A dissipative algorithm for wave-like equations in the characteristic formulation

TL;DR

This paper introduces a dissipative numerical algorithm for solving nonlinear wave equations on characteristic surfaces, enhancing stability in highly nonlinear regimes relevant to electromagnetism, Yang-Mills, and general relativity.

Contribution

It presents a novel dissipative algorithm specifically designed for wave-like equations on characteristic surfaces, improving stability in complex nonlinear scenarios.

Findings

Algorithm is stable for linear waves on Minkowski background.

Effective in simulating wave scattering off a Schwarzschild black hole.

Applicable to hyperbolic systems in electromagnetism, Yang-Mills, and general relativity.

Abstract

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the highly nonlinear regime where previous methods have failed to give a stable evolution in three dimensions. The algorithm presented in this work is directly applicable to hyperbolic systems proper of Electromagnetism, Yang-Mills and General Relativity theories. We carry out an analysis of the stability of the algorithm and test its properties with linear waves propagating on a Minkowski background and the scattering off a Scwharszchild black hole in General Relativity.