ape_hbs1d

Julia code for the a posteriori estimation of Hermite-Gaussian basis set errors on a toy model in 1D. This code is used in our paper A posteriori error estimates for Schrödinger operators discretized with linear combinations of atomic orbitals available on arXiv.

Requirements

Julia 1.10.5 with the libraries:

• Test, BoundaryValueDiffEq for testing;
• LinearAlgebra, Polynomials, SpecialPolynomials, KrylovKit, ForwardDiff for the computations;
• JSON3 for saving results;
• PyPlot, LaTeXStrings for plotting results.

Install and test

In the root directory, open a Julia shell with julia --project and then run

using Pkg
Pkg.instantiate()
Pkg.test()

Usage

include("run.jl")

This program runs all calculations at once, stores results in json format and then generates figures in the img directory. Note that the out directory of the present git repo already contains all precalculated results. Running all the computations from scratch takes around 30 minutes.

To configure your own graphic display options used for plots, you can modify the common.jl file. Note that the scienceplots style used in our paper is not the default one in the code.

Authors

Mi-Song Dupuy (Sorbonne Université), Geneviève Dusson (Université de Franche Comté, CNRS), Ioanna-Maria Lygatsika (Sorbonne Université).

Credits

This code heavily uses modified routines originally found in the git repo gkemlin/1D_basis_optimization (https://github.com/gkemlin/1D_basis_optimization.git) from the author Gaspard Kemlin.

Support of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement EMC2 No 810367).