Adaptive Mesh Refinement for Characteristic Codes

TL;DR

This paper presents an adaptive mesh refinement algorithm designed for characteristic coordinate systems, demonstrated on Einstein-Klein-Gordon equations, with potential for higher dimensions and parallelization.

Contribution

The paper introduces a novel adaptive mesh refinement algorithm specifically for characteristic codes in wave-like equations, applicable to higher dimensions and parallel computing.

Findings

Developed an AMR algorithm for characteristic coordinates

Implemented a code for Einstein-Klein-Gordon system in spherical symmetry

Discussed generalization to higher dimensions and parallelization methods

Abstract

The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon system of equations in spherical symmetry. We discuss how the algorithm can trivially be generalized to higher dimensional systems, and suggest a method that can be used to parallelize a characteristic code.