Automated extension of fixed point PDE solvers for optimal design with bounded retardation
Abstract
In this project we investigate the "one shot"-method for solving optimal design problems, where the constraints are given by a state equation in a very large number of state and design variables.
The "one shot"-method aims at attaining feasibility and optimality of the minimization problem by simultaneously updating the design, the state and the dual variables instead of solving a discretization of the state equation in each iteration.
Therefore, the progress of the iterative method is monitored by an appropriate primal-dual augmented Lagrangian merit-function and the convergence is guaranteed by a suitable choice of design space preconditioner.
In the current research we focus on problems wit the objective and constraint function being nonseparable.
Besides that we will investigate several topics such as the introduction of stability constraints, a closer retardation factor analysis for a number of control problems as well as a mesh independence principle of the retardation factor.
Furthermore, we discuss the applicability of the "one shot" approach for time dependent problems.
Principal investigators
Financer
DFG Individual Research Grant
Duration of project
Start date: 09/2009
End date: 06/2013
