COFFEE—An MPI-parallelized Python package for the numerical evolution of differential equations

Doulis, Georgios; Frauendiener, Jörg; Stevens, Chris; Whale, Ben

doi:10.1016/j.softx.2019.100283

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…The temporal discretization is also equidistant in this study with timestep given by dt = dr/2 giving a Courant-Friedrichs-Lewy number of 0.5. The MPIparallelized Python package COFFEE [7] contains all the necessary numerical methods to evolve this initial boundary value problem. The standard explicit Runge-Kutta fourth order method is used to march in time, Strand's fourth order summation-by-parts finite difference operator (third order on the boundary) [27] is used to approximate radial derivatives and the simultaneous-approximation-method [5] is used to stably impose maximally dissipative boundary conditions.…”

Section: Overview Of the Gcfe And Its Numerical Ibvp Implementationmentioning

confidence: 99%

The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

Frauendiener¹,

Goodenbour²,

Stevens³

2023

Preprint

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In this paper we continue our study of the non-linear response of a Schwarzschild black hole to an ingoing gravitational wave by computing the Newman-Penrose (NP) constants. The NP constants are five complex, supertranslation-invariant quantities defined on null infinity I + and although put forward in the 60's, they have never been computed in a non-stationary setting. We accomplish this through a numerical implementation of Friedrich's generalized conformal field equations whose semi-global evolution yields direct access to I + . Generalizations of the NP constants' integral expressions are made to allow their computation in a more general gauge that better suits the output of a numerical evolution. Canonical methods of fixing inherent degrees of freedom in their definitions are discussed. The NP constants are then computed for a variety of different ingoing wave profiles in axisymmetry, and then with no symmetry assumptions in 3+1 for which all five are non-zero.

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Section: Overview Of the Gcfe And Its Numerical Ibvp Implementationmentioning

confidence: 99%

The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

Frauendiener¹,

Goodenbour²,

Stevens³

2023

Preprint

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“…We use the MPI-parallelized Python package COFFEE [5] to evolve the system. It contains a large selection of time integrators, finite difference operators with the summation-by-parts property as well as the ability to use the pseudo-spectral code presented in [1,2].…”

Section: Numerical Setupmentioning

confidence: 99%

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

Frauendiener¹,

Stevens²

2021

Class. Quantum Grav.

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Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity. Although being an attractive option for studying global quantities by way of local differential geometrical methods, how viable are the GCFE for study of quantities arising in the physical space-time? In particular, how long can the evolution track phenomena that need a constant proper physical timestep to be accurately resolved? We address this question by studying the curvature oscillations induced on the Schwarzschild spacetime by a non-linear gravitational perturbation. For small enough amplitudes, these are the well approximated by the linear quasinormal modes, where each mode rings at a frequency determined solely by the Schwarzschild mass. We find that the GCFE can indeed resolve these oscillations, which quickly approach the linear regime, but only for a short time before the compactification becomes "too fast" to handle numerically.

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“…We utilize the Python package COFFEE [24], which contains all the necessary functionality to perform a numerical evolution using the method of lines. We discretize the zdirection into equi-distant points in the interval [−1,1] and approximate the z-derivative using Strand's finite difference stencil [25] which is fourth order in the interior, third order on the boundary and has the summation-by-parts property [26].…”

Section: Numerical Setupmentioning

confidence: 99%

Can Gravitational Waves Halt the Expansion of the Universe?

2021

Self Cite

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We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant λ are written in the Friedrich–Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with λ=0, critical behaviours are found with λ>0 and are based on the relationship between the wave profile and λ. We find that choosing boundary data close to one of these bifurcations results in a “false” steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Tsamis and Woodard, which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire space–time. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.

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COFFEE—An MPI-parallelized Python package for the numerical evolution of differential equations

Cited by 8 publications

References 19 publications

The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

Can Gravitational Waves Halt the Expansion of the Universe?

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