A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices - Richters, Dorothee; Lass, Michael; Walther, Andrea; Plessl, Christian; Kühne, Thomas (Communications in Computational Physics)
We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter q always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.

Arbitrary sensitivity for inverse problems in piezoelectricity - Jurgelucks, Benjamin; Schulze, Veronika; Feldmann, Nadine; Claes, Leander

Vollständige Charakterisierung von piezoelektrischen Scheiben mit Ringelektroden - Feldmann, Nadine; Jurgelucks, Benjamin; Claes, Leander; Henning, Bernd

Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation - Jurgelucks, Benjamin; Claes, Leander; Walther, Andrea; Henning, Bernd (Optimization Methods and Software)

Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity - Jurgelucks, Benjamin; Feldmann, Nadine; Claes, Leander; Henning, Bernd; Walther, Andrea (Proceedings of Meetings on Acoustics)

Modeling and simulation of metallic, particle-damped spheres for lightweight materials - Steinle, Tobias
Lightweight materials play an ever growing role in today's world. Saving on the mass of a machine will usually translate into a lower energy consumption. However, lightweight applications are prone to develop performance problems due to vibration induced by the operation of the machine. The Fraunhofer Institute for Manufacturing Technology and Advanced Materials in Dresden conducts research into the damping properties of composite materials. They are experimenting with hollow, particle filled spheres embedded in the lightweight material. Such a system is the technical motivation of this thesis. Ultimately, a numerical experiment to derive the coefficient of restitution is required. The simulation developed in this thesis is based on a discrete element method to track the individual particle and sphere trajectories. Based on a potential based approach for the particle interactions deployed in molecular dynamics, the behavior of the particles can be controlled effectively. The simulated volume is using reflecting boundaries and encloses the hollow sphere. In this work, a highly flexible memory structure was used with a linked cell approach to cope with the highly flexible mass of particles. This allows for a linear complexity of the method in regard to the particle number by reducing the computational overhead of the interaction computation. Multiple numerical experiments show the great effect the particles have on the damping behavior of the system.

Increasing the Sensitivity of Impedance with Respect to Material Parameters of Triple-Ring Electrode Piezoelectric Transducers using Algorithmic Differentiation - Jurgelucks, Benjamin; Claes, Leander

Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation - Jurgelucks, Benjamin; Claes, Leander (AD2016 The 7th International Conference on Algorithmic Differentiation)

Simulative Ultraschall-Untersuchung von Pitch-Catch-Messanordnungen für große zylindrische Stahl-Prüflinge und gradientenbasierte Bildgebung - Hegler, Sebastian; Statz, Christoph; Mütze, Marco; Mooshofer, Hubert; Goldammer, Matthias; Fendt, Karl; Schwarzer, Stefan; Feldhoff, Kim; Flehmig, Martin; Markwardt, Ulf; E. Nagel, Wolfgang; Schütte, Maria; et al. (tm - Technisches Messen)
Große zylindrische Stahlprüflinge werden mittels der Methode der finiten Differenzen im Zeitbereich (engl. finite differences in time domain, FDTD) simulativ untersucht. Dabei werden Pitch-Catch-Messanordnungen verwendet. Es werden zwei Bildgebungsansätze vorgestellt: ersterer basiert auf dem Imaging Principle nach Claerbout, letzterer basiert auf gradientenbasierter Optimierung eines Zielfunktionals.

Numerical Simulation of the Damping Behavior of Particle-Filled Hollow Spheres - Steinle, Tobias; Vrabec, Jadran; Walther, Andrea (Proc. Modeling, Simulation and Optimization of Complex Processes (HPSC))
In light of an increasing awareness of environmental challenges, extensive research is underway to develop new light-weight materials. A problem arising with these materials is their increased response to vibration. This can be solved using a new composite material that contains embedded hollow spheres that are partially filled with particles. Progress on the adaptation of molecular dynamics towards a particle-based numerical simulation of this material is reported. This includes the treatment of specific boundary conditions and the adaption of the force computation. First results are presented that showcase the damping properties of such particle-filled spheres in a bouncing experiment.