundaries. The method stays as smaller truncation errors in border, so can improve the calculation ac-curacy.