Unter dem Titel "Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation" veröffentlichten Benjamin Jurgelucks und Andrea Walther (beide Fachgebiet Mathematik und ihre Anwendungen) gemeinsam mit Leander Claes und Bernd Henning aktuelle Forschungsergebnisse im Journal Optimization Methods and Software. In dem von der DFG geförderten Forschungsprojekt (FKZ: HE 2897/8-1 sowie WA 1607/14-1) erarbeiten beide Fachgebiete gemeinsam Methoden zur vollständigen Bestimmung von Materialparametersätzen piezokeramischer Materialien anhand einzelner Probekörper.
Data of material properties given by manufacturers of piezoelectric ceramics is often flawed due to, for example, slightly different manufacturing conditions for each production batch. Hence, the need for more reliable data arises. Recently published material parameter estimation methods are based on the solution of an inverse problem fitting impedance measurements of the piezoelectric ceramic to simulations by varying the material parameters in the simulation. However, the sensitivity of impedance with respect to some material parameters is close to zero and thus alternative measurement quantities which require expensive and error-prone measurement devices would be required. In order to assist in experiment design, the simulation software must be able to compute accurate sensitivity information. We applied the algorithmic differentiation (AD) package ADOL-C to the C++-based sophisticated simulation software CFS++ and thus are now able to compute the sensitivity of impedance with respect to material parameters without the use of finite differences. As these sensitivities depend on the geometry of the piezoelectric ceramic and the electrodes, we then use these sensitivities as a cost function for maximization. We compare the results of optimization with results of optimization previously obtained using a finite difference scheme. We document implementation issues and limits for integrating ADOL-C into CFS++. Nevertheless, we show the now much improved results of optimization using AD instead of finite differences and its potential for further optimization.