A Spectral Algorithm for the Time-Dependent Kohn--Sham Equations: Accurately Treating External Potentials Based on Frozen Gaussian Approximations

DOI10.1137/19M1245104zbMath1448.65181MaRDI QIDQ5112637

Ricardo Delgadillo, Di Liu

Publication date: 2 June 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

spectral methodtime dependent density functional theoryscientific computingfrozen Gaussian approximationquantum chemisty

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Computational density functional analysis in statistical mechanics (82M36)

Cites Work

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• Frozen Gaussian approximation for high frequency wave propagation
• A mathematical justification for the Herman-Kluk propagator
• Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations
• A new method of computation of wave fields using Gaussian beams
• Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
• Effective dynamics for Bloch electrons: Peierls substitution and beyond
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schrödinger equation in the semiclassical regime
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Multiscale modeling and computation of optically manipulated nano devices
• A Multiscale Method for Optical Responses of Nanostructures
• Convergence of frozen Gaussian approximation for high-frequency wave propagation
• Frozen Gaussian Approximation for General Linear Strictly Hyperbolic Systems: Formulation and Eulerian Methods
• A Wigner-Measure Analysis of the Dufort--Frankel Scheme for the Schrödinger Equation
• Motion of Electrons in Adiabatically Perturbed Periodic Structures

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