Fast solution of elliptic control problems
Fast solution of elliptic control problems
复制标题
椭圆控制问题的快速求解
DOI：
10.1007/bf00934478
复制
发表时间：
1980
影响因子：
1.9
通讯作者：
W. Hackbusch
中科院分区：
文献类型：
--
作者：
W. Hackbusch
具有二次代价泛函的椭圆控制问题需要求解两个椭圆边值问题的系统。我们提出了一个快速迭代过程的数值解这个问题。该方法可以应用于非常特殊的问题（例如，泊松方程的矩形）以及一般方程（任意尺寸，一般区域）。也可以处理非线性问题。所需的功与单个椭圆方程的数值解所做的功成比例。
Elliptic control problems with a quadratic cost functional require the solution of a system of two elliptic boundary-value problems. We propose a fast iterative process for the numerical solution of this problem. The method can be applied to very special problems (for example, Poisson equation for a rectangle) as well as to general equations (arbitrary dimensions, general region). Also, nonlinear problems can be treated. The work required is proportional to the work taken by the numerical solution of a single elliptic equation.