Exploring Critical Collapse in the Semilinear Wave Equation using Space-Time Finite Elements
General Relativity and Quantum Cosmology
2020-05-19 v2 Numerical Analysis
Numerical Analysis
Computational Physics
Abstract
A fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) and 2 + 1 dimensions to explore critical collapse and search for self-similar solutions. Previous work studied this behavior by exploring the threshold of singularity formation using time marching finite difference techniques while this work introduces an adaptive time parallel numerical method to the problem. The semilinear wave equation with a term is examined in spherical symmetry. The impact of mesh refinement and the time additive Schwarz preconditioner in conjunction with Krylov Subspace Methods are examined.
Cite
@article{arxiv.1410.0708,
title = {Exploring Critical Collapse in the Semilinear Wave Equation using Space-Time Finite Elements},
author = {Hyun Lim and Matthew Anderson and Jung-Han Kimn},
journal= {arXiv preprint arXiv:1410.0708},
year = {2020}
}