Parallel Implementation of the Dirac Equation

The objective of this research is to acquire an understanding of the numerical components of an effective Dirac equation simulation with hopes that similar procedures can be implemented for other related differential equation models from physical phenomena. The Dirac equation is a relativistic wave equation that describes spin- \textonehalf particles and is related to other equations such as the Klein-Gordon equation, where it is the square root of the Klein-Gordon. Parallel implementations of the Dirac equation and corresponding numerical performances are studied with various numerical options. The C language and the Portable, Extensible Toolkit for Scientific Computation (PETSc) libraries, such as Krylov Subspace Methods (KSP) and Preconditioners (PC) are the main tools used in this research. The effectiveness of our procedure for the parallel execution of the Dirac matrix will be analyzed.