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.

arXiv comment19 pages, 17 figures

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Cited by in corpus (8)

• Critical phenomena in the collapse of gravitational waves
• Boson star head-on collisions with constraint-violating and constraint-satisfying initial data
• Adaptive mesh refinement in binary black holes simulations
• Twist-free axisymmetric critical collapse of a complex scalar field
• Formulation Improvements for Critical Collapse Simulations
• Simulating binary black hole mergers using discontinuous Galerkin methods
• Twist and higher modes of a complex scalar field at the threshold of collapse
• Pseudospectral implementation of the Einstein-Maxwell system