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Research Programme

Project Area A • Mathematical Foundations

Mathematical foundations deals with general and fundamental questions concerning the analysis and numerics of wave phenomena, often by analyzing characteristic examples.

Projects

A1 Random signals in nonlinear fiber optics (Hundertmark, Kunstmann, Weis)

A2 Numerical methods for wave problems with nontrivial boundary conditions (Hochbruck, Lubich)

A3 Adaptive implicit space-time discretization for wave equations (Dörfler, Wieners)

A4 Time integration of Maxwell equations (Hochbruck, Jahnke, Schnaubelt)

A5 Qualitative behavior of nonlinear Maxwell equations (Schnaubelt, Weis)

A6 Time-periodic solutions for nonlinear Maxwell equations (Plum, Reichel)

A7 Numerical methods for highly oscillatory problems (Hochbruck, Jahnke, Lubich)

A8 Failure of amplitude equations (Schneider)

A9 Spectral methods for dispersive equations (Kunstmann, Weis)

Project Area B • Dynamical Models

Dynamical models investigates in detail properties of wave-type solutions to specific models which are motivated by applications.

Projects

B1 Klein-Gordon-Zakharov systems in high-frequency regimes (Schneider, Schratz)

B2 Dispersion Management (Hundertmark, Schnaubelt)

B3 Frequency combs (Jahnke, Koos, Reichel)

B4 Effective characterization of optical metamaterials beyond a local response (Plum, Rockstuhl)

B5 Biharmonic wave maps (Lamm, Schnaubelt)

B6 Stability of patterns for hyperbolic-parabolic equations (Plum, Rottmann-Matthes)

B7 Dynamics of electro-cardiac depolarization waves (Dössel, Wieners)

Project Area C • Identification and Design

Identification and design groups together projects which address parameter identification tasks (considered as inverse problems) related to different types of wave equations or which seek optimal material layouts for wave propagation.

Projects

C1 Local inversion for linear seismic imaging (Kunstmann, Rieder)

C2 Seismic imaging by full waveform inversion (Bohlen, Kirsch, Rieder, Wieners)

C4 Modeling, design and optimization of 3D waveguides (Dörfler, Koos, Reichel, Rockstuhl)

Associated projects

AP1 Optimal Design of Chiral Structures (Arens, Hettlich, Kirsch, Rockstuhl)

AP2 Nonlinear Helmholtz equations and systems (Mandel)

AP3 Numerical multiscale methods (Gallistl)