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parGeMSLR: A Parallel Multilevel Schur Complement Low-Rank Preconditioning and Solution Package for General Sparse Matrices

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arXiv 2022年

作者： Xu, Tianshi Kalantzis, Vassilis Li, Ruipeng Xi, Yuanzhe Dillon, Geoffrey Saad, Yousef Department of Computer Science and Engineering University of Minnesota MinneapolisMN55455 United States Thomas J. Watson Research Center IBM Research Yorktown HeightsNY10598 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory P.O. Box 808 L-561 LivermoreCA94551 United States Department of Mathematics Emory University AtlantaGA30322 United States Department of Mathematics University of South Carolina ColumbiaSC29208 United States

This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner implemented in parGeMSLR is based on algebraic domain decomposition and partitions the symmetrized adjacency graph recursively into several non-overlapping partitions via a p-way vertex separator, where p is an integer multiple of the total number of MPI processes. From a numerical perspective, parGeMSLR builds a Schur complement approximate inverse preconditioner as the sum between the matrix inverse of the interface coupling matrix and a low-rank correction term. To reduce the cost associated with the computation of the approximate inverse matrices, parGeMSLR exploits a multilevel partitioning of the algebraic domain. The parGeMSLR library is implemented on top of the Message Passing Interface and can solve both real and complex linear systems. Furthermore, parGeMSLR can take advantage of hybrid computing environments with in-node access to one or more Graphics Processing Units. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLR is demonstrated on a few model problems arising from discretizations of 3D Partial Differential Equations. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

Impact of eccentricity and mean anomaly in numerical relativity mergers

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arXiv 2025年

作者： Nee, Peter James Gamboa, Aldo Pfeiffer, Harald P. Pompili, Lorenzo Ramos-Buades, Antoni Varma, Vijay Boyle, Michael Buonanno, Alessandra Enficiaud, Raffi Kidder, Lawrence E. Scheel, Mark A. Am Mühlenberg 1 Potsdam14476 Germany Departament de Física Universitat de les Illes Balears IAC3 – IEEC Crta. Valldemossa km 7.5 PalmaE-07122 Spain Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts Darmouth MA02747 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Department of Physics University of Maryland College ParkMD20742 United States Theoretical Astrophysics 350-17 California Institute of Technology PasadenaCA91125 United States

Accurate modelling of black hole binaries is critical to achieve the science goals of gravitational-wave detectors. Modelling such configurations relies strongly on calibration to numerical-relativity (NR) simulations. Binaries on quasi-circular orbits have been widely explored in NR, however, coverage of the broader 9-dimensional parameter space, including orbital eccentricity, remains sparse. This article develops a new procedure to control orbital eccentricity of binary black hole simulations that enables choosing initial data parameters with precise control over eccentricity and mean anomaly of the subsequent evolution, as well as the coalescence time. We then calculate several sequences of NR simulations that nearly uniformly cover the 2-dimensional eccentricity–mean anomaly space for equal mass, non-spinning binary black holes. We demonstrate that, for fixed eccentricity, many quantities related to the merger dynamics of binary black holes show an oscillatory dependence on mean anomaly. The amplitude of these oscillations scales nearly linearly with the eccentricity of the system. We find that for the eccentricities explored in this work, deviations in various quantities such as the merger amplitude and peak luminosity can approach ∼ 5% of their quasi-circular value. We use our findings to explain eccentric phenomena reported in other studies. We also show that methods for estimating the remnant mass employed in the effective-one-body approach exhibit similar deviations, roughly matching the amplitude of the oscillations we find in NR simulations. This work is an important step towards a complete description of eccentric binary black hole mergers, and demonstrates the importance of considering the entire 2-dimensional parameter subspace related to eccentricity. Copyright © 2025, The Authors. All rights reserved.

关键词： Relativity

Removing degeneracy and multimodality in gravitational wave source parameters

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Physical Review D 2022年第12期106卷 123015-123015页

作者： Javier Roulet Seth Olsen Jonathan Mushkin Tousif Islam Tejaswi Venumadhav Barak Zackay Matias Zaldarriaga Kavli Institute for Theoretical Physics University of California at Santa Barbara Santa Barbara California 93106 USA Department of Physics Princeton University Princeton New Jersey 08540 USA Department of Particle Physics and Astrophysics Weizmann Institute of Science Rehovot 76100 Israel Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics University of California at Santa Barbara Santa Barbara California 93106 USA International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA

Quasicircular binary black hole mergers are described by 15 parameters, of which gravitational wave observations can typically constrain only ∼10 independent combinations to varying degree. In this work, we devise coordinates that remove correlations, and disentangle well- and poorly-measured quantities. Additionally, we identify approximate discrete symmetries in the posterior as the primary cause of multimodality, and design a method to tackle this type of multimodality. The resulting posteriors have little structure and can be sampled efficiently and robustly. We provide a python package for parameter estimation, cogwheel, that implements these methods together with other algorithms for accelerating the inference process. One of the coordinates we introduce is a spin azimuth that is measured remarkably well in several events. We suggest this might be a sensitive indicator of orbital precession, and we anticipate that it will shed light on the occurrence of spin-orbit misalignment in nature.

