9 papers
Computing nonlinear Schrödinger equations with Hermite functions beyond harmonic traps
Valeria Banica, Georg Maierhofer, Katharina Schratz
Hermite basis functions are a powerful tool for the spatial discretisation of Schrödinger equations with harmonic potential. In this work, we show that their stability properties…
On scattering for NLS: rigidity properties and numerical simulations via the lens transform
Rémi Carles, Georg Maierhofer
We analyse the scattering operator associated with the defocusing nonlinear Schr{ö}dinger equation which captures the evolution of solutions over an infinite time-interval under t…
Symmetric resonance based integrators and forest formulae
Yvonne Alama Bronsard, Yvain Bruned, Georg Maierhofer +1
In the present work we introduce a unified framework that allows for the very first systematic construction of symmetric resonance-based integrators to approximate a wide class of…
G-Adaptivity: optimised graph-based mesh relocation for finite element methods
James Rowbottom, Georg Maierhofer, Teo Deveney +6
We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice…
A Wong--Zakai resonance-based integrator for nonlinear Schrödinger equation with white noise dispersion
Jianbo Cui, Georg Maierhofer
We introduce a novel approach to numerical approximation of nonlinear Schrödinger equation with white noise dispersion in the regime of low-regularity solutions. Approximating suc…
Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation
Erwan Faou, Georg Maierhofer, Katharina Schratz
The use of symplectic numerical schemes on Hamiltonian systems is widely known to lead to favorable long-time behaviour. While this phenomenon is thoroughly understood in the conte…