EVENTO
Block iterative algorithms for the solution of parabolic optimal control problems
Tipo de evento: Seminário LNCC
We consider block iterative methods for the solution of large scale linear-quadratic optimal control problems rising from the control of parabolic partial differential equations over a finite control horizon. The spatial discretization by a finite element method requires the optimal control of $n$ coupled ordinary differential equations, where $n$ can be quite large. The solution of this system of equations by conventional methods can be prohibitively expensive in terms of computational cost and memory requirements. We describe two iterative algorithms. The first algorithm employs a CG method to solve a symmetric positive definite reduced linear system for the unknown control variable. A preconditioner is described, which we prove yields a rate of convergence independent of the space and time discretization parameters, however, double iteration is required. A second algorithm is designed to avoid double iteration by introducing an auxiliary variable. It yields a symmetric indefinite system, and for this system a positive definite block preconditioner is described. We prove a rate of convergence independent of the space and time discretization parameters when MINRES acceleration is used. Numerical results are presented for test problems.
Data Início: 06/12/2007 Hora: 12:00 Data Fim: Hora: 13:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Christian E. Schaerer - IMPA - IMPA - cschaer@impa.br
