Event Title

Numerical solution of differential equations for analyzing black hole event horizons

Location

PANEL: Physical Investigations from Galactic Phenomena to the Classroom
Adam Joseph Lewis Center Hallock Auditorium

Document Type

Presentation

Start Date

5-13-2022 10:00 AM

End Date

5-13-2022 11:00 AM

Abstract

We present a solver capable of numerically computing the solution to a system of nonlinear partial differential equations (PDEs). Our long-term goal is to solve the embedding problem of a black hole horizon in Euclidean space by adding this solver to the Spectral Einstein Code (SpEC). Knowing that the PDEs involved in this problem are strongly nonlinear and nonstandard, we have used simple models of varying complexity to approximate the embedding conditions at each version. Current results imply a robust and efficient method combining the Newton-Raphson method (N-R) for the nonlinear equations and a generalized version of the biconjugate gradient stabilized method (BiCGSTAB) for the linear equations at each step of N-R.

Keywords:

Black hole, Embedding, Event horizon, Physics

Notes

Presenter: Iago Braz Mendes

Award

Science & Technology Research for a New Generation (STRONG)

Project Mentor(s)

Robert Owen, Physics; Computer Science

2022

This document is currently not available here.

Share

COinS
 
May 13th, 10:00 AM May 13th, 11:00 AM

Numerical solution of differential equations for analyzing black hole event horizons

PANEL: Physical Investigations from Galactic Phenomena to the Classroom
Adam Joseph Lewis Center Hallock Auditorium

We present a solver capable of numerically computing the solution to a system of nonlinear partial differential equations (PDEs). Our long-term goal is to solve the embedding problem of a black hole horizon in Euclidean space by adding this solver to the Spectral Einstein Code (SpEC). Knowing that the PDEs involved in this problem are strongly nonlinear and nonstandard, we have used simple models of varying complexity to approximate the embedding conditions at each version. Current results imply a robust and efficient method combining the Newton-Raphson method (N-R) for the nonlinear equations and a generalized version of the biconjugate gradient stabilized method (BiCGSTAB) for the linear equations at each step of N-R.