Second order gauge invariant discretizations to the Schr "odinger and\n Pauli equations

2015/05/29 by Snorre H. Christiansen, Christiansen, Snorre Harald, Tore Gunnar Halvorsen +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #65N25 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1505.08040

openalex publication_date 2015/05/29 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

We introduce a numerical method, based on finite elements and lattice gauge\ntheory, to compute approximate solutions to Schr "odinger and Pauli equations.\nThe crucial geometric property of the method is discrete gauge invariance. The\nmain new achievement is second order convergence. This is proved by\ninterpreting the method as defined on gauge potential dependent finite element\nspaces and providing an analysis of such spaces in terms of gauge potential\ndependent norms on simplices of all dimensions.\n

Citations

• Stability of an upwind Petrov Galerkin discretization of convection\n diffusion equations

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• Interpretation of a Discrete de Rham method as a Finite Element System

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