GraFiDi swMATH ID: 37734 Software Authors: Christophe Besse, Romain Duboscq, Stefan Le Coz Description: Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library. Nonlinear quantum graphs are metric graphs equipped with a nonlinear Schr{ö}dinger equation. Whereas in the last ten years they have known considerable developments on the theoretical side, their study from the numerical point of view remains in its early stages. The goal of this paper is to present the Grafidi library, a Python library which has been developed with the numerical simulation of nonlinear Schr{ö}dinger equations on graphs in mind. We will show how, with the help of the Grafidi library, one can implement the popular normalized gradient flow and nonlinear conjugate gradient flow methods to compute ground states of a nonlinear quantum graph. We will also simulate the dynamics of the nonlinear Schr{ö}dinger equation with a Crank-Nicolson relaxation scheme and a Strang splitting scheme. Finally, in a series of numerical experiments on various types of graphs, we will compare the outcome of our numerical calculations for ground states with the existing theoretical results, thereby illustrating the versatility and efficiency of our implementations in the framework of the Grafidi library. Homepage: https://plmlab.math.cnrs.fr/cbesse/grafidi Source Code: https://github.com/SegFaultAX/graffiti Dependencies: Python Keywords: Analysis of PDEs; arXiv_math.AP; Numerical Analysis; arXiv_math.NA; Pattern Formation and Solitons; arXiv_nlin.PS; Python Related Software: Python; Matplotlib; NumPy; SciPy; NetworkX Cited in: 3 Documents Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year Numerical simulations on nonlinear quantum graphs with the GraFiDi library. Zbl 07525072Besse, Christophe; Duboscq, Romain; Le Coz, Stefan 2022 Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library Christophe Besse, Romain Duboscq, Stefan Le Coz 2021 Cited by 5 Authors 2 Besse, Christophe 2 Duboscq, Romain 2 Le Coz, Stefan 1 Dovetta, Simone 1 Tentarelli, Lorenzo Cited in 3 Serials 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SMAI Journal of Computational Mathematics 1 Annales Henri Lebesgue Cited in 4 Fields 3 Partial differential equations (35-XX) 2 Numerical analysis (65-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Quantum theory (81-XX) Citations by Year