关键词： Gravitational waves Astronomical black holes

DiuSST: A conceptual model of diurnal warm layers for idealized atmospheric simulations with interactive SST

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arXiv 2022年

作者： Börner, Reyk Haerter, Jan O. Fiévet, Romain Niels Bohr Institute University of Copenhagen Copenhagen Denmark Department of Mathematics and Statistics University of Reading Reading United Kingdom Leibniz Center for Tropical Marine Research Bremen Germany Constructor University Bremen Bremen Germany Department of Physics and Astronomy University of Potsdam Potsdam Germany Scientific Computing Lab. Max Planck Institute for Meteorology Hamburg Germany

The diurnal variability of sea surface temperature (SST) may play an important role for cloud organization above the tropical ocean, with implications for precipitation extremes, storminess, and climate sensitivity. Recent cloud-resolving simulations demonstrate how imposed diurnal SST oscillations can strongly, and delicately, impact mesoscale convective organization. In spite of this nuanced interaction, many idealized modeling studies of tropical convection either assume a constant, homogeneous SST or, in case of a responsive sea surface, represent the upper ocean by a slab with fixed thickness. Here we show that slab ocean models with constant heat capacity fail to capture the wind-dependence of observed diurnal sea surface warming. To alleviate this shortcoming, we present a simple, yet explicitly depth-resolved model of upper-ocean temperature dynamics under atmospheric forcing. Our modular scheme describes turbulent mixing as diffusion with a wind-dependent diffusivity, in addition to a bulk mixing term and heat fluxes entering as sources and sinks. Using observational data, we apply Bayesian inference to calibrate the model. In contrast with a slab model, our model captures the exponential reduction of the diurnal warming amplitude with increasing wind speed. Further, our model performs comparably to a more elaborately parameterized diurnal warm layer model. Formulated as a single partial differential equation with three key tuning parameters, the model is suitable as an interactive numerical boundary condition for idealized atmospheric simulations. © 2022, CC BY-SA.

关键词： Surface temperature

Phenomenology and origin of late-time tails in eccentric binary black hole mergers

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arXiv 2024年

作者： Islam, Tousif Faggioli, Guglielmo Khanna, Gaurav Field, Scott E. van de Meent, Maarten Buonanno, Alessandra Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Max Planck Institute for Gravitational Physics Albert Einstein Institute Am M¨uhlenberg 1 Potsdam14476 Germany Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 Copenhagen2100 Denmark

We investigate the late-time tail behavior in gravitational waves from merging eccentric binary black holes (BBH) using black hole perturbation theory. For simplicity, we focus only on the dominant quadrupolar mode of the radiation. We demonstrate that such tails become more prominent as eccentricity increases. Exploring the phenomenology of the tails in both spinning and non-spinning eccentric binaries, with the spin magnitude varying from χ = −0.6 to χ = +0.6 and eccentricity as high as e = 0.98, we find that these tails can be well approximated by a slowly decaying power law. We study the power law for varying systems and find that the power law exponent lies close to the theoretically expected value −4. Finally, using both plunge geodesic and radiation-reaction-driven orbits, we perform a series of numerical experiments to understand the origin of the tails in BBH simulations. Our results suggest that the late-time tails are strongly excited in eccentric BBH systems when the smaller black hole is in the neighborhood of the apocenter, as opposed to any structure in the strong field of the larger black hole. Our analysis framework is publicly available through the gwtails Python package. Copyright © 2024, The Authors. All rights reserved.

关键词： Black holes

Impacts of oxytactic microorganisms and viscous dissipation in Carreau nanoliquid featuring ferromagnetic nanoparticles

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Partial Differential Equations in Applied mathematics 2025年 13卷

作者： Tabrez, Muhammad Hussain, I. Khan, W.A. Khan, S.U. Waqas, M. Rashid, Rzgar Farooq Anwar, M.I. Ammar, Mohamed Ben Zamri, Nurnadiah Abiyev, Ruzimurod Garalleh, Hakim AL Department of Mathematics Mohi-ud-Din Islamic University Nerian Sharif Azad Jammu and Kashmir 12010 Pakistan Department of Mathematics Namal University Mianwali 42250 Pakistan NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Medical Laboratory Science College of Science Knowledge University Erbil 44001 Iraq Department of Medical Laboratory Technique College of Medical Technology AL-Kitab University Kirkuk Iraq Department of Mathematics School of Sciences and Humanities Nazarbayev University Astana Kazakhstan Center for Scientific Research and Entrepreneurship Northern Border University Arar 73213 Saudi Arabia Department of Mathematics and its Teaching Methods in Primary Education Tashkent State Pedagogical University Tashkent Uzbekistan Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia

