区域分解算法边界控制近似方法

摘要

The domain decomposition algorithms utilizing the method ofboundary control is studied. The determination of the value of the solution of the partial equation is transformed into a boundary control problem and the ill-posedness of the control problem is overcome by regularization and the convergence of the regularized control is proven. The equations to characterize the optimal control for both elliptic and parabolic equation are given.%采用最优控制的方法解决区域分解算法中内交界面上方程解的值的确定问题.将确定内交界面值的问题转化为边界控制问题,为克服控制问题的不适定性引入了正则化方法,证明了正则最优边界的存在性和收敛性,给出了表征最优边界的耦合方程组.