一类无结构三角网上抛物方程的有限差分区域分解算法

FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHM ON UNSTRUCTURED TRIANGULAR MESH FOR PARABOLIC EQUATION

本文讨论了一类在无结构三角网上数值求解二维热传导方程的有限差分区域分解算法．在这个算法中,将通过引进两类不同类型的内界点,将求解区域分裂成若干子区域．一旦内界点处的值被计算出来,其余子区域上的计算可完全并行．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和较高的收敛阶．

In this paper, a finite difference domain decomposition algorithm on an unstructured triangular mesh 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 two kinds of interface points. Once interface values between subdomains are obtained, subdomain problems can be solved in parallel. Stability condition and maximum norm error estimate for this procedure is derived, which demonstrates that our scheme has satisfactory stability and higher convergence order.