Pseudospectral method for gravitational wave collapse

Abstract

We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed and the numerical method is critically examined and specialized for the task at hand. In particular we investigate formulation parameters, gauge and constraint preserving boundary conditions well-suited to non-vanishing gauge source functions. Different types of axisymmetric twist-free moment of time symmetry gravitational wave initial data are discussed. A treatment of the axisymmetric apparent horizon condition is presented with careful attention to regularity on axis. Our apparent horizon finder is then evaluated in a number of test cases. Moving on to evolutions, we investigate modifications to the generalized harmonic gauge constraint damping scheme to improve conservation in the strong field regime. We demonstrate strong-scaling of our pseudospectral penalty code. We employ the Cartoon method to efficiently evolve axisymmetric data in our 3+1 dimensional code. We perform test evolutions of Schwarzschild perturbed by gravitational waves and by gauge pulses, both to demonstrate the use of our blackhole excision scheme and for comparison with earlier results. Finally numerical evolutions of supercritical Brill waves are presented to demonstrate durability of the excision scheme for the dynamical formation of a blackhole.

Critical phenomena in the aspherical gravitational collapse of radiation fluids

“…In addition to studying critical phenomena in the aspherical collapse of radiation fluids, this paper serves as a demonstration that an unconstrained evolution code, using "movingpuncture" coordinates, is suitable for the study of critical collapse, at least for some matter models (see also [10,23,24] for recent discussions of this issue.) We denote gridpoints with r i and define…”

“…(8) and (9) below) have proven particularly useful for simulations of spacetimes containing black holes. How suitable these codes are for simulations of critical collapse, however, remains a somewhat open question (see also [10,23,24] for recent discussions.) Our findings here demonstrate that, at least for some matter models, unconstrained evolution codes with the 1+log and Gamma-driver coordinate conditions can indeed be used to study critical phenomena.…”

Solving 3D relativistic hydrodynamical problems with weighted essentially nonoscillatory discontinuous Galerkin methods

“…A cell is marked as troubled if at least one of these indications results in a troubled state. To apply the one-dimensional algorithm, the boundary values used in (14) have to be modified, since the cell boundaries are not longer single points, but lines or surfaces. Therefore, we redefine u AE j by the boundary averages, i.e.…”

“…Throughout this article we employ the bamps code [14]. It is based on the method of lines with a pseudospectral decomposition in the spatial part and an explicit fourth order Runge-Kutta for the time stepping.…”

“…It has been successfully used to study the gravitational wave collapse and it allows long term simulations of single black hole spacetimes with excision techniques. The program exhibits a hybrid p-thread/message passing interface (MPI) parallelization strategy and shows almost ideal scaling for up to several thousands of computing cores in vacuum simulations; see [14] for more details.…”