PDE Constrained Optimization Based on Adaptive Model Reduction with Applications to Shape Optimization of Microfluidic Biochips and to Blood Flow in Microchannels

This project within the area of PDE constrained optimization focuses on the development, analysis and implementation of optimization algorithms that combine ecient solution techniques from the numerics of PDEs, namely multilevel iterative solvers, and state-of-the-art optimization approaches, the so-called `all-at-once optimization methods. It is well-known that multilevel techniques provide ecient PDE solvers of optimal algorithmic complexity. On the other hand, optimization methods within the all-at-once approach, such as sequential quadratic programming (SQP) methods and primal-dual Newton interior-point methods, have the appealing feature that in contrast to more traditional approaches, the numerical solution of the state equations is an integral part of the optimization routine. This is realized by incorporating the PDEs as constraints into the optimization routine. The developed PDE constrained optimization algorithms will be applied to the optimal design of micro uidic biochips with emphasis on the optimization of the geometry of the devices (shape optimization) in order to achieve an optimal operational behavior. Here, the state equations consist of a system of partial dierential equations describing the transport of micro uids driven by piezoelectrically agitated surface acoustic waves.

DFG-Verfahren Schwerpunktprogramme

Teilprojekt zu SPP 1253:  Optimierung mit partiellen Differentialgleichungen

Ehemaliger Antragsteller Professor Dr. Achim Wixforth, bis 7/2009