arXiv subjects

Mark A. Scheel

Publications and source records attributed to Mark A. Scheel.

At least 19 recordsLinked to original sources

arXiv2026

A catalog of long, eccentric and precessing binary black hole simulations from ICTS-TIFR

We present a catalogue of 31 binary black hole simulations performed with the Spectral Einstein Code (SpEC) on the Sonic cluster at ICTS-TIFR, Bengaluru between August 2023 and December 2024, targeting the sparsely covered corner of parameter space in which orbital eccentricity and spin-orbit precession are present simultaneously: 17 configurations are both eccentric and precessing, spanning mass ratios $1 \le q \le 11$ and initial eccentricities up to $\hat{e}_0 = 0.40$. The longest, EccPrecDiff002, inspirals for 80 orbits (159 gravitational-wave cycles), to our knowledge the longest simultaneously eccentric and precessing binary black hole evolution to date. Compile-time optimisation of SpEC and its third-party library stack for the AMD Zen-2 architecture delivered a 90% speedup of the initial-data solver and a 40% speedup of the evolution, roughly half of the latter traceable to a single defect in how pre-2.34 glibc reported cache topology on AMD processors. The campaign consumed $1.18 \times 10^{6}$ CPU-hours. We document the post-processing pipeline and validate the frame transformation and waveforms. Eccentricity is measured from the waveforms and compared against the initial data. The first law of binary black hole mechanics, a test of approximate helical symmetry, is satisfied to better than 0.54% for every configuration with $e_ω < 0.2$, and we show that even precessing systems can be regarded as possessing approximate helical symmetry in the co-precessing frame. Using the aligned-spin simulations to calibrate the numerical floor, the co-precessing approximation's mirror-symmetry violation lies three to four ordersof magnitude above it, growing from 0.7% to 5.3%with opening angle. EccPrecDiff002 spans the band above 5 Hz without hybridisationfor $M \le 62\,M_\odot$, giving a single-interferometer signal-to-noise ratio of 961 in Cosmic Explorer at 1 Gpc.

gr-qc↗

arXiv2026

Calculating gravitational waves at infinity: the missing link

Gravitational-wave science requires waveform templates to be computed at future null infinity, the asymptotic boundary of spacetime. Numerical solutions of Einstein's equations typically rely on a Cauchy evolution on a finite computational domain, but can produce waveforms at infinity by performing a subsequent characteristic evolution that compactifies the spacetime. Such waveforms capture expected physical effects, like gravitational-wave memory and late-time, power-law tails. But this characteristic evolution requires initial data consistent with the interior Cauchy solution to avoid producing spurious, long-lived transients. A careful analysis shows that previous prescriptions for this initial data were not sufficiently consistent and provides a way to remedy the problem. The new initial data yield accurate waveforms from the first cycle onward. The construction is independent of the Cauchy formulation and enables the production of catalogs of robust waveforms at infinity.

gr-qc↗

arXiv2026

Accurate initial data for Cauchy-characteristic evolution

Accurate gravitational-wave (GW) templates from numerical-relativity (NR) simulations are essential for GW science. These templates are typically computed at finite radii and extrapolated to future null infinity $\mathscr{I}^{+}$, the asymptotic boundary of spacetime. However, this procedure is known to not accurately capture momentum fluxes and memory effects, limiting the accuracy of waveform models and data analyses that rely on them. Cauchy-characteristic evolution (CCE) instead integrates Einstein's equations along outgoing null hypersurfaces from a Cauchy simulation's finite-radius worldtube to $\mathscr{I}^{+}$. Its accuracy, though, has been limited by initial data that produce long-lived spurious transients, which contaminate several cycles of the waveform emitted by the binary coalescence. We identify incorrect initial angular coordinates as the source of these transients. We construct initial data that matches the Cauchy worldtube data through second order in the radial derivatives and solve for the angular coordinates consistent with the resulting radial profile. These improvements remove the unphysical transient: a $10\%$ modulation of a binary black hole's $(2,2)$ mode amplitude lasting over $1000\,M$ disappears, and the late-time tail of a head-on black hole collision is recovered. The construction is independent of the Cauchy formulation and allows archived simulations to be reprocessed with CCE, paving the way for improved GW catalogs.

gr-qc↗

arXiv2026

How accurate is Spectral Einstein Code (SpEC)? And what limits its accuracy?

