Model Reduction and Preconditioning for PDE-Constrained Optimization

Ekkehard Sachs* and Xuancan Ye

Reduced order models such as proper orthogonal decomposition have been used successfully for the numerical solution of PDE-constrained optimization problems. Here we present another venue on how to use these reduced order models. We consider a variant of Krylov subspace methods, the deflated Minres method, and show how the deflated subspace can be created by proper orthogonal decomposition. We give numerical results that indicate that this approach seems to be successful and further research in this direction should be fruitful.

Mathematics Subject Classification: 49M15 65K05 90C55

Keywords: Deflated Minres, proper orthogonal decomposition

Minisymposion: Preconditioning for PDE-Constrained Optimization