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arXiv · 2103.14588

A Spacetime Finite Elements Method to Solve the Dirac Equation

Rylee Sundermann·Hyun Lim·Jace Waybright·Jung-Han Kimn
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Abstract

In this work, a fully implicit numerical approach based on space-time finite element method is presented to solve the Dirac equation in 1 (space) + 1 (time), 2 + 1, and 3 + 1 dimensions. We utilize PETSc/Tao library to implement our linear system and for using Krylov subspace based solvers such as GMRES. We demonstrate our method by analyzing several different cases including plane wave solution, Zitterbewegung, and Klein paradox. Parallel performance of this implementation is also presented.

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Rylee Sundermann, Hyun Lim, Jace Waybright, Jung-Han Kimn. 2021-03-25. A Spacetime Finite Elements Method to Solve the Dirac Equation. https://arxiv.org/abs/2103.14588

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