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This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…

Numerical Analysis · Mathematics 2025-08-11 Benjamin Mann , Ulrich Rüde

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

Numerical Analysis · Mathematics 2019-12-12 Stefano Berrone , Andrea Borio , Alessandro D'Auria

Adaptive mesh refinement efficiently facilitates the computation of gravitational waveforms in numerical relativity. However, determining precisely when, where, and to what extent to refine when solving the Einstein equations poses…

General Relativity and Quantum Cosmology · Physics 2025-07-24 William K. Black , David Neilsen , Eric W. Hirschmann , David F. Van Komen , Milinda Fernando

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…

Numerical Analysis · Mathematics 2020-10-13 Stefan A. Funken , Anja Schmidt

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Frans Pretorius , Matthew W. Choptuik

To fully unlock the scientific potential of upcoming gravitational wave (GW) interferometers, numerical relativity (NR) simulation accuracy will need to be greatly enhanced. We present three infrastructure-agnostic improvements to the…

General Relativity and Quantum Cosmology · Physics 2024-09-19 Zachariah B. Etienne

Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes,…

We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=m_1/m_2=1/15$ nonspinning case, we…

General Relativity and Quantum Cosmology · Physics 2020-11-11 Carlos O. Lousto , James Healy

Observation and characterisation of gravitational waves from binary black holes requires accurate knowledge of the expected waveforms. The late inspiral and merger phase of the waveform is obtained through direct numerical integration of…

General Relativity and Quantum Cosmology · Physics 2019-03-27 Ian Hinder , Serguei Ossokine , Harald P. Pfeiffer , Alessandra Buonanno

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…

Numerical Analysis · Mathematics 2026-03-04 Annalisa Buffa , Denise Grappein , Rafael Vázquez

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of "generic" binary black-hole evolutions using the pseudo-spectral evolution code…

General Relativity and Quantum Cosmology · Physics 2013-05-29 Béla Szilágyi , Lee Lindblom , Mark A. Scheel

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of non-precessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid…

General Relativity and Quantum Cosmology · Physics 2016-02-10 Sebastian Khan , Sascha Husa , Mark Hannam , Frank Ohme , Michael Pürrer , Xisco Jiménez Forteza , Alejandro Bohé

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Philippos Papadopoulos , Edward Seidel , Lee Wild

Gravitational waves from binary black hole mergers provide a glimpse of gravitational dynamics in its most extreme observable regime, potentially enabling precision tests of general relativity (GR) and of the Kerr description of black…

General Relativity and Quantum Cosmology · Physics 2026-05-14 Ayush Roy , Lorenzo Küchler , Adam Pound , Rodrigo Panosso Macedo

Gravitational wave detection has opened up new avenues for exploring and understanding some of the fundamental principles of the universe. The optimal method for detecting modelled gravitational-wave events involves template-based matched…

General Relativity and Quantum Cosmology · Physics 2025-01-15 Damon Beveridge , Alistair McLeod , Linqing Wen , Andreas Wicenec

For the first time, we construct an inspiral-merger-ringdown waveform model within the effective-one-body formalism for spinning, nonprecessing binary black holes that includes gravitational modes beyond the dominant $(\ell,|m|) = (2,2)$…

General Relativity and Quantum Cosmology · Physics 2022-07-22 Roberto Cotesta , Alessandra Buonanno , Alejandro Bohé , Andrea Taracchini , Ian Hinder , Serguei Ossokine

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…

General Relativity and Quantum Cosmology · Physics 2023-05-31 Sarah Renkhoff , Daniela Cors , David Hilditch , Bernd Brügmann

The measurement of multiple ringdown modes in gravitational waves from binary black hole mergers will allow for testing fundamental properties of black holes in General Relativity, and to constrain modified theories of gravity. To enhance…

General Relativity and Quantum Cosmology · Physics 2017-04-26 Huan Yang , Kent Yagi , Jonathan Blackman , Luis Lehner , Vasileios Paschalidis , Frans Pretorius , Nicolas Yunes

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

Numerical Analysis · Mathematics 2021-12-21 Stefano Berrone , Alessandro D'Auria

We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…

Numerical Analysis · Mathematics 2022-02-08 Niklas Kolbe , Nikolaos Sfakianakis