Explore the computational methods and techniques used to solve Einstein's field equations numerically in this 20-minute conference talk from the International Centre for Theoretical Sciences. Learn about the fundamental principles of numerical relativity, which plays a crucial role in modeling gravitational wave sources such as black hole mergers and neutron star collisions. Discover how sophisticated computational algorithms simulate the complex dynamics of spacetime in strong gravitational fields, providing essential theoretical predictions for gravitational wave detectors like LIGO and Virgo. Understand the mathematical frameworks, discretization methods, and computational challenges involved in solving the nonlinear partial differential equations of general relativity. Gain insights into how numerical relativity simulations contribute to our understanding of gravitational wave astronomy and help interpret observational data from current and future gravitational wave detectors.