Mathematical theory and numerical methods for Bose-Einstein condensation
In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …
Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations
In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …
Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
V Gradinaru, GA Hagedorn - Numerische Mathematik, 2014 - Springer
We propose a new algorithm for solving the semiclassical time-dependent Schrödinger
equation. The algorithm is based on semiclassical wavepackets. The focus of the analysis is …
equation. The algorithm is based on semiclassical wavepackets. The focus of the analysis is …
[HTML][HTML] Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I: The linear case
W Auzinger, O Koch, M Thalhammer - Journal of Computational and …, 2012 - Elsevier
We introduce a defect correction principle for exponential operator splitting methods applied
to time-dependent linear Schrödinger equations and construct a posteriori local error …
to time-dependent linear Schrödinger equations and construct a posteriori local error …
A posteriori error control and adaptivity for Crank–Nicolson finite element approximations for the linear Schrödinger equation
T Katsaounis, I Kyza - Numerische Mathematik, 2015 - Springer
We derive optimal order a posteriori error estimates for fully discrete approximations of linear
Schrödinger-type equations, in the L^ ∞ (L^ 2) L∞(L 2)-norm. For the discretization in time …
Schrödinger-type equations, in the L^ ∞ (L^ 2) L∞(L 2)-norm. For the discretization in time …
A Posteriori Error Analysis for Evolution Nonlinear Schrodinger Equations Up to the Critical Exponent
T Katsaounis, I Kyza - SIAM Journal on Numerical Analysis, 2018 - SIAM
We provide a posteriori error estimates in the L^∞(0,T;L^2(Ω))-norm for relaxation time
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime
W Wang, J Tang - Applied Numerical Mathematics, 2020 - Elsevier
The design of efficient numerical methods, which produce an accurate approximation of the
solutions, for solving time-dependent Schrödinger equation in the semiclassical regime …
solutions, for solving time-dependent Schrödinger equation in the semiclassical regime …
[PDF][PDF] A Time–Splitting for the Semiclassical Schrödinger Equation
V Gradinaru, GA Hagedorn - SAM Research Report, 2012 - sam.math.ethz.ch
We propose a new algorithm for solving the semiclassical time–dependent Schrödinger
equation. The algorithm is based on semiclassical wavepackets. Convergence is proved to …
equation. The algorithm is based on semiclassical wavepackets. Convergence is proved to …