Multilevel parallel-in-time methods for advection-dominated PDEs

The predictions arising from the numerical simulation of partial differential equations are used throughout many areas of science. I present, design, and analyse new algorithms for the numerical simulation of partial differential equations that describe time-dependent phenomena, such as those that govern the conduction of electricity through a wire, or that describe the airflow across an airplane wing, for example. For the specific types of equations that I consider, my new algorithms enable these equations to be simulated faster and more efficiently than with existing approaches.