Owing to rapid progress in field of nanotechnology, various mathematical model has been proposed regarding the flow of nanofluids. Based on boosted thermal properties, multidisciplinary applications of such materials has been claimed in various engineering and industrial processes. In current work, a theoretical analysis is performed for bioconvective flow of Carreau fluid with applications of magnetic dipole. The significance of magnetic dipole are presented with interaction of ferrofluid. The applications of viscous dissipation have also been entertained. The flow is subject to applications of stretched surface. Similarity variables are used for making transformation to obtain set of nonlinear ODEs from set of PDEs. The numerical computation is also made by using of well-known numerical method termed as bvp4c. Influences of various non dimensional fluid parameters like Brownian motion, viscous dissipation, Curie temperature, Weissenberg number, motile difference parameter and bioconvection Paclet number are examined and expressed graphically. It is perceived that ferrofluid's concentration declines when Brownian diffusive variable is augmented while opposite characteristics are reported for Schmidt number. Current results conveying applications in the biofuels, better heat transport medium, fertilizers, catalysts, electronics, paints, semiconductors, speakers, drug delivery, fertilizers etc. © 2024 The Author(s)

关键词： Bioconvection Carreau fluid Ferromagnetic flow Magnetic dipole Viscous dissipation

Impact of subdominant modes on the interpretation of gravitational-wave signals from heavy binary black hole systems

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Physical Review D 2020年第12期101卷 124054-124054页

作者： Feroz H. Shaik Jacob Lange Scott E. Field Richard O’Shaughnessy Vijay Varma Lawrence E. Kidder Harald P. Pfeiffer Daniel Wysocki Department of Physics Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Center for Computational Relativity and Gravitation Rochester Institute of Technology Rochester New York 14623 USA Department of Mathematics and the Center for Scientific Computing & Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Theoretical Astrophysics California Institute of Technology Pasadena California 91125 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 14476 Potsdam Germany

Over the past year, a handful of new gravitational wave models have been developed to include multiple harmonic modes thereby enabling for the first time fully Bayesian inference studies including higher modes to be performed. Using one recently developed numerical relativity surrogate model, NRHybSur3dq8, we investigate the importance of higher modes on parameter inference of coalescing massive binary black holes. We focus on examples relevant to the current three-detector network of observatories, with a detector-frame mass set to 120 M⊙ and with signal amplitude values that are consistent with plausible candidates for the next few observing runs. We show that for such systems the higher mode content will be important for interpreting coalescing binary black holes, reducing systematic bias, and computing properties of the remnant object. Even for comparable-mass binaries and at low signal amplitude, the omission of higher modes can influence posterior probability distributions. We discuss the impact of our results on source population inference and self-consistency tests of general relativity. Our work can be used to better understand asymmetric binary black hole merger events, such as GW190412. Higher modes are critical for such systems, and their omission usually produces substantial parameter biases.

关键词： Gravitational waves

Numerical simulations of black hole-neutron star mergers in scalar-tensor gravity

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Physical Review D 2023年第12期107卷 124051-124051页

作者： Sizheng Ma Vijay Varma Leo C. Stein Francois Foucart Matthew D. Duez Lawrence E. Kidder Harald P. Pfeiffer Mark A. Scheel TAPIR 350-17 California Institute of Technology 1200 E California Boulevard Pasadena California 91125 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-14476 Potsdam Germany Department of Physics Cornell University Ithaca New York 14853 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics and Astronomy The University of Mississippi University Mississippi 38677 USA Department of Physics and Astronomy University of New Hampshire 9 Library Way Durham New Hampshire 03824 USA Department of Physics and Astronomy Washington State University Pullman Washington 99164 USA

We present a numerical-relativity simulation of a black hole-neutron star merger in scalar-tensor (ST) gravity with binary parameters consistent with the gravitational wave event GW200115. In this exploratory simulation, we consider the Damour-Esposito-Farèse extension to Brans-Dicke theory, and maximize the effect of spontaneous scalarization by choosing a soft equation of state and ST theory parameters at the edge of known constraints. We extrapolate the gravitational waves, including tensor and scalar (breathing) modes, to future null-infinity. The numerical waveforms undergo ∼22 wave cycles before the merger, and are in good agreement with predictions from post-Newtonian theory during the inspiral. We find the ST system evolves faster than its general-relativity (GR) counterpart due to dipole radiation, merging a full gravitational-wave cycle before the GR counterpart. This enables easy differentiation between the ST waveforms and GR in the context of parameter estimation. However, we find that dipole radiation’s effect may be partially degenerate with the NS tidal deformability during the late inspiral stage, and a full Bayesian analysis is necessary to fully understand the degeneracies between ST and binary parameters in GR.

关键词： Alternative gravity theories General relativity Gravitation Gravitational waves

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The RQR algorithm

Linear Algebra and Its Applications 2025年

作者： Camps, Daan Mach, Thomas Vandebril, Raf Watkins, David S. National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory United States University of Potsdam Institute of Mathematics Karl-Liebknecht-Str. 24–25 Potsdam14476 Germany Department of Computer Science KU Leuven Belgium Department of Mathematics Washington State University United States

Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A−λB. It is natural to try to devise a pole-swapping algorithm that solves the standard eigenvalue problem for a single matrix A. This paper introduces such an algorithm and shows that it is competitive with Francis's bulge-chasing QR algorithm. © 2025 Elsevier Inc.

关键词： Eigenvalues and eigenfunctions