Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Analysis-Seminar Augsburg-München


Professor Dr. Katharina Schratz
Karlsruher Institut für Technologie

spricht am
Donnerstag, 17. Januar 2019
15:00 Uhr
Raum 2004 (L1)
über das Thema:

»Low regularity integrators for the Schrödinger equation«

A large toolbox of numerical schemes for the nonlinear Schrödinger equation has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full equation into a series of simpler subproblems (e.g., splitting methods). In many situations these classical schemes allow a precise and efficient approximation. This, however, drastically changes whenever "non-smooth" phenomena enter the scene such as for problems at low-regularity and high oscillations. Classical schemes fail to capture the oscillatory parts within the solution which leads to severe instabilities and loss of convergence. In this talk I present a new class of Fourier integrators for the nonlinear Schrödinger equation at low-regularity. The key idea in the construction of the new schemes is to tackle and hardwire the underlying structure of resonances into the numerical discretization.​ These terms are the cornerstones of theoretical analysis of the long time behaviour of differential equations and their numerical discretizations and offer the new schemes strong geometric structure at low regularity.


Hierzu ergeht herzliche Einladung.
Prof. Dr. Malte Peter

[Impressum]      [Datenschutz],     Fr 21-Dez-2018 09:56:38 MEZ