Abstract
AbstractWe consider the optimal control problem of a phase field system with distributed control. A reduction of the computational complexity is achieved by a POD‐Galerkin approach where the expensive high‐fidelity PDE systems are replaced by low‐dimensional approximations. The POD basis functions are computed from snapshots which are space‐adapted finite element solutions of the governing equations. Within the trust‐region framework, the accuracy of the surrogate models is controlled in the course of the optimization. In the numerical example we compare the use of a relaxed double‐obstacle free energy with a smooth free energy concerning the influence on the accuracy of the solution and the optimization performance.
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