Abstract: 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 rate 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.

Key words: heat equation , central difference scheme, partition of unity, subspace correction, domain decomposition