Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.00561 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909379543957504 |
|---|---|
| author | Goodman, Roy H. Conte, Grace Marzuola, Jeremy L. |
| author_facet | Goodman, Roy H. Conte, Grace Marzuola, Jeremy L. |
| contents | We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations) and more. It overcomes the major challenge of discretizing quantum graphs -- the enforcement of vertex conditions -- using non-square differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00561 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | QGLAB: A MATLAB Package for Computations on Quantum Graphs Goodman, Roy H. Conte, Grace Marzuola, Jeremy L. Numerical Analysis Analysis of PDEs 65N35 We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations) and more. It overcomes the major challenge of discretizing quantum graphs -- the enforcement of vertex conditions -- using non-square differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class. |
| title | QGLAB: A MATLAB Package for Computations on Quantum Graphs |
| topic | Numerical Analysis Analysis of PDEs 65N35 |
| url | https://arxiv.org/abs/2401.00561 |