热传导方程二阶并行区域分解差分算法

Two order parallel domain decomposition finite difference algorithm for heat equation

提出了一类新的计算热传导方程数值解的并行差分算法.算法基于区域分解和子区域校正,在每个子区域上进行残量修正,各子域之间可以并行计算.证明了算法的收敛性,并且理论分析表明,在每一时间步,只需校正一次或两次,即可达到最优的收敛阶.数值试验表明了算法的有效性和优越性.

An efficient parallel finite difference scheme based upon overlapping domain decomposition is proposed for solving heat equations numerically. The algorithm is based upon the domain decomposition and the subspace correction methods. The residual is modified on each subspace, and the computation is completely parallel. Optimal convergent rote is proved. The result shows that it is just needed to iterate once or twice at each time step. Numerical experiments also confirm the efficiency and superiority of the algorithm.