Bulletin of the American Physical Society
APS April Meeting 2023
Volume 68, Number 6
Minneapolis, Minnesota (Apr 15-18)
Virtual (Apr 24-26); Time Zone: Central Time
Session K08: Numerical Methods II |
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Sponsoring Units: DGRAV Chair: Geoffrey Lovelace, California State University, Fullerton Room: Symphony III - 2nd Floor |
Sunday, April 16, 2023 3:45PM - 3:57PM |
K08.00001: Simple conversion of gravitational waveforms to a transverse frame in numerical relativity Bernard J Kelly The dominant method of extracting gravitational waveforms from numerical simulations of compact-object mergers is through calculating the "outgoing" Weyl curvature scalar $psi_4$ at large but finite coordinate radii. While independent of the spacetime coordinates, this application of the Newman-Penrose formalism still depends on the choice of a suitable null tetrad field to define the "outgoing" direction, and a poorly chosen tetrad leads to pollution of the true outgoing radiation by other curvature quantities. In principle, this can be corrected by solving an eigenvalue problem involving all the numerical Weyl scalars, and using it to create a new null tetrad field in a transverse frame that eliminates the pollution of $psi_4$; however this is an unwieldy procedure that is usually not worth the additional computational effort. Here, we demonstrate a shortcut that allows a much simpler generation of the "unpolluted" $psi_4$ from the original $psi_i$ without explicit regeneration of the tetrad field. |
Sunday, April 16, 2023 3:57PM - 4:09PM |
K08.00002: Faster finite difference schemes for numerical relativity David W Neilsen, Yosef Zlochower, Milinda Fernando, Hari Sundar, Eric Hirschmann, Andrew Carroll, liwei Ji, Jackson Bates, David Van Komen Future advances in gravitational wave detector technology will provide both more accurate observations of merger events and observations from a wider variety of sources. The challenge for numerical relativity is to improve our numerical solutions of Einstein's equations by a commensurate amount. Dendro-GR is a new code for numerical relativity, which uses Wavelet Adaptive Multi-Resolution (WAMR) to construct unstructured meshes for massively parallel simulations. To further improve Dendro-GR's performance, we are testing compact finite difference schemes for evolving the Einstein equations in the BSSN formulation. Compact finite difference stencils can achieve equal or higher accuracy than standard finite differences with less communication for parallel runs. We will present some initial tests of compact finite differences with the BSSN equations in Dendro-GR, including measures of accuracy and performance gains. We will discuss some of the challenges that were encountered, and plans to further improve the code's performance for production-level simulations. |
Sunday, April 16, 2023 4:09PM - 4:21PM |
K08.00003: The discontinuous Galerkin method in the Nmesh program Wolfgang H Tichy, Liwei Ji, Ananya Adhikari, Alireza Rashti, Michal Pirog We present an introduction to the new Nmesh code, which uses a discontinuous Galerkin (DG) method that is intended to parallelize well. We explain our implementation of the DG method. In particular, we discuss a simplification in the normalization of the domain boundary normals. We are able to normalize them with a flat metric, even when the physical metric is far from flat. We also present recent results from single neutron star evolutions with and without a perturbation. Since the star matter is not smooth across the neutron star surface, this is challenging for a DG method. To address this problem we have developed a positivity limiter that together with exponential filters is enough to stabilize the evolution. |
Sunday, April 16, 2023 4:21PM - 4:33PM |
K08.00004: A discontinuous Galerkin method for the distributionally-sourced s=0 Teukolsky equation MANAS VISHAL, Scott E Field, Gaurav Khanna, Katie Rink The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) is primarily sensitive to Extreme Mass Ratio Inspirals (EMRI) where the mass ratio between two black holes is higher than 105. For the matched filtering process, we need a highly accurate template wave bank. In this talk, I will describe a Discontinuous Galerkin (DG) method for simulating waveforms from EMRI systems. We reduce the Teukolsky equation, which governs the behavior of EMRIs, to a set of coupled 1+1D wave equations and apply the DG method to it with a delta source term, acting like the secondary black hole in an EMRI system. Unlike other numerical schemes, our DG method can exactly incorporate the point particle behavior of the smaller black hole in the form of a delta function. Due to the spectral convergence properties of the scheme, our efficient method generates highly accurate waveforms in a very short time as compared to other methods. We have also introduced the hyperboloidal layers in our time domain solver that gives us access to the solution at null infinity. We verify our computation by computing Price tail power laws and scalar energy fluxes at null infinity. |
