Computing and Visualization in Science

, Volume 14, Issue 3, pp 91–103 | Cite as

A POD framework to determine robust controls in PDE optimization

  • A. BorzìEmail author
  • G. von Winckel


A strategy for the fast computation of robust controls of PDE models with random-field coefficients is presented. A robust control is defined as the control function that minimizes the expectation value of the objective over all coefficient configurations. A straightforward application of the adjoint method on this problem results in a very large optimality system. In contrast, a fast method is presented where the expectation value of the objective is minimized with respect to a reduced POD basis of the space of controls. Comparison of the POD scheme with the full optimization procedure in the case of elliptic control problems with random reaction terms and with random diffusivity demonstrates the superior computational performance of the POD method.


PDE-constrained optimization Proper orthogonal decomposition Random fields 

Mathematics Subject Classification (2000)

15A18 49K20 60H35 93B11 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WürzburgWürzburgGermany
  2. 2.Institut für Mathematik und Wissenschaftliches RechnenKarl-Franzens-Universität GrazGrazAustria

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