Testing a new mesh refinement code in the evolution of a spherically symmetric Klein-Gordon field

TL;DR

This paper introduces a new adaptive mesh refinement code for simulating the evolution of a spherically symmetric Klein-Gordon field, demonstrating improved accuracy and speed in numerical evolution and boundary management.

Contribution

The paper presents a novel AMR code with fourth order discretization and compactification, enhancing simulation accuracy and efficiency for Klein-Gordon fields.

Findings

Mesh refinement maintains precision longer in the central region.

The AMR algorithm is two orders of magnitude faster with 10 refinement levels.

Boundary regions are effectively managed for different AMR parameters.

Abstract

Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system is non-interacting thus the initial disturbance is entirely radiated away. The main aim is to simulate its propagation until it vanishes near scri^+. By numerical investigations of the violation of the energy balance relations, the space-time boundaries of ``well-behaving'' regions are determined for different values of the AMR parameters. An important result is that mesh refinement maintains precision in the central region for longer time even if the mesh is only refined outside of this region. The speed of the algorithm was also tested, in case of 10 refinement levels the algorithm was two orders of magnitude faster than the extrapolated time of the corresponding unigrid run.