The improved sensitivity of upcoming gravitational-wave detectors will require correspondingly more accurate binary black hole (BBH) simulations. Given the high cost of such simulations, it is essential to understand their sources of error and use computational resources efficiently. We study sources of error in BBH simulations performed with the Spectral Einstein Code (SpEC) and seek to understand what limits their accuracy. In particular, we focus on the inspiral phase because it is the longest-running part of the simulation and accounts for the majority of the waveform error. We find that targeted changes to simulation parameters and resolution in different parts of the computational domain reduce constraint violations and gravitational waveform differences. We also discuss more fundamental limitations on our accuracy that become important at higher resolutions: floating-point errors and large differences in the scales of the fundamental variables. Addressing these limitations will require substantial changes to both the SpEC code and the formulation it uses to evolve Einstein's equations. Many of the improvements and changes discussed in this paper are likely to be relevant to other numerical relativity codes.

gr-qc↗

arXiv2026

Quadratic Gravitational-Wave Scattering by Kerr Black Holes

Second-order black-hole perturbation theory will be an important component of precision gravitational-wave modeling and tests of strong-field gravity with next-generation detectors. Beyond quasinormal modes (QNMs), whose quadratic interactions have been the focus of recent work in black-hole spectroscopy, a generic retarded solution consists of a continuum of real-frequency scattering states whose nonlinear interactions in Kerr remain comparatively less explored. We use numerical relativity to study the quadratic response of Kerr black holes to nearly monochromatic $(\ell,m)=(2,\pm2)$ incident gravitational waves, measuring the complex self-coupling to the outgoing $(\ell,m)=(4,4)$ daughter at twice the parent frequency for black-hole spins up to $a=0.95$. At low frequencies, the coupling is strongly suppressed and exhibits opposite spin dependence for prograde and retrograde scattering. At higher prograde frequencies, we identify a daughter-mode resonance whose frequency and width extracted from the nonlinear response track the fundamental $(\ell,m,n)=(4,4,0)$ QNM. Near the fundamental $(2,2,0)$ QNM frequency, the in-mode coupling grows with spin, in contrast to the decreasing quadratic QNM coupling, demonstrating that the nonlinear response depends on the full parent scattering state rather than on its frequency alone. A complementary semi-analytic second-order Teukolsky calculation reproduces the nonlinear response from our numerical relativity simulations. Our numerical-relativity results and their semi-analytic extension provide a basis for generic homogeneous radiative perturbations of Kerr at second order, with applications to dynamical tides, near-extremal dynamics, and second-order gravitational self-force theory.

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arXiv2026

Data-Driven Acceleration of Eccentricity Reduction for Binary Black Hole Simulations

Reducing orbital eccentricity in numerical relativity simulations of binary black holes is essential for producing astrophysically relevant gravitational wave models, as many of these systems are expected to be near-circular in nature. Standard eccentricity reduction procedures rely on iterative schemes, often requiring four or more trial simulations to achieve desired thresholds. This approach is computationally expensive because each trial simulation adds ~10% to the total simulation run time of multiple weeks to months. We introduce a data-driven approach that accelerates this process by learning the values of the initial orbital frequency, Omega_0, and radial velocity, adot_0, that yield an evolution with small eccentricity. This is done using a Gaussian Process Regression model trained on an archive of previously eccentricity-reduced numerical relativity simulations. For all configurations tested, using the trained model consistently reduces the number of required eccentricity reduction iterations to just zero or one, significantly lowering computational costs relative to post-Newtonian initial guesses. These results demonstrate the power of data-driven methods in accelerating expensive numerical relativity simulations.

