Parallel D–D type domain decomposition algorithm for optimal control problem governed by parabolic partial differential equation

Abstract

Abstract A parallel domain decomposition algorithm for solving an optimal control problem governed by a parabolic partial differential equation is proposed. This algorithm is based upon non-overlapping domain decomposition. In every iteration, the global problem is reduced to solve simultaneously some implicit subproblems on many sub-domains by using explicit flux approximations near inner-boundaries at each time-step. Both a priori error bounds of optimal orders and optimal rates of convergence for the iterative schemes are presented. Numerical experiments are also performed to verified the theoretical analysis.