Scalable solvers for non-conforming polytopal hybrid discretization methods

Modern engineering simulations — modelling fluid flow, heat transfer, or structural deformation — require solving enormous mathematical systems on computers. Accuracy improves when computational grids are finer and more geometrically flexible, but this creates systems that are far too large to solve directly. This thesis develops fast solution algorithms, called preconditioners, that make high-accuracy simulations on complex, irregular real-world geometries practical. In particular, we develop preconditioners for advanced discretization methods designed to work on generic polytopal meshes and complex geometries. Together, these tools bring high-fidelity computational simulations significantly closer to routine use in science and engineering.