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二维热传导方程有限差分区域分解算法

吕桂霞,马富明   

  1. 北京应用物理与计算数学研究所计算物理实验室;吉林大学数学科学学院 北京 100088;长春 130012
  • 出版日期:2006-02-20 发布日期:2006-02-20

吕桂霞,马富明. 二维热传导方程有限差分区域分解算法[J]. 数值计算与计算机应用, 2006, 27(2): 96-105.

FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHM FOR THE TWO-DIMENSIONAL HEAT EQUATION

  1. L(u|¨) Guixia (Laboratory of Computational Physics, IAPCM, Beijing 100088) Ma Fuming (Institute of Mathematics, Jilin University, Changchun 130012)
  • Online:2006-02-20 Published:2006-02-20
本文讨论了一类数值求解二维热传导方程的并行差分格式.在这个算法中,通过引进内界点将求解区域分裂成若干子区域.在子区域间内界点上采用非对称格式计算,一旦这些点的值被计算出来,各子区域间的计算可完全并行.本文得到了稳定性条件和最大模误差估计.它表明我们的格式有令人满意的稳定性,并且有着较高的收敛阶.
In this paper, a parallel finite difference scheme for numerically solving the two-dimensional heat equation is studied. In this procedure, the domain over which the problem is defined is divided into subdomains by introducing interface points. Interface values between subdomains are found by asymmetric schemes, once these values are calculated, subdomain problems can be solved in parallel. Stability conditions and maximum norm error estimates for these procedures are derived, which demonstrate that our schemes have satisfactory stability and higher convergence order.
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