A Galerkin-Collocation domain decomposition method: application to the evolution of cylindrical gravitational waves

TL;DR

This paper introduces a domain decomposition Galerkin-Collocation method for simulating cylindrical gravitational waves, demonstrating high accuracy in modeling wave dynamics and nonlinear energy exchange.

Contribution

The paper develops a novel Galerkin-Collocation domain decomposition algorithm specifically for evolving cylindrical gravitational waves, enhancing accuracy and efficiency.

Findings

Successfully reproduces initial data with high localized gradients.

Provides highly accurate gravitational wave dynamics.

Identifies potential gravitational Faraday effect imprint.

Abstract

We present a Galerkin-Collocation domain decomposition algorithm applied to the evolution of cylindrical unpolarized gravitational waves. We show the effectiveness of the algorithm in reproducing initial data with high localized gradients and in providing highly accurate dynamics. We characterize the gravitational radiation with the standard Newman-Penrose Weyl scalar $\Psi_4$. We generate wave templates for both polarization modes, $\times$ and $+$, outgoing and ingoing, to show how they exchange energy nonlinearly. In particular, considering an initially ingoing $\times$ wave, we were able to trace a possible imprint of the gravitational analog of the Faraday effect in the generated templates.