کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
762819 | 896711 | 2011 | 6 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Distributed control and constraint preconditioners Distributed control and constraint preconditioners](/preview/png/762819.png)
Optimization problems with constraints that involve a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDE-constrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2- and 3-dimensional Poisson problem is the PDE. Large dimensional linear systems result from the discretization and need to be solved: these systems are of saddle-point type. We introduce an optimal preconditioner for these systems that leads to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases. The theoretical proof indicates that these approaches may have much broader applicability for other partial differential equations.
Journal: Computers & Fluids - Volume 46, Issue 1, July 2011, Pages 461–466