Adaptivity and memory-reduced adjoints for optimization problems with parabolic PDE-constraints
Kunibert Siebert (University of Stuttgart) and Andrea Walther (University of Paderborn)
During the last decade there has been a substantial progress in the analysis and numerics of PDE constrained optimization. The computational complexity of such problems requires efficient numerical methods for an efficient simulation. Among others, adaptive finite element discretization have become popular in case of stationary PDEs. Turning
to transient problems the computation effort dramatically increases since the solution
of the associated optimality system requires information about the discrete variables on
the space-time domain.
Adaptive discretization of such optimal control problems with parabolic PDE constraints
are not well established by now for the following reason. When using a discretization
of the space-time domain one can directly apply techniques that are well established
for steady problems at the cost of (d+1) dimensional discretization. Although such an
approach is meaningful for optimal control problems, the application of this procedure
for many real life problems is out of question due to the curse of dimensionality.
Resorting to the more popular time-stepping schemes one has to utilize efficient compression or checkpointing methods to avoid storing full information of the space-time
domain. This is imperative for large-scale simulation. To our best knowledge there are
no adaptive algorithms using such efficient solution strategies.
With the envisaged mini-symposium we want to build a bridge between the fields of
adaptive methods and memory-efficient adjoints. We aim at initiating a serious discussions between the two communities to pave the way for future collaborations. Such
a joint work is the only base to tackle the multiple challenges in creating an efficient
adaptive solver for this kind of optimal control problems.