Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Numerical Approximation of an SQP-Type Method for Parameter Identification
SIAM Journal on Numerical Analysis
| Hi-index | 0.00 |
The paper deals with an efficient solution technique to large-scale discretized shape and topology optimization problems. The efficiency relies on multigrid preconditioning. In case of shape optimization, we apply a geometric multigrid preconditioner to eliminate the underlying state equation while the outer optimization loop is the sequential quadratic programming, which is done in the multilevel fashion as well. In case of topology optimization, we can only use the steepest-descent optimization method, since the topology Hessian is dense and large-scale. We also discuss a Newton-Lagrange technique, which leads to a sequential solution of large-scale, but sparse saddle-point systems, that are solved by an augmented Lagrangian method with a multigrid preconditioning. At the end, we present a sequential coupling of the topology and shape optimization. Numerical results are given for a geometry optimization in 2-dimensional nonlinear magnetostatics.