Multiplicative Schwarz methods for parabolic problems

摘要

Based on domain decomposition, we give a multiplicative Schwarz domain decomposition method for semi-linear parabolic problems. We consider the relation between the convergence rate and discretization parameters, including the diameter of the sub-domain. We give the error estimate, which tells us that the convergence of the approximate solution is independent of the iteration number at each time level. Finally we give a numerical example.