Numerical relativity: Computational methods by Harald Pfeiffer

PROGRAM : GRAVITATIONAL WAVE ASTROPHYSICS (ONLINE)

ORGANIZERS : Parameswaran Ajith, K. G. Arun, Sukanta Bose, Bala R. Iyer, Resmi Lekshmi and B Sathyaprakash

DATE : 18 May 2020 to 22 May 2020
VENUE : ONLINE Meeting

Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the summer school will be conducted through online lectures. ​

The program involves two components. The first fortnight (18﹣22 May) involves a summer school for students and young researchers, that is part of the annual summer schools on gravitational-wave astronomy. The second fortnight (25 May﹣5 June) involves a workshop for active researchers working on gravitational wave astronomy, astrophysics, and related areas.

This year’s summer school will focus on the multimessenger modeling of compact binary mergers, involving four graduate-level courses on numerical relativity, numerical hydrodynamics, and the modeling of short gamma-ray bursts and kilonovae.

The workshop will focus on two broad themes: The first week (25 ﹣ 29 May) will focus on compact binary merger physics and multimessenger astrophysics, while the second week (1 ﹣ 5 June) will focus on black hole physics and astrophysics using gravitational-wave observation.

0:00:00 Numerical solution of PDES
0:04:02 Hyperbolic
0:05:31 First Order Reduction of wave equation
0:10:42 e.g Scalar wave
0:11:07 Characteristic Modes
0:15:43 Eigenvalue problem
0:18:00 Theorem
0:20:06 Example
0:23:00 Characteristic fields of the solar wave
0:24:04 3 zero - speed fields
0:28:33 Numerical Solution of PDES
0:32:37 Finite Differences
0:34:06 represent solution at discrete points
0:36:03 FD formulas by Taylor exp
0:38:25 into Example Equations
0:42:48 Method of Lines
0:46:15 Example solution, advection equation
0:49:42 Exercise
0:55:01 Runge - Kutta 2 aka midpoint rule
0:59:03 Runge - Kutta 4
0:59:14 Dormand - Prinu 853
1:04:55 Spectral Methods
1:05:40 Consider Fourier Suite
1:08:39 Exponential decay - fecs basis - function give high accuracy.
1:09:20 How to implement?
1:11:30 Method of lines as in FD
1:13:31 Non-periodic domains
1:14:59 Non smooth data
1:15:46 In Practice - Spectral Einstein Code
1:17:26 Discontinuous Galerkin
1:19:11 On each element, expand in basis functions
1:22:57 Basin - functions flexible
1:24:37 Interpolating Lagrange Polynomials
1:27:51 Evaluate
1:29:06 Reguine Local
1:31:03 Define unique flux
1:32:35 Integrate by parts backwards
1:33:20 Towards Equations for coefficients
1:38:05 Methods of Lines Form
1:39:56 Q&A