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arXiv2026

NRSur7dq4v2: A multi-domain precessing surrogate model with improved accuracy

Numerical relativity simulations provide the most accurate waveforms for binary black hole coalescences, but are prohibitively expensive for direct use in gravitational-wave data analysis. Surrogate models overcome this cost, and NRSur7dq4 is commonly used in parameter estimation for this reason. However, there is evidence in the literature that NRSur7dq4's accuracy could be improved in the merger-ringdown portion of the waveform, which is particularly important for the analysis of high-mass binary black hole events. Motivated by these observations, we construct NRSur7dq4v2, a multi-domain extension of NRSur7dq4 in which overlapping temporal subdomains allow tighter, independent error control over the inspiral and merger-ringdown portions of the waveform before they are smoothly combined. To assess the new model's performance in the merger-ringdown regime, we infer the mass and spin of the remnant black hole from quasi-normal fits to the ringdown portion of the surrogate waveform. We find that NRSur7dq4v2 produces significantly improved remnant mass and spin estimates, with gains of roughly factors of $3$ to $10$ over NRSur7dq4. Compared to NRSur7dq4, NRSur7dq4v2 also includes modes up to $\ell=5$, includes more accurate modeling of certain subdominant modes, and introduces a runtime model-complexity feature that gives users direct control over the tradeoff between evaluation cost and accuracy. Finally, alongside the model development, we have optimized the gwsurrogate package to achieve a fourfold speedup for precessing surrogates. The resulting precessing surrogates called through gwsurrogate are now slightly faster than their LALSimulation counterparts.

gr-qc↗

arXiv2026

Enabling gravitational-wave astronomy with spin-precessing black holes on generic orbits

Binary black holes (BBHs) formed in dense stellar environments or in hierarchical triples can coalesce on eccentric orbits and carry spins of arbitrary orientation, leaving distinctive imprints on their gravitational-wave (GW) emission. We present SEOBNRv6EPHM: the first generic-orbit, spin-precessing model in the effective-one-body SEOBNR family, whose waveforms have underpinned LIGO-Virgo GW analyses since 2011. The model describes the dynamics and multipolar GW signal of generic BBHs, covering the inspiral-merger-ringdown of coalescing binaries and extending to dynamical captures and scattering encounters. We perform the first systematic accuracy assessment of a generic-orbit model against numerical relativity (NR) waveforms of spin-precessing BBHs, using 1437 quasi-circular (QC) and 87 eccentric simulations: median waveform mismatches remain below $1 \%$, matching the accuracy of the QC model SEOBNRv5PHM, and improving on the state-of-the-art generic-orbit model TEOBResumS-Dalí by a median factor of $ 4 $. The model also reproduces the non-perturbative phenomenology observed in NR simulations of generic-spin BBH scattering. It is $\sim 2 - 3$ times faster than SEOBNRv5PHM in the QC limit, and up to an order of magnitude faster than TEOBResumS-Dalí, bringing eccentric inference to the cost of current QC analyses. As a proof of principle, we analyze eleven GW events and focus on GW200129, strengthening its evidence for eccentricity $-$ a result supported by injection-recovery studies with synthetic NR signals of eccentric, spin-precessing BBHs. SEOBNRv6EPHM thus enables, for the first time, accurate and efficient GW analyses that jointly account for eccentricity and spin precession.

gr-qc↗

arXiv2026

Finding black hole spins efficiently during a numerical binary evolution

The dynamics of a binary black hole system depend on its masses and spins. For a binary at finite separation, it is not possible to define these quantities in an unambiguous way; however, there are several reasonable definitions that reduce to the expected values in the limit of infinite separation. Approximate Killing vector (AKV) spin is one of the spin definitions used in the numerical relativity code SpEC. AKV spin requires finding approximate Killing vectors on an apparent horizon, which reduces to a generalized eigenvalue problem of size $\mathcal{O}(L^2)$, and a direct solve has time complexity $\mathcal{O}(L^6)$, where $L$ is the highest spherical harmonic mode used to represent the apparent horizon. This scaling means that the cost of computing AKV spins increases rapidly as we simulate systems at higher resolutions, especially those with high spin or mass ratios. We describe a new algorithm for computing AKV spins that is much faster than the current algorithm.

gr-qc↗

arXiv2026

Towards long and accurate numerical relativity waveforms of binary black holes beyond general relativity

Numerical relativity (NR) simulations of compact binaries in theories beyond general relativity (GR) will be pivotal for the continued development of future tests of gravity with gravitational waves (GWs). In this Letter, we show that the combination of spectral methods and the "fixing-the-equations" approach allows us to produce the longest waveforms in the literature for a genuine beyond-GR theory, thus bringing NR methods for alternative theories of gravity closer to the state-of-the-art in GR. For concreteness, we focus on the well-known shift-symmetric version of scalar Gauss-Bonnet gravity, a theory postulating the existence of an additional dynamical scalar and describing black holes (BHs) different from the Kerr solution. We extract the gravitational and scalar waveforms at future null infinity for equal-mass, nonspinning, eccentricity-reduced BH binaries, and quantify the phase errors to be $\lesssim$ 1 rad after 40+ GW cycles (20+ orbits). We also show that the GW phase corrections in this alternative theory are distinguishable from Einstein's theory and lead to an earlier coalescence time than in GR. Obtaining such waveforms is a stepping stone to perform precise comparisons with Post-Newtonian theory and to calibrate waveform models beyond GR.

