40 citations · 93 across the 16 of their papers we have counts for
20 papers
Construction of adaptive exponential multi-operator splitting methods
Othmar Koch, Koray Acar, Winfried Auzinger +3
We construct splitting methods suitable for the solution of the equations of magnetohydrodynamics (MHD). Due to the physical significance of the involved operators, splittings into…
Efficient Adaptive Computation of the Dynamics of Mott Transistors
Winfried Auzinger, Lukas Einramhof, Karsten Held +4
We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice o…
Efficient Magnus-type integrators for solar energy conversion in Hubbard models
Winfried Auzinger, Juliette Dubois, Karsten Held +7
Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields…
Chaos-induced depletion of a Bose-Einstein condensate
Ralf Wanzenböck, Stefan Donsa, Harald Hofstätter +3
The mean-field limit of a bosonic quantum many-body system is described by (mostly) non-linear equations of motion which may exhibit chaos very much in the spirit of classical part…
An Algorithm for Computing Coefficients of Words in Expressions Involving Exponentials and its Application to the Construction of Exponential Integrators
Harald Hofstätter, Winfried Auzinger, Othmar Koch
This paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type me…
Adaptive Exponential Integrators for MCTDHF
Winfried Auzinger, Alexander Grosz, Harald Hofstätter +1
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the…
Non-existence of generalized splitting methods with positive coefficients of order higher than four
Winfried Auzinger, Harald Hofstätter, Othmar Koch
We prove that generalized exponential splitting methods making explicit use of commutators of the vector fields are limited to order four when only real coefficients are admitted.…
Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime
Winfried Auzinger, Harald Hofstätter, Othmar Koch +2
Time dependent Schrödinger equations with conservative force field U commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the…
Computable upper error bounds for Krylov approximations to matrix exponentials and associated -functions
Tobias Jawecki, Winfried Auzinger, Othmar Koch
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approxi…
Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations
Winfried Auzinger, Harald Hofstätter, Othmar Koch
Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that…
Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four
Harald Hofstätter, Othmar Koch
We consider commutator-free exponential integrators as put forward in [Alverman, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems.…
Long-time expansion of a Bose-Einstein condensate: Can Anderson localization be observed?
Stefan Donsa, Harald Hofstätter, Othmar Koch +2
We numerically explore the long-time expansion of a one-dimensional Bose-Einstein condensate in a disorder potential employing the Gross-Pitaevskii equation. The goal is to search…
Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
Winfried Auzinger, Harald Hofstaetter, Othmar Koch
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of suc…
Setup of Order Conditions for Splitting Methods
Winfried Auzinger, Wolfgang Herfort, Harald Hofstätter +1
This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the…
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
Winfried Auzinger, Thomas Kassebacher, Othmar Koch +1
The error behavior of exponential operator splitting methods for nonlinear Schr{ö}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods,…
Pixel matrices: An elementary technique for solving nonlinear systems
David I. Spivak
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuo…
The BCH-Formula and Order Conditions for Splitting Methods
Winfried Auzinger, Wolfgang Herfort, Othmar Koch +1
As an application of the BCH-formula, order conditions for splitting schemes are derived. The same conditions can be obtained by using non-commutative power series techniques and i…
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
Winfried Auzinger, Harald Hofstätter, David Ketcheson +1
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular sche…
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
Winfried Auzinger, Othmar Koch, Michael Quell
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under perio…
Total-Variation-Diminishing Implicit-Explicit Runge-Kutta Methods for the Simulation of Double-Diffusive Convection in Astrophysics
Friedrich Kupka, Natalie Happenhofer, Inmaculada Higueras +1
We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit-explicit Runge-Kutta methods for the time integration of the equatio…