北京理工大学学报（英文版）
北京理工大學學報（英文版）
북경리공대학학보（영문판）
JOURNAL BEIIJING INSTITUTE OF TECHNOLOGY
2000年
2期
113-119
,共7页
区域分解算法(DDM)%边界控制%正则化%耦合方程
區域分解算法(DDM)%邊界控製%正則化%耦閤方程
구역분해산법(DDM)%변계공제%정칙화%우합방정
domain decomposition methods(DDM)%boundary control%regularization%coupling equations
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.
研究橢圓型方程的區域分解算法.使用邊界控製的方法確定區域界麵上方程解的值和正則化方法剋服控製問題的不適定性.將區域分解算法的關鍵步驟--確定區域界麵上方程解的值轉化為一箇邊界控製問題,引入正則化方法剋服瞭原控製問題的不適定性,證明瞭正則控製解的收斂性,給齣瞭錶徵最優控製的耦閤方程組,從而使得未知解在區域界麵上的值可通過求解一繫列耦閤方程得到.區域分解算法可利用邊界控製的方法實現.
연구타원형방정적구역분해산법.사용변계공제적방법학정구역계면상방정해적치화정칙화방법극복공제문제적불괄정성.장구역분해산법적관건보취--학정구역계면상방정해적치전화위일개변계공제문제,인입정칙화방법극복료원공제문제적불괄정성,증명료정칙공제해적수렴성,급출료표정최우공제적우합방정조,종이사득미지해재구역계면상적치가통과구해일계렬우합방정득도.구역분해산법가이용변계공제적방법실현.
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.
