A Spacetime Finite Elements Method to Solve the Dirac Equation

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.

References in corpus (5)

• Chiral tunneling and the Klein paradox in graphene
• Accelerating the Fourier split operator method via graphics processing units
• Quark-antiquark production from classical fields in heavy ion collisions: 1+1 dimensions
• A Numerical Approach to Space-Time Finite Elements for the Wave Equation
• A Study of Space-Time Discretizations for the Dirac Equation