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.