20 citations · 24 across the 13 of their papers we have counts for
17 papers
Computing nonlinear Schrödinger equations with Hermite functions beyond harmonic traps
Valeria Banica, Georg Maierhofer, Katharina Schratz
Hermite basis functions are a classical tool for the spatial discretisation of Schrödinger equations with harmonic potential. In this work, we prove that their favourable stability…
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 th…
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…
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 such…
Explicit symmetric low-regularity integrators for the nonlinear Schrödinger equation
Yue Feng, Georg Maierhofer, Chushan Wang
The numerical approximation of low-regularity solutions to the nonlinear Schrödinger equation is notoriously difficult and even more so if structure-preserving schemes are sought.…
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 fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
Tianyu Jin, Georg Maierhofer, Katharina Schratz +1
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically…
An accelerated Levin-Clenshaw-Curtis method for the evaluation of highly oscillatory integrals
Arieh Iserles, Georg Maierhofer
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive i…
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…
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
Yue Feng, Georg Maierhofer, Katharina Schratz
We introduce a new non-resonant low-regularity integrator for the cubic nonlinear Schrödinger equation (NLSE) allowing for long-time error estimates which are optimal in the sense…
Numerical integration of Schrödinger maps via the Hasimoto transform
Valeria Banica, Georg Maierhofer, Katharina Schratz
We introduce a numerical approach to computing the Schrödinger map (SM) based on the Hasimoto transform which relates the SM flow to a cubic nonlinear Schrödinger (NLS) equation. I…
Bridging the gap: symplecticity and low regularity in Runge-Kutta resonance-based schemes
Georg Maierhofer, Katharina Schratz
Recent years have seen an increasing amount of research devoted to the development of so-called resonance-based methods for dispersive nonlinear partial differential equations. In…
An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions
Georg Maierhofer, Daan Huybrechs
In recent work (Maierhofer & Huybrechs, 2022, Adv. Comput. Math.), the authors showed that least-squares oversampling can improve the convergence properties of collocation methods…
Convergence analysis of oversampled collocation boundary element methods in 2D
Georg Maierhofer, Daan Huybrechs
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lower-dimen…
Learning the Sampling Pattern for MRI
Ferdia Sherry, Martin Benning, Juan Carlos De los Reyes +5
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly int…
Mirror, Mirror, on the Wall, Who's Got the Clearest Image of Them All? - A Tailored Approach to Single Image Reflection Removal
Daniel Heydecker, Georg Maierhofer, Angelica I. Aviles-Rivero +4
Removing reflection artefacts from a single image is a problem of both theoretical and practical interest, which still presents challenges because of the massively ill-posed nature…
Peekaboo - Where are the Objects? Structure Adjusting Superpixels
Georg Maierhofer, Daniel Heydecker, Angelica I. Aviles-Rivero +2
This paper addresses the search for a fast and meaningful image segmentation in the context of -means clustering. The proposed method builds on a widely-used local version of Ll…