Thomas Richter
Department Mathematik, Universität Erlangen-Nürnberg

Goal-oriented adaptivity and optimization for fluid-structure interactions
In this talk, we present a sensitivity based framework for adaptive finite element simulations and optimization of fluid-structure interactions.

The talk will be split into three parts. First, we will introduce basic concepts of sensitivity analysis for error estimation, mesh adaptivity and gradient based optimization tools. The focus will be on easy and efficient applicability for such complex problems as fluid-structure interactions. In particular, a residual based error estimator will be presented, that does not require jump-terms or evaluation of strong operators involving second derivatives. This will be a substantial improvement over standard estimators.

Second, we will derive dual formulations for fluid-structure interactions. With the help of linearized adjoint problems, we will be able to compute sensitivities with respect to technical goal values, such as drag- or lift-coefficients, stress measures or flow rates. Finally, we will use these adjoint solutions to derive reliable error estimates controlling mesh adaptivity and to guide simple gradient based optimization schemes.