5 citations · 9 across the 10 of their papers we have counts for
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Third order, uniform in low to high oscillatory coefficients, exponential integrators for Klein-Gordon equations
Karolina Kropielnicka, Karolina Lademann
Allowing for space- and time-dependence of mass in Klein--Gordon equations resolves the problem of negative probability density and of violation of Lorenz covariance of interaction…
Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
Karolina Kropielnicka, Karolina Lademann, Katharina Schratz
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range…
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…
Solving the linear semiclassical Schrödinger equation on the real line
Arieh Iserles, Karolina Kropielnicka, Katharina Schratz +1
The numerical solution of a linear Schrödinger equation in the semiclassical regime is very well understood in a torus . A raft of modern computational methods are pr…
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…
The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures
José A. Carrillo, Piotr Gwiazda, Karolina Kropielnicka +1
The Escalator Boxcar Train (EBT) method is a well known and widely used numerical method for one-dimensional structured population models of McKendrick-von Foerster type. Recently…
Compact schemes for laser-matter interaction in Schrödinger equation
Arieh Iserles, Karolina Kropielnicka, Pranav Singh
Numerical solutions for laser-matter interaction in Schrödinger equation has many applications in theoretical chemistry, quantum physics and condensed matter physics. In this paper…
Magnus-Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential
Arieh Iserles, Karolina Kropielnicka, Pranav Singh
The computation of the Schrödinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications ofte…
Magnus-Zassenhaus methods for the semiclassical Schrödinger equation with oscillatory time-dependent potentials
Arieh Iserles, Karolina Kropielnicka, Pranav Singh
Schrödinger equations with time-dependent potentials are of central importance in quantum physics and theoretical chemistry, where they aid in the simulation and design of systems…
Efficient methods for time-dependence in semiclassical Schrödinger equations
Philipp Bader, Arieh Iserles, Karolina Kropielnicka +1
We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schrödinger equation subject with explicitly time-dependent potentials. The method is…