TL;DR
Numerical relativity has matured significantly over the past three decades, with advances in theory, numerical methods, and software enabling complex 3D simulations of matter and black holes.
Contribution
This paper provides a comprehensive review of the current state of numerical relativity, highlighting recent theoretical and computational advancements.
Findings
Development of advanced 3D codes for matter and black holes
Improved understanding of theoretical issues like well-posedness and gauge conditions
Progress in numerical methods and software engineering
Abstract
Numerical relativity has come a long way in the last three decades and is now reaching a state of maturity. We are gaining a deeper understanding of the fundamental theoretical issues related to the field, from the well posedness of the Cauchy problem, to better gauge conditions, improved boundary treatment, and more realistic initial data. There has also been important work both in numerical methods and software engineering. All these developments have come together to allow the construction of several advanced fully three-dimensional codes capable of dealing with both matter and black holes. In this manuscript I make a brief review the current status of the field.
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