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.
翻译:在这项工作中,提出了基于时空有限要素法的完全隐含的数字方法,以解决1(空间)+1(时间)、2+1和3+1维的Dirac方程式。我们利用PETSC/Tao图书馆实施我们的线性系统,并使用Krylov 子空基解决器,如GMRES。我们通过分析包括飞机波溶液、Zitterbegung和Klein悖论在内的若干不同案例来展示我们的方法。还介绍了这一执行的平行绩效。