Adaptive Pseudospectral Evolutions of Wave Models on Hyperboloidal Slices

This thesis extends the bamps framework to solve the wave equation on both hyperboloidal slices and hyperboloidal layers. We demonstrate that the implemented methods achieve promising convergence results in both settings. We further investigate how our code handles the inclusion of perturbations in our initial conditions for the hyperboloidal layers setup, again obtaining encouraging numerical results.

Building on this framework, we study the cubic wave equation, exploring both decaying and blowup solutions through numerical simulations. By tuning initial data toward the threshold of blowup, we obtain solutions approaching critical behavior within the limitations of our numerical implementation. In addition, we provide numerical support for several results from modern partial differential equations theory by computing the blowup rate of numerically generated blowup solutions and evaluating the associated power indices across the computational domain for decaying solutions.

As part of this work, we also developed the foundation of an analysis software suite intended to become a central component of the future bamps development workflow.