Lessons for adaptive mesh refinement in numerical relativity (original) (raw)
Related papers
Computational relativistic astrophysics with adaptive mesh refinement: Testbeds
Physical Review D, 2005
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a 1025 3 regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations. PACS numbers: 95.30.Sf, 04.40.Dg, 04.30.Db, 97.60.Jd a. Introduction Numerical study of compact systems has received much attention due to observations in high-energy astronomy and the promise of gravitational wave astronomy. Most effort focuses on solving the Einstein equations with finite differencing methods. The main difficulty of this approach is that many general relativistic astrophysical processes of interest, e.g., processes involving black holes and neutron stars, require computational resources that are beyond what present day computers allow. The reasons that they are computationally demanding are 1. the lack of symmetry in realistic astrophysical situations, requiring the solving of the full set of Einstein equations coupled to the general relativistic hydrodynamic (GRHydro) equations in 3+1 dimensional spacetime; and 2. the involvement of many length scales.
Adaptive computation of gravitational waves from black hole interactions
Physical Review D, 1998
We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast with the usual approach, a single equation treats all radiative l-m modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes. ͓S0556-2821͑98͒01214-4͔
Adaptive mesh refinement approach to the construction of initial data for black hole collisions
Classical and Quantum Gravity, 2000
The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a secondorder accurate approach to the solution of the constraint equations on a non-uniformly refined high resolution Cartesian mesh including second-order accurate treatment of boundary conditions at the black hole throats. Results of test computations show convergence of the solution as the numerical resolution is increased. FTT-based mesh refinement reduces the required memory and computer time by several orders of magnitude compared to a uniform grid. This opens up the possibility of using Cartesian meshes for very high resolution simulations of black hole collisions.
Adaptative mesh refinement in numerical relativity
1994
We discuss the use of Adaptative Mesh Re nement (AMR) techniques in dynamical black hole spacetimes. We compare results between traditional xed grid methods and a new AMR application for the 1-D Schwarzschild case.
The Black Hole Accretion Code: adaptive mesh refinement and constrained transport
Journal of Physics: Conference Series, 2018
With the forthcoming VLBI images of Sgr A* and M87, simulations of accretion flows onto black holes acquire a special importance to aid with the interpretation of the observations and to test the predictions of different accretion scenarios, including those coming from alternative theories of gravity. The Black Hole Accretion Code (BHAC) is a new multidimensional general-relativistic magnetohydrondynamics (GRMHD) module for the MPI-AMRVAC framework. It exploits its adaptive mesh refinement techniques (AMR) to solve the equations of ideal magnetohydrodynamics in arbitrary curved spacetimes with a significant speedup and saving in computational cost. In a previous work, this was shown using a Generalized Lagrange Multiplier (GLM) to enforce the solenoidal constraint of the magnetic field. While GLM is fully compatible with MPI-AMRVAC 's AMR infrastructure, we found that simulations were sensible to the divergence control technique employed, resulting in an improved behavior for those using Constrained Transport (CT). However, cell-centered CT is incompatible with AMR, and several modifications were required to make AMR compatible with staggered CT. We present here preliminary results of these new additions, which achieved machine precision fulfillment of the solenoidal constraint and a significant speedup in a problem close to the intended scientific application.
Three-dimensional adaptive evolution of gravitational waves in numerical relativity
Physical Review D, 2000
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal, the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run. 04.25.Dm, 04.30.Nk
Physical Review D, 2009
Gravitational waveforms from the inspiral and ring-down stages of the binary black-hole coalescences can be modeled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the nonperturbative merger phase of the binary black-hole coalescence problem. This enables us to coherently search for all three stages of the coalescence of nonspinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ringdown stages of the coalescence of nonspinning binary black holes that follow quasicircular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only effectual in detecting the signals from black-hole coalescences, but also faithful in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black-hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass range, potentially bringing about remarkable improvement in the event rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using nonspinning black-hole waveforms produced by numerical relativity.
2009
Gravitational waveforms from the inspiral and ring-down stages of the binary black-hole coalescences can be modeled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the nonperturbative merger phase of the binary black-hole coalescence problem. This enables us to coherently search for all three stages of the coalescence of nonspinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ringdown stages of the coalescence of nonspinning binary black holes that follow quasicircular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only effectual in detecting the signals from black-hole coalescences, but also faithful in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black-hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass range, potentially bringing about remarkable improvement in the event rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using nonspinning black-hole waveforms produced by numerical relativity.