Abstract

Primal-Dual Newton Interior Point Methods for PDE constrained optimization problems with applications in shape and topology optimization

Ronald H.W. Hoppe
Universitat Augsburg

Joint with

Svetozara Petrova
Universitat Augsburg

We consider optimization problems with equality and inequality constraints on
both the state variables and the design parameters as they typically arise in
shape and topology optimization. In particular, the state variables are subject
to a PDE or systems of PDEs describing the operating behavior of the device or
system to be optimized. Relying on appropriate finite element discretizations, for
the numerical solution of the discrete problems we concentrate on an all-in-one
approach where the numerical solution of the discretized state equations is an
integral part of the optimization routine. In particular, we focus on primal-dual
Newton interior-point methods and transforming iterations for the solution of the
condensed primal-dual Hessian system.
As applications, we firstly deal with the topology optimization of electric drives
in high power electronics. Here, the state equation is given by the quasistationary
limit of Maxwell's equations which are discretized by means of curl-conforming
edge elements. Secondly, we are concerned with the shape optimization of biotem-plated
microcellular biomorphic ceramics based on homogenization modeling.