Delve into the second lecture of a comprehensive series on the theory and numerical methods for partial differential equations, delivered by Harald Pfeiffer from the Albert Einstein Institute. Explore advanced concepts in numerical relativity as part of the Summer School on Gravitational-Wave Astronomy, organized by the International Centre for Theoretical Sciences. Gain insights into the mathematical foundations and computational techniques essential for modeling complex astrophysical phenomena such as black hole mergers, neutron star collisions, and gravitational wave events. Enhance your understanding of the interplay between general relativity, magnetohydrodynamics, and high-performance computing in the context of modern astrophysics and gravitational wave astronomy.