Application of the Space-Time Finite Element Method and High-Performance Computing to Physics Field Theory — 38p — Samara Overvaag, Jax Wysong, with Dr. Hyun Lim (LANL) and Dr. Jung-Han Kimn (SDSU)

The objective of this study is to investigate the dynamic stability of ghost-ridden systems existing in field theory using numerical methods and high-performance computing. Systems that contain the Ostragradsky Ghost have traditionally been considered physically unstable due to reaching an arbitrarily large value within a finite time. This ghost originates due to the system’s oppositely signed kinetic terms and time derivatives higher than second order. However, recent studies have shown that ghost systems can have stable evolution for certain scenarios. To study this phenomenon, the fully implicit Space-Time Finite Element Method is implemented to our wave-like ghost system, and a simulation is created via our C code and PETSc (the Portable, Extensible Toolkit for Scientific Computation), developed by Argonne National Laboratory. This numerical method treats time and space simultaneously. However, this approach is computationally expensive, hence the need for HPC and PETSc. Previous work has shown stable evolution in lower dimensional cases, but this work has not been extended to higher dimensions. With this method, a numerical approximation for our system is simulated in d+1 dimensions, where d represents the number of spatial dimensions plus one temporal dimension. A numerical model in the 1+1 case is in progress, but future work will be extended to the 2+1 and 3+1 cases. Further investigation of the system’s nonlinear potential term may be included. Simulation in 3+1 dimensions will allow us to further investigate the complexity of the system and its application to the real world.

South Dakota State University
Dr. Hyun Lim (LANL) and Dr. Jung-Han Kimn (SDSU)