gr-qc↗

arXiv2026

High-accuracy drivers to simulate black hole binaries beyond general relativity with the fixing-the-equations approach

We implement the "fixing-the-equations" approach [Phys.Rev.D 96 (2017) 8, 084043] in spectre, an NR code using a pseudo-spectral discontinuous Galerkin scheme, to produce long and accurate NR waveforms in the well-known shift-symmetric version of scalar Gauss-Bonnet (sGB) gravity. To achieve this, we introduce a new family of comoving driver equations that exploits the approximate symmetries of quasicircular binary systems and is designed to recover the exact (quasi-)stationary solutions of the fully-coupled theory. We validate our single black hole (BH) solutions against analytic predictions and show that, even for binary BHs in the early inspiral, the intrinsic BH quantities are relatively insensitive to the timescales entering the driver equation. Attention is given to the prescription of driver equations for tensors, for which we give an example of how treating tensor components as scalars can lead to undesired behaviour over long timescales, including spurious growth of the BH spins. A more appropriate generalization to the tensor case is given for the comoving driver, which is shown to avoid these issues. Overall, our implementation leverages state-of-the-art methods for eccentricity reduction and wave extraction with Cauchy Characteristic Evolution to simulate systems with eccentricity $\lesssim 10^{-3}$. We obtain waveforms with phase errors $\lesssim \mathcal{O}(1) \, \mathrm{rad}$ over almost 40 GW-cycles, which naturally incorporate memory contributions.

gr-qc↗

arXiv2026

Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes

We present SEOBNRv5HM, a more accurate and faster inspiral-merger-ringdown gravitational waveform model for quasi-circular, spinning, nonprecessing binary black holes within the effective-one-body (EOB) formalism. Compared to its predecessor, SEOBNRv4HM, the waveform model i) incorporates recent high-order post- Newtonian results in the inspiral, with improved resummations, ii) includes the gravitational modes (l, |m|) = (3, 2), (4, 3), in addition to the (2, 2), (3, 3), (2, 1), (4, 4), (5, 5) modes already implemented in SEOBNRv4HM, iii) is calibrated to larger mass-ratios and spins using a catalog of 442 numerical-relativity (NR) simulations and 13 additional waveforms from black-hole perturbation theory, iv) incorporates information from second-order gravitational self-force (2GSF) in the nonspinning modes and radiation-reaction force. Computing the unfaithfulness against NR simulations, we find that for the dominant (2, 2) mode the maximum unfaithfulness in the total mass range $10-300 M_{\odot}$ is below $10^{-3}$ for 90% of the cases (38% for SEOBNRv4HM). When including all modes up to l = 5 we find 98% (49%) of the cases with unfaithfulness below $10^{-2} (10^{-3})$, while these numbers reduce to 88% (5%) when using SEOBNRv4HM. Furthermore, the model shows improved agreement with NR in other dynamical quantities (e.g., the angular momentum flux and binding energy), providing a powerful check of its physical robustness. We implemented the waveform model in a high-performance Python package (pySEOBNR), which leads to evaluation times faster than SEOBNRv4HM by a factor 10 to 50, depending on the configuration, and provides the flexibility to easily include spin-precession and eccentric effects, thus making it the starting point for a new generation of EOBNR waveform models (SEOBNRv5) to be employed for upcoming observing runs of the LIGO-Virgo-KAGRA detectors.

