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100 years after Einstein's prediction, the first gravitational wave detection in 2015 from a binary black hole (BBH) merger and the first signal from a binary neutron star (BNS) merger in 2017, along with counterparts across other spectra, ushered us into the current epoch of multimessenger astrophysics. The analysis of these signals, be it through match-filtering using waveform template banks or more detailed targeted ones, depends extensively on numerical relativistic simulations of these compact binary inspiral, coalescence, and post-merger dynamics. In this talk, I will focus specifically on the simulation of neutron stars. I will explore simulating BNSs and studying the associated gravitational waves and matter dynamics, discussing how we navigate the space of BNS initial data configurations and incorporate new microphysics. These are fundamental to analyzing the signals observed by the current and upcoming LIGO-Virgo-Kagra. Additionally, I will discuss numerical relativistic methods needed to meet the speed and accuracy requirements of next-generation gravitational observatories such as the Einstein Telescope and Cosmic Explorer. |