assembleFermiMatrix swMATH ID: 10419 Software Authors: Clason, Christian; von Winckel, Gregory Description: A general spectral method for the numerical simulation of one-dimensional interacting fermions. This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows for an accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schr”odinger equation. Homepage: http://www.cpc.cs.qub.ac.uk/summaries/AEKO_v1_0.html Keywords: Schr”odinger equation; fermions; numerical solution; spectral method; { t MATLAB} Related Software: Matlab; QUCON; corr2el Cited in: 3 Publications Cited by 2 Authors 3 von Winckel, Gregory 2 Clason, Christian Cited in 1 Serial 2 Computer Physics Communications Cited in 5 Fields 3 Partial differential equations (35-XX) 2 Numerical analysis (65-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year