gr-qc↗

arXiv2026

A comprehensive look into the accuracy of SpEC binary black hole waveforms

Numerical relativity simulations provide a full description of the dynamics of binary systems, including gravitational radiation. The waveforms produced by these simulations have a number of applications in gravitational-wave detection and inference. In this work, we revisit the accuracy of the waveforms produced by the Spectral Einstein Code. Motivated by the wide range of waveform applications, we propose and explore three accuracy metrics between simulation resolutions: (i) the generalized frequency-weighted mismatch, (ii) the relative amplitude difference, and (iii) the phase difference at different times. We confirm that numerical errors accumulate over the binary evolution, but the error is not intrinsically larger during the latest, more dynamical stages. Studying errors across the parameter space, we identify a positive correlation between both the mismatch and the phase difference with precessing spin, but little correlation with aligned spin or eccentricity. Lastly, amplitude and phases differences are symmetric upon exchanging resolutions across the catalog, suggesting that the dominant source of error is random, rather than something systematic that affects all waveforms similarly.

gr-qc↗

arXiv2026

Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model SEOBNRv6EHM

Accurate and computationally efficient waveform models are required to infer the parameters of compact binaries from their gravitational wave (GW) emission. Among these parameters, orbital eccentricity serves as a smoking gun for dynamical formation channels and must be accounted for to avoid systematic errors in GW analyses. Here, we present SEOBNRv6EHM, a time-domain, multipolar waveform model for binaries on generic planar orbits, calibrated to quasi-circular (QC) numerical-relativity (NR) simulations from the SXS collaboration. In addition to the dominant $(2,2)$ mode, the model provides the $(2,1)$, $(3,3)$, $(3,2)$, $(4,4)$, and $(4,3)$ multipoles for the full inspiral-merger-ringdown process of coalescing binaries, as well as for dynamical captures and scattering encounters. The model is built within the effective-one-body (EOB) framework, and it employs novel resummations of the radiation-reaction force and waveform modes. We validate its accuracy through comparisons against 592 QC, 319 eccentric, one dynamical-capture, and two scattering SXS NR waveforms, and through scattering-angle comparisons against 61 SXS NR simulations. For QC and small-eccentricity binaries, its accuracy is comparable to previous-generation SEOBNRv5 models. For highly eccentric systems, however, SEOBNRv6EHM attains unprecedented accuracy, with waveform mismatches remaining below or close to $ 2\% $ across the total mass range $ 20-200\, \mathrm{M}_\odot $ for eccentricities up to $\sim 0.9$ at 14 periastron passages before merger. Additionally, SEOBNRv6EHM achieves waveform-generation walltimes that are $ 2 - 6 $ times faster than other state-of-the-art EOB eccentric models, enabling efficient and accurate applications in GW astronomy.

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arXiv2026

Assessing the Relative Importance of Neutrino Matter Interaction Channels in Post-Merger Remnant of Binary Neutron Stars

Neutron star mergers are amongst the most promising sources for the joint detection of gravitational waves and electromagnetic signals. They are also potential sites for the production of r-process elements and probes of the equation of state of matter above nuclear saturation density. Neutrino-matter interactions during and after merger strongly influence the thermodynamic evolution and composition of the remnant and its outflows, thereby affecting kilonova emission and nucleosynthesis yields. However, existing merger simulations remain limited by significant approximations in the treatment of neutrino transport and interaction rates. In this work, we assess the thermodynamic conditions under which neutrinos decouple from matter and show the effect of charged-current absorption, quasi-elastic scattering on nucleons and nuclei, pair-production processes, and inelastic neutrino-electron scattering for electron neutrinos, electron antineutrinos, and heavy-lepton neutrinos in the different thermodynamical conditions sampled by a simulation using an energy-dependent Monte Carlo neutrino transport. We first estimate opacities in the post-merger remnant assuming neutrinos in equilibria with the fluid, and find results consistent with previous studies performed on simulations using a gray two-moment scheme. We note the very distinct regions in which nucleon-nucleon Bremmstrahlung and electron-positron annihilation are active (high and low density regions, respectively). We then evaluate opacities using the actual distribution function of neutrinos within a Monte Carlo simulation. We show greatly increased pair annihilation rates in cold, low-density regions, especially for heavy-lepton neutrinos. We also show that inelastic scattering on electrons, which has not been included in merger simulations so far, makes important contributions to the thermalization of heavy-lepton neutrinos.

