QGLAB: A MATLAB Package for Computations on Quantum Graphs
Roy Goodman, Gracie Conte, and Jeremy Marzuola. SIAM Journal on Scientific Computing, 2025.
Mar 31, 2025·
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0 min read
Roy Goodman
Gracie Conte
Jeremy Marzuola
Abstract
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 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.
Type
Publication
SIAM Journal on Scientific Computing, 47(2), B428–B453
Authors
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences
I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.
I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.
Authors
Senior Professional Staff I
I helped Jeremy Marzuola advise Gracie on her Ph.D. dissertation on numerical methods for quantum graphs at UNC-Chapel Hill.
