Explore numerical relativity and its crucial role in next-generation gravitational-wave observatories in this 46-minute lecture by Geoffrey Lovelace from California State University, Fullerton. Delve into the dynamics of warped spacetime, learn how to solve Einstein's equations in vacuum, and understand the generalized harmonic formulation. Examine the challenges in modeling signals for future detectors, including the need for increased accuracy and handling very unequal masses. Discover the SXS Catalog and its variety of configurations. Gain insights into how numerical relativity is essential for interpreting strong gravitational-wave events and enabling sensitive searches for new physics embedded in these signals.