Invited Session Thu.3.H 0111

Thursday, 15:15 - 16:45 h, Room: H 0111

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Adjoint-based methods and algorithmic differentiation in large scale optimization


Chair: Andreas Griewank



Thursday, 15:15 - 15:40 h, Room: H 0111, Talk 1

Nikolai Strogies
A time-labeling approach for open pit mine planning

Coauthor: Andreas Griewank


For open pit mine planning, integer or mixed integer programming approaches are well understood and investigated. In this talk a function space formulation will be presented. So called time labeling functions (TLF) assign the time of excavation to each spatial coordinate. An additional pointwise constraint replaces the predecessor relationship and ensures the physical stability of the resulting sequence of profiles. The capacity of the mine is expressed via a density function and is allowed to vary over time. In all points this approach allows a significantly more detailed modeling of the mining operation than the usual block model. We formulate the dynamic open pit mine planning problem in a suitable function space and present a stationarity condition. Moreover we discuss properties of the TLF.



Thursday, 15:45 - 16:10 h, Room: H 0111, Talk 2

Emre Ă–zkaya
Automatic differentiation of an unsteady RANS solver for optimal active flow control

Coauthors: Nicolas Gauger, Anil Nemili


We present the development of a discrete adjoint solver for the
optimal active flow control of viscous flows, governed by the unsteady
incompressible Reynolds-averaged Navier Stokes (RANS) equations. The
discrete adjoint solver is developed by applying automatic differentiation
(AD) in reverse mode to the underlying primal flow solver. Employing AD
for discrete adjoint code generation results in a robust adjoint solver,
which gives accurate sensitivities for turbulent flows with separation. If
AD is applied in a black-box fashion then the resulting adjoint code will
have prohibitively expensive memeory requirements. Further, a significant
amount of CPU time is spent on storing and retrieving the data from the
memory. In order to reduce the excessive storage and CPU costs, various
techniques such as checkpointing and reverse accumulation are employed.
Numerical results are presented for the test cases of optimal active flow
control around a rotating cylinder and a NACA4412 airfoil.



Thursday, 16:15 - 16:40 h, Room: H 0111, Talk 3

Stephan Schmidt
Large scale shape optimization


Shape optimization problems are a special sub-class of PDE constrained optimization problems. As such, they pose additional difficulties stemming from the need to compute derivatives with respect to geometry changes or variations of the domain itself. In addition to the adjoint methodology, this talk also considers how these derivatives with respect to the domain can be computed very efficiently. To this end, shape calculus is considered. The Hadamard theorem states that given sufficient regularity, the directional derivative of a shape optimization problem can be computed as a boundary scalar product with the normal component of the perturbation field and the shape gradient. Thus, knowledge of this shape gradient can be used to formulate an extremely fast optimization scheme, as tangential calculus can be used to derive gradient formulations that exist on the boundary of the domain only, thereby circumventing the need to know sensitivities of the mesh deformation inside the domain. Furthermore, approximate Newton methods can be employed in order to construct higher order optimization schemes. The Newton-type shape update can also be used to incorporate a desired boundary regularit


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