摘要
To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.
研究椭圆型方程的区域分解算法 .使用边界控制的方法确定区域界面上方程解的值和正则化方法克服控制问题的不适定性 .将区域分解算法的关键步骤———确定区域界面上方程解的值转化为一个边界控制问题 ,引入正则化方法克服了原控制问题的不适定性 ,证明了正则控制解的收敛性 ,给出了表征最优控制的耦合方程组 ,从而使得未知解在区域界面上的值可通过求解一系列耦合方程得到 .区域分解算法可利用边界控制的方法实现 .
