SFB 1173:  Wave phenomena: analysis and numerics

• Subject Area: Mathematics ; Geosciences ; Computer Science, Systems and Electrical Engineering ; Medicine ; Physics
• Term: since 2015
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

Waves fascinate scientists in general and mathematicians in particular. Two of our senses – seeing and hearing – are based on the propagation of light and sound waves, the human heartbeat is driven by depolarization waves, and most modern communication is based on electromagnetic waves. Waves are everywhere, and understanding their behavior leads us to understand nature. For mathematicians there is a second reason to study waves: The beauty and diversity of the related mathematics itself. Wave propagation is described by a number of intriguing equations with beautiful properties, and the mathematics of these equations has brought about many celebrated results. The goal of this Collaborative Research Centre (CRC) is to analytically understand, numerically simulate, and eventually manipulate wave propagation under realistic scenarios by intertwining analysis and numerics. Our research focuses on typical wave phenomena such as the emergence of standing and traveling waves or wave fronts, oscillations and resonances, dispersion, reflection, refraction and scattering of waves. The outstanding potential of our CRC lies in the close cooperation of specialists from analysis and numerics. Five project leaders from optics and photonics, biomedical engineering, and applied geophysics provide an interface to applications. This unique interdisciplinary research environment has already led to substantial results that have advanced the knowledge in the field. In addition, a wealth of exciting research questions has emerged which will be answered in the coming funding period. The integrated Research Training Group enables promising doctoral and postdoctoral researchers to benefit from this advantageous cooperation, and it fosters the early career of a new generation of mathematicians.

• DFG Programme: Collaborative Research Centres
• International Connection: Austria

Current projects

• A01 - Large signals in nonlinear fiber optics (Project Heads Hundertmark, Dirk ;  Kunstmann, Peer Christian ;  Weis, Lutz )
• A02 - Numerical methods for wave problems with nontrivial boundary conditions and nonlocal material laws (Project Heads Hochbruck, Marlis ;  Lubich, Christian )
• A03 - Adaptive implicit space-time discretization for wave equations (Project Heads Dörfler, Willy ;  Wieners, Christian )
• A04 - Time integration of Maxwell and wave-type equations (Project Heads Hochbruck, Marlis ;  Jahnke, Tobias ;  Schnaubelt, Roland )
• A05 - Qualitative behavior of nonlinear Maxwell equations (Project Heads Schnaubelt, Roland ;  Weis, Lutz )
• A06 - Localized solutions for nonlinear Maxwell and wave-type equations (Project Heads Plum, Michael ;  Reichel, Wolfgang )
• A07 - Numerical methods for highly oscillatory problems (Project Heads Hochbruck, Marlis ;  Jahnke, Tobias ;  Lubich, Christian )
• A11 - Electromagnetic fields interacting with quantum matter (Project Heads Anapolitanos, Ioannis ;  Hundertmark, Dirk )
• A12 - Dynamics of the Gross-Pitaevskii equation and related dispersive equations (Project Heads Liao, Xian ;  Schneider, Guido )
• A13 - Dispersive estimates for wave-type equations with low regularity coefficients (Project Heads Frey, Dorothee ;  Schnaubelt, Roland )
• A14 - Nonlinear stability of periodic waves in dissipative-dispersive systems (Project Heads Frey, Dorothee ;  de Rijk, Björn )
• B03 - Frequency combs (Project Heads Jahnke, Tobias ;  Koos, Christian ;  Reichel, Wolfgang )
• B04 - Homogenization of time-varying metamaterials (Project Heads Plum, Michael ;  Rockstuhl, Carsten ;  Verfürth, Barbara )
• B07 - Dynamics of cardiac electrophysiological depolarization waves (Project Heads Dössel, Ph.D., Olaf ;  Jahnke, Tobias ;  Loewe, Axel ;  Wieners, Christian )
• B08 - Theory and numerics of the coupled Maxwell-Landau-Lifshitz-Gilbert equations (Project Heads Dörfler, Willy ;  Feischl, Michael ;  Fernandez-Corbaton, Ph.D., Ivan )
• B09 - Dynamical low-rank approximation for the simulation of radiation heat waves (Project Heads Frank, Martin ;  Lubich, Christian )
• B10 - Numerical methods for nonlinear optics in plasmonic nanogaps (Project Heads Dörich, Benjamin ;  Hochbruck, Marlis )
• C01 - Local inversion for linear seismic imaging (Project Heads Kunstmann, Peer Christian ;  Rieder, Andreas )
• C02 - Seismic imaging by full waveform inversion (Project Heads Bohlen, Thomas ;  Griesmaier, Roland ;  Kirsch, Andreas ;  Rieder, Andreas ;  Wieners, Christian )
• C05 - Optimal design of chiral structures (Project Heads Arens, Tilo ;  Fernandez-Corbaton, Ph.D., Ivan ;  Griesmaier, Roland ;  Rockstuhl, Carsten )
• C06 - Uncertainty principles for inverse source and inverse scattering problems (Project Heads Arens, Tilo ;  Griesmaier, Roland )
• MGKIRTG - Integrated Research Training Group (Project Heads Dörfler, Willy ;  Griesmaier, Roland ;  Schnaubelt, Roland )
• Z - Central Tasks (Project Heads Hochbruck, Marlis ;  Reichel, Wolfgang )

Completed projects

• A08 - Failure of amplitude equations (Project Head Schneider, Guido )
• A09 - Spectral methods for dispersive equations (Project Heads Kunstmann, Peer Christian ;  Weis, Lutz )
• A10 - Standing and moving pulses in periodic media (Project Heads Reichel, Wolfgang ;  Schneider, Guido )
• B01 - Klein-Gordon-Zakharov systems in high-frequency regimes (Project Heads Schneider, Guido ;  Schratz, Katharina )
• B02 - Dispersion management (Project Heads Hundertmark, Dirk ;  Schnaubelt, Roland )
• B05 - Geometric wave equations (Project Heads Lamm, Tobias ;  Schnaubelt, Roland ;  Schörkhuber, Birgit )
• B06 - Stability of patterns for hyperbolic-parabolic equations (Project Heads Plum, Michael ;  Rottmann-Matthes, Jens )
• C04 - Modeling, design and optimization of 3D waveguides (Project Heads Dörfler, Willy ;  Koos, Christian ;  Reichel, Wolfgang ;  Rockstuhl, Carsten )

• Applicant Institution: Karlsruher Institut für Technologie
• Participating University: Eberhard Karls Universität Tübingen; Rheinische Friedrich-Wilhelms-Universität Bonn; Technische Universität Wien; Universität Stuttgart
• Partner Organisation: Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
• Spokesperson: Professorin Dr. Marlis Hochbruck