astro-ph.HE↗

arXiv2026

Biased parameter inference of eccentric, spin-precessing binary black holes

While the majority of gravitational wave (GW) events observed by the LIGO and Virgo detectors are consistent with mergers of binary black holes (BBHs) on quasi-circular orbits, some events are also consistent with non-zero orbital eccentricity, indicating that the binaries could have formed via dynamical interactions. Moreover, there may be GW events which show support for spin-precession, eccentricity, or both. In this work, we study the interplay of spins and eccentricity on the parameter estimation of GW signals from BBH mergers. We inject eccentric signals with no spins, aligned spins, and precessing spins using hybrids, TEOBResumS-DALI, and new Numerical Relativity (NR) simulations, respectively, and study the biases in the posteriors of source parameters when these signals are recovered with a quasi-circular precessing-spin waveform model, as opposed to an aligned-spin eccentric waveform model. We find significant biases in the source parameters, such as chirp mass and spin-precession ($χ_p$), when signals from highly-eccentric BBHs are recovered with a quasi-circular waveform model. Moreover, we find that for signals with both eccentricity and spin-precession effects, Bayes factor calculations confirm that an eccentric, aligned-spin model is preferred over a quasi-circular precessing-spin model. Our study highlights the complex nature of GW signals from eccentric, precessing-spin binaries and the need for readily usable inspiral-merger-ringdown eccentric, spin-precessing waveform models for unbiased parameter estimation.

gr-qc↗

arXiv2026

Including higher-order modes in a quadrupolar eccentric numerical relativity surrogate using universal eccentric modulation functions

\texttt{gwNRHME} is a framework that converts multi-modal (i.e., containing several spherical harmonic modes) quasi-circular waveforms into their eccentric counterparts, provided the quadrupolar eccentric mode is known, by exploiting universal eccentric modulation functions. Leveraging this framework, we combine the quasi-circular NR surrogate model \texttt{NRHybSur3dq8} with the quadrupolar, non-spinning, eccentric surrogate \texttt{NRSurE\_q4NoSpin\_22} to construct a multi-modal, non-spinning, eccentric model, denoted as \model{}, which includes nine modes: $(2,\{1,2\})$, $(3,\{1,2,3\})$, $(4,\{2,3,4\})$, and $(5,5)$. When compared against 156 eccentric SXS NR waveforms, \model{} achieves median frequency-domain mismatches (computed using the Advanced LIGO design sensitivity) of $\sim 9\times 10^{-5}$, with a standard deviation of $\sim 2 \times 10^{-4}$. To demonstrate the modularity of the framework, we further combine \texttt{NRSurE\_q4NoSpin\_22} with effective-one-body (EOB) models \texttt{SEOBNRv5HM} and \texttt{TEOBResumS-Dali} in their non-spinning limits, yielding eccentric waveforms with median mismatches of $\sim 2\times10^{-4}$ and $\sim 10^{-3}$, respectively, with standard deviation of $\sim 2 \times 10^{-3}$ and $\sim 2 \times 10^{-2}$ respectively. Finally, we provide both a surrogate model, \texttt{gwEccEvolve\_q4NoSpin\_Sur}, and an analytical model, \texttt{gwEccEvNSv2}, for the eccentricity evolution up to $2M$ before merger, based on eccentricity definitions derived from the universal modulation functions. The \texttt{gwNRHME} framework is publicly available through the \texttt{gwModels} package, and the resulting waveform models will be released via the \texttt{gwsurrogate} package.

gr-qc↗

arXiv2026

Gauge Boundary conditions to mitigate center-of-mass drift in BBH simulations

Long-term numerical relativity (NR) simulations of binary black hole (BBH) systems in the Spectral Einstein Code (SpEC) code exhibit an unexpected exponential drift of the center-of-mass (CoM) away from the simulation's origin. In our work, we analyze this phenomenon and demonstrate that it is not a physical effect but rather a manifestation of a gauge artifact. The origin of this drift is the reflection of the gauge waves off the outer boundary of the computational domain. These reflections are introduced by inaccuracies in the gauge boundary condition, specifically, the application of the Sommerfeld condition to the time derivative of the gauge fields. Such an approach fails to completely suppress or correctly absorb the outgoing modes, thereby generating artificial feedback into the simulation. To mitigate this problem, we introduce a modified boundary condition that incorporates an explicit CoM correction source term designed to counteract the CoM motion. Our numerical experiments, performed with the SpEC code, reveal that this new boundary treatment reduces the CoM drift by several orders of magnitude compared to the standard implementation, and does not introduce any unwanted physical artifacts.

gr-qc↗