Numerical Relativity Excercises and Lectures for PiTP 2009

see the group resources page for some information on the required software

Lecture Notes (pdf format)

     Small amplitude scalar field evolution
     Large amplitude scalar field evolution
     Critical amplitude scalar field evolution---code coordinates
     Critical amplitude scalar field evolution---log coordinates
     Critical amplitude reflection anti-symmetric data
     Constraint damping example (single black hole)
     Black hole merger, lapse function
     Black hole merger, gravitational waves
     Lapse function, harmonic gauge (soliton collision)
     Lapse function, damped harmonic gauge (soliton collision)
     Scalar field, compactified (code) coordinates
     Scalar field, uncompactified coordinates
     Apparent horizon from black hole merger


Project 1: Scalar Wave Evolution on a Schwarzschild Background

The following project is one of the problems given at the Graduate Summer School on General Relativistic Hydrodynamics, in Vancouver, 2003.

Project Handout

Using the following as a template for this project:

How to solve a 1D flat space wave equation with RNPL. Code: w1dcnm.tar.gz

RNPL source, Makefile and sample ID file demonstrating how to add Kreiss Oliger dissipation to the Klein-Gordon equation in spherically symmetric Minkowksi spacetime: kg_rnpl, Makefile, id0

Project 2: Gravitational collapse in the Einstein-Klein-Gordon system

Project Handout

If you want to begin from scratch, use your code from Project 1 as a skeleton to begin Project 2.
Source and Makefile for model elliptic problem: model_elliptic.f, Makefile

Alternatively, here is source code for a program including the elements up to Problem 5 in the handout: emkg_5.tar.gz
This compressed tar-ball contains the source, plus a couple of example run time parameter files in two directories "strong_field_id" (forms a black hole) and "weak_field_id" (does not). See the ".laliases" file in each directory for an alias command that demonstrates how to use these parameter files.

Some of the material presented here is based upon work supported in part by the National Science Foundation under Grant No. 0745779

last updated: July 27, 2009