Mukherjee, Soham2022-08-182022-08-182022-08-182022-08-15http://hdl.handle.net/10012/18572This thesis addresses a collection of topics that are either directly related to, or have implications for, current challenges in computational relativity. In the first part, we explore a spacetime discretization method for computational relativity. This offers unique computational advantages, for distributing the computation over a large number of processes, as well as for studying spacetime regions close to black hole singularities. In the second part, we present a method to construct initial conditions for numerical evolution of charged, spinning black hole binaries. The evolution of these initial conditions provides a proxy for binary black hole waveforms in modified theories of gravity. In the third part of the thesis, we focus on building an empirical understanding of why Boolean Satisfiability (SAT) solvers are efficient for real-world problems, when, theoretically, the Boolean SAT problem is computationally intractable.enGeneral relativityNumerical relativityGravitational wave physicsBoolean satisfiability problemSpacetime methodsDoctoral Thesis