Numerical Relativity: Solving Einstein's Equations on the Computer, by Th.W. Baumgarte and S.L. Shapiro

Myridis, Nikolaos E.

doi:10.1080/00107514.2011.586052

Cited by 3 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This extra equation is useful in producing initial data in quasi-equilibrium. For a more detailed review of initial data construction, see [40][41][42].…”

Section: Bbh Initial Data Formalismmentioning

confidence: 99%

“…The standard practice in SpEC has been to choose quasi-equilibrium apparent/isolated horizon boundary conditions on the inner excision surfaces [19,45]. We refer the reader to [40,46,47] for a review of the properties of apparent and isolated horizons. We require boundary conditions on the conformal factor, the shift vector, and the lapse function.…”

Section: Horizon Boundary Conditionsmentioning

confidence: 99%

“…3 Notice that for the denominator of Eqs. (40) and (41) Convergence test for the spectral elliptic solver in solving the XCTS equations for the different initial data types listed in Table. I. Shown is the Hamiltonian-momentum constraint energy (Eq.…”

Section: Convergence Of Initial Datamentioning

confidence: 99%

See 2 more Smart Citations

Comparison of binary black hole initial data sets

2018

View full text Add to dashboard Cite

We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial data construction. We find that this improves initial data constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial data sets that are intended to be astrophysically equivalent but use different free data, boundary conditions, and initial gauge conditions. These include free data chosen as a superposition of two black holes in time-independent horizon-penetrating harmonic and damped harmonic coordinates. We also implement initial data for which the initial gauge satisfies the harmonic and damped harmonic gauge conditions; this can be done independently of the free data, since this amounts to a choice of the time derivatives of the lapse and shift. We compare these initial data sets by evolving them. We show that the gravitational waveforms extracted during the evolution of these different initial data sets agree very well after excluding initial transients. However, we do find small differences between these waveforms, which we attribute to small differences in initial orbital eccentricity, and in initial BH masses and spins, resulting from the different choices of free data. Among the cases considered, we find that superposed harmonic initial data leads to significantly smaller transients, smaller variation in BH spins and masses during these transients, smaller constraint violations, and more computationally efficient evolutions. Finally, we study the impact of initial data choices on the construction of zero-eccentricity initial data.

show abstract

“…This extra equation is useful in producing initial data in quasi-equilibrium. For a more detailed review of initial data construction, see [40][41][42].…”

Section: Bbh Initial Data Formalismmentioning

confidence: 99%

Section: Horizon Boundary Conditionsmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of binary black hole initial data sets

2018

View full text Add to dashboard Cite

show abstract

“…The metric in a general spacetime can be written in the standard space plus time form (See, e.g., [50] or [51]), ds 2 = g µν dx µ dx ν = −α 2 dt 2 + γ ab (dx a + β a dt)(dx b + β b dt) .…”

Section: Preliminaries and Notationmentioning

confidence: 99%

SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics

Kidder

Field

Foucart

et al. 2017

Journal of Computational Physics

116

108

View full text Add to dashboard Cite

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A taskbased parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22, 380 nodes using 671, 400 threads. variety of astrophysics codes (e.g., Refs. [6,[9][10][11][12][13][14]) have been designed based on these fundamental building blocks.These strategies work well when the computations are reasonably homogeneous or when one seeks good parallelization to only a few thousand cores. As the number of MPI processes increases, so does the cost of communication which, together with non-uniform workload typical of astrophysics problems, limits the maximum number of useful cores that codes can run on. Efficient core utilization becomes non-trivial, often requiring careful optimization by hand to achieve good scalability [15]. Standard finite-volume and finitedifference methods achieve higher order accuracy with increasingly large (overlapping) stencil sizes, and may require additional effort to achieve scalability on massively parallel machines.As one looks ahead to the arrival of exascale computing, it will become increasingly important to focus on developing algorithms that can take full advantage of these very large machines.Discontinuous Galerkin (DG) methods [16-21], together with a task-based parallelization strategy, have the potential to tackle many of these problems. DG methods offer high-order accuracy in smooth regions (although, for stability, increasing the scheme's order requires decreasing the timestep, which restricts the largest usable order in practice), robustness for shocks and other discontinuities, and grid flexibility including a formulation that allows for comparatively straightforward hp-adaptivity and local timestepping. DG methods can be combined with positivity preserving strategies [22][23][24] or "atmosphere treatments" [25] which seek to maintain non-negative values of the pressure and density in challenging regions such as those containing high-speed astrophysical flow. DG methods are also well suited for parallelization: Their formulation in terms of l...

show abstract

“…The parameters of the BBHs were inferred [4-8, 10, 11] using fast, analytical waveform models [12][13][14][15][16][17] calibrated to numerical relativity (NR) simulations [18][19][20][21][22]. The latter are obtained by directly solving the fully nonlinear Einstein equations for BBH spacetimes [23]. The detection efficiency and the accuracy of parameter estimation are directly affected by the accuracy of both analytical and numerical waveform models [24].…”

mentioning

confidence: 99%

Gravitational waveforms for high spin and high mass-ratio binary black holes: A synergistic use of numerical-relativity codes

et al. 2019

View full text Add to dashboard Cite

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 the full 3-dimensional Einstein equations. The Spectral Einstein Code (SpEC) utilizes a multi-domain pseudo-spectral method tightly adapted to the geometry of the black holes; it is computationally efficient and accurate, but-for high mass-ratios and large spins-sometimes requires manual fine-tuning for the merger-phase of binaries. The Einstein Toolkit (ET) employs finite difference methods and the moving puncture technique; it is less computationally efficient, but highly robust. For some mergers with high mass ratio and large spins, the efficient numerical algorithms used in SpEC have failed, whereas the simpler algorithms used in the ET were successful. Given the urgent need of testing the accuracy of waveform models currently used in LIGO and Virgo inference analyses for high mass ratios and spins, we present here a synergistic approach to numericalrelativity: We combine SpEC and ET waveforms into complete inspiral-merger-ringdown waveforms, taking advantage of the computational efficiency of the pseudo-spectral code during the inspiral, and the robustness of the finite-difference code at the merger. We validate our method against a case where complete waveforms from both codes are available, compute three new hybrid numerical-relativity waveforms, and compare them with analytical waveform models currently used in LIGO and Virgo science. All the waveforms and the hybridization code are publicly available.

show abstract

Numerical Relativity: Solving Einstein's Equations on the Computer, by Th.W. Baumgarte and S.L. Shapiro

Cited by 3 publications

References 0 publications

Comparison of binary black hole initial data sets

Comparison of binary black hole initial data sets

SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics

Gravitational waveforms for high spin and high mass-ratio binary black holes: A synergistic use of numerical-relativity codes

Contact Info

Product

Resources

About