Invited Session Mon.1.MA 415

Monday, 10:30 - 12:00 h, Room: MA 415

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

Applications of PDE-constrained optimization


Chair: Michael Ulbrich



Monday, 10:30 - 10:55 h, Room: MA 415, Talk 1

Rene Pinnau
Exploiting model hierarchies in space mapping optimization


The solution of optimization problems in industry often requires information on the adjoint variables for very complex model equations. Typically, there is a whole hierarchy of models available which allows to balance the computational costs and the exactness of the model. We exploit these hierarchies in combination with space mapping techniques to speed up the convergence of optimization algorithms. The use of surrogate models yields finally a suboptimal design or control, which is typically near to the optimal design. In this talk we present three applications where this approach proved to be very successful. We will cover questions from semiconductor design, the control of particles in fluids and shape optimization for filters.



Monday, 11:00 - 11:25 h, Room: MA 415, Talk 2

Michael Ulbrich
An adaptive semismooth Newton-CG method for constrained parameter identification in seismic tomography

Coauthor: Christian Böhm


Seismic tomography infers the material properties of the Earth based on seismograms. This can be stated as an optimization problem that minimizes the misfit between observed and simulated seismograms.

We present a semismooth Newton-CG method for full-waveform seismic inversion with box constraints on the material parameters. It uses a Moreau-Yosida regularization and a trust-region globalization. The matrix-free implementation relies on adjoint-based gradient and Hessian-vector computations and a PCG method. The state equation is a coupled system of the elastic and acoustic wave equations. Our MPI-parallelized solver uses a high order continuous Galerkin method and an explicit Newmark time stepping scheme.
We address ill-posedness by a regularization and, in addition, by inverting sequentially for increasing frequencies. Thereby, the parameter grid is adaptively refined using goal-oriented a posteriori
error estimates.
Numerical results are shown for the application of our method to a dataset of marine geophysical exploration in the North Sea.
%This work is supported by the Munich Centre of Advanced Computing and the DFG.


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