Adaptive hp-Refinement for Spectral Elements in Numerical Relativity

Abstract: When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code bamps in the form of fully adaptive, physics-agnostic hp-refinement. We describe the foundations of mesh refinement in the context of spectral element methods, the precise algorithm used to perform refinement in bamps, as well as several indicator functions used to drive it. Finally, we test the performance, scaling, and the accuracy of the code in treating several 1d and 2d example problems, showing clear improvements over static mesh configurations. In particular, we consider a simple non-linear wave equation, the evolution of a real scalar field minimally coupled to gravity, as well as nonlinear gravitational waves.