Propagators for the time-dependent Kohn–Sham equations: Multistep, Runge–Kutta, exponential Runge–Kutta, and commutator free Magnus methods
A Gomez Pueyo, MAL Marques, A Rubio… - Journal of chemical …, 2018 - ACS Publications
We examine various integration schemes for the time-dependent Kohn–Sham equations.
Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear …
Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear …
All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework
Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to
model quantum dynamics by real-time propagation without the linear response …
model quantum dynamics by real-time propagation without the linear response …
A μ-mode integrator for solving evolution equations in Kronecker form
In this paper, we propose a μ-mode integrator for computing the solution of stiff evolution
equations. The integrator is based on a d-dimensional splitting approach and uses exact …
equations. The integrator is based on a d-dimensional splitting approach and uses exact …
Robust quantum optimal control with trajectory optimization
The ability to engineer high-fidelity gates on quantum processors in the presence of
systematic errors remains the primary barrier to achieving quantum advantage. Quantum …
systematic errors remains the primary barrier to achieving quantum advantage. Quantum …
Fast, high precision dynamics in quantum optimal control theory
M Dalgaard, F Motzoi - Journal of Physics B: Atomic, Molecular …, 2022 - iopscience.iop.org
Quantum optimal control theory is becoming increasingly crucial as quantum devices
become more precise, but the need to quickly optimize these systems classically remains a …
become more precise, but the need to quickly optimize these systems classically remains a …
Exponential integrators for resistive magnetohydrodynamics: Matrix-free Leja interpolation and efficient adaptive time stepping
PJ Deka, L Einkemmer - The Astrophysical Journal Supplement …, 2022 - iopscience.iop.org
We propose a novel algorithm for the temporal integration of the resistive
magnetohydrodynamics (MHD) equations. The approach is based on exponential …
magnetohydrodynamics (MHD) equations. The approach is based on exponential …
Challenges in computing matrix functions
This manuscript summarizes the outcome of the focus groups at" The f (A) bulous workshop
on matrix functions and exponential integrators", held at the Max Planck Institute for …
on matrix functions and exponential integrators", held at the Max Planck Institute for …
[HTML][HTML] An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs
M Caliari, L Einkemmer, A Moriggl… - Journal of Computational …, 2021 - Elsevier
Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …
for the time integration of linear partial differential equations with imaginary eigenvalues …
Modelling ground‐penetrating radar wave propagation using graphics processor unit parallel implementation of the symplectic Euler method
H Fang, J Lei, J Zhang, J An, F Wang - Near Surface Geophysics, 2019 - earthdoc.org
Inversion of ground‐penetrating radar signals requires accurate and efficient forward
modelling. The symplectic Euler method promises good results when simulating ground …
modelling. The symplectic Euler method promises good results when simulating ground …
Exponential propagators for the Schrödinger equation with a time-dependent potential
We consider the numerical integration of the Schrödinger equation with a time-dependent
Hamiltonian given as the sum of the kinetic energy and a time-dependent potential …
Hamiltonian given as the sum of the kinetic energy and a time-dependent potential …