1 / 25

Apply discontinous Galerkin method to Einstein equations

This paper explores the application of the discontinuous Galerkin method to the Einstein equations, with a focus on challenges in template construction for future detectors and related work in numerical relativity computation.

edwardlemon
Download Presentation

Apply discontinous Galerkin method to Einstein equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Apply discontinous Galerkin method to Einstein equations Zhoujian Cao Department of Astronomy, BNU 2019-1-4 Xiamen-CUSTIPEN workshop on EOS in the era of GWA

  2. Content • Introduction about GW data analysis and NR • Challenges about template construction for future detectors • Related work about NR computation • Summary

  3. arXiv: 1811.12907

  4. GW151226 ? 13, 5sigma

  5. Matched filtering and template

  6. GW template construction GW source? Solve Einstein equation!? NR

  7. History of NR • Hahn and Lindquist, first BBH simulation (1964) Unstable, Unstable, Unstable!!! • F. Pretorius, PRL 95, 121101 (2005); M. Campanelli et al, PRL 96, 111101 (2006); J. Baker et al, PRL 96, 111102 (2006) Stable finite difference code is available! • Caltech&Cornell group, PRD 79, 024003 (2009) Stable and extremely acurate spectral code is available! Only for BH • Caltech&Cornell group, JCP 335, 84 (2017) Highly parallel efficient finite element code is available! Only for GR fluid

  8. Future GW detectors • Mass ratio: 1<q<1e-10 • Eccentricity: 0<e<1 • Tidal disruption and tidal deformation • Neutron star right after merger • ……beyond GR, unexpected sources 1712.07345

  9. AMR within spectral method Divide the space to multi spectral domains One domain, one cpu Typically 60-80 cpus Most serious problem: hard to adjust domains for large mass ratio BBH

  10. Parallel problem of AMR Cao 2009

  11. FE numerical scheme Combine advantages: High convergence as spectra method + As high even more parallel ability as finite difference Brand new topic in NR!! Ji, Cai and Cao, 2018

  12. From Harmonic to GH require Still unstable! denote

  13. Move on to first order systems Unstable !

  14. Linearly degenerate or not ( ) Principle matrix: Characteristic variables: Characteristic speed:

  15. Linearly degenerate or not In order to make the system linearly degenerate, we need analytically But numerical error makes it fail to be linearly degenerate except Avoid numerical shocks, but Unstable!

  16. Linearly degenerate or not In order to make the system linearly degenerate, we need Avoid numerical shocks, but Unstable! Simplified estimate:

  17. Shock forms, but really stable!

  18. Simplified estimate:

  19. Cai, Cao, Fu, Ji, and Xia 2018

  20. P0: leading order polynomial P1: sub leading order polynomial

  21. Summary • GW data analysis and NR • Template for high mass ratio BBH; Post-merger waveform; …… [high efficiency] • Finite element with DG method for Einstein equations

More Related