Discontinuous Galerkin method for the spherically reduced BSSN system with second-order operators

TL;DR

This paper introduces a high-order discontinuous Galerkin method for the spherically-reduced BSSN system using second-order operators, achieving spectral accuracy and stability for numerical relativity simulations.

Contribution

It develops and verifies a novel multi-domain DG scheme tailored for the BSSN system with second-order operators, enhancing accuracy and stability.

Findings

Achieves global spectral accuracy in simulations.

Demonstrates long-time stability on short domains.

Provides detailed implementation and verification.

Abstract

We present a high-order accurate discontinuous Galerkin method for evolving the spherically-reduced Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system expressed in terms of second-order spatial operators. Our multi-domain method achieves global spectral accuracy and long-time stability on short computational domains. We discuss in detail both our scheme for the BSSN system and its implementation. After a theoretical and computational verification of the proposed scheme, we conclude with a brief discussion of issues likely to arise when one considers the full BSSN system.