Sunday, April 16, 2023 4:33PM - 4:45PM |
K08.00005: A new adaptive mesh refinement method in the GR-Athena++ code Alireza Rashti It is barely feasible to find the analytical solution to astrophysically cataclysmic events, such as the merger of a binary black hole system. As such, the numerical relativity community has developed various techniques and infrastructures (codes) to find the answer and get insight into the physics of these astrophysical systems. Due to the lack of efficiency and the limited computational resources, numerical relativity codes refrain from using a monolithic and uniformly resolved mesh. Instead, an adaptive mesh refinement (AMR) is utilized in which the mesh adaptively uses different patches with a proportional resolution to resolve physical features of interest wherever necessary. Therefore, deciding what regions of the computational grid should be refined requires an appropriate criterion for the AMR. To achieve this goal, we look at the truncation error of the finite difference derivative in the GR-Athena++ code. In this method, refinement or de-refining of a region takes place according to this error. One of the advantages of this method is that the knowledge of the apparent horizons or the location of the punctures is not required. In other words, the refinement is smart enough to automatically resolve the region around the punctures, where it is needed most. Furthermore, this method ensures the magnitude of error is more or less uniform across the computational grid, i.e., unnecessary refinement is not taking place. Here, after a short introduction to GR-Athena++ code, we present some preliminary results of this new AMR method for an evolution of a binary black hole system. |
Sunday, April 16, 2023 4:45PM - 4:57PM |
K08.00006: Cauchy-Characteristic Matching in SpECTRE Kyle C Nelli, Sizheng Ma, Jordan E Moxon, Mark A Scheel The goal of numerical relativity is to extract waveforms at future null infinity so that they can be used in LIGO. A characteristic evolution of Einstein’s equations is well suited to do this because the equations are evolved on null hypersurfaces. However, these equations are ill-suited near the black holes (BHs) because the null hypersurfaces form caustics. So near the horizons we evolve Einstein's equations as a Cauchy initial value problem. The combination of using a Cauchy evolution near the BHs and a characteristic evolution in the wave-zone is known as Cauchy-Characteristic Evolution (CCE). This procedure is still subject to error because of the imperfect outer boundary conditions for the Cauchy evolution which are imposed at a finite radius. Cauchy-Characteristic Matching (CCM) solves this problem by imposing exact outer boundary conditions at null infinity for the characteristic evolution and hence for the Cauchy evolution by the matching conditions imposed at the finite outer boundary. I will present results of CCM simulations done with the SpECTRE code and compare them to simulations of CCE. |
Sunday, April 16, 2023 4:57PM - 5:09PM |
K08.00007: On constructing asymptotically flat initial data using the evolutionary formulation of the constraints Karoly Z Csukas Since the introduction of the evolutionary forms of the vacuum Einstein constraints, it has been a great challenge and desire to be able to construct asymptotically flat initial data sets. Here we introduce a method that, by controlling only the monopole part of a single freely specifiable variable, guarantees the asymptotic flatness of solutions to either the parabolic-hyperbolic or algebraic-hyperbolic formulations. Furthermore, our method includes a tuning parameter that allows the production of either strongly asymptotically flat or weakly asymptotically flat initial data with prescribed fall-off rates. To support our claims, we construct near Kerr initial data with various fall-off rates by integrating the evolutionary forms of the constraints numerically. |
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