Foilset Search Full Index for Scripted foilset

Detailed Discussion of Numerical Formulation and Solution of Collision 0f two Black Holes

Given by Geoffrey C. Fox at CPSP713 Case studies in Computational Science on Spring Semester 1996. Foils prepared 15 March 1996

This describes the structure of Numerical Relativity as a set of differential equations but it does discuss state of the art solvers involving adaptive meshes
Basic Motivation of General Relativity and its experimental tests
Metric Tensor, its derivatives and Einstein's equations
Initial value formulation and structure of elliptic and hyperbolic equations
Examination of particular finite difference scheme for the Wave equation in three dimensions -- a study to understand large distances issues in solving numerical relativity

This mixed presentation uses parts of the following base foilsets which can also be looked at on their own!
Master Foilset of Detailed Discussion of Numerical Formulation and Solution of Collision of two Black Holes
Collection of GIF Images for General NPAC Projects April96-

Table of Contents for Detailed Discussion of Numerical Formulation and Solution of Collision 0f two Black Holes

There are two types of foils -- html and image which are each available in basic and JavaScript enabled "focused" style
(basic:)(focus style:) Denote Foils where Image Critical
(basic:)(focus style:) Denote Foils where HTML is sufficient
Numerical Relativity and Solution as set of PDE's
1 CPS713 Module on Numerical Simulation of the Collision of two Black Holes as part of Case Study (II) on CFD and Numerical Relativity
2 Abstract of Module on Numerical Simulation of the Collision of two Black Holes
3 References for CPS713 Module on Numerical Simulation of the Collision of two Black Holes
4 The Spirit of General Relativity as a Description of Gravitational Forces as the Structure of Space-Time
5 General Relativity as a Theory of Distorted Space-Time
6 The Space-Time Structure Created by a Heavy Bowling Ball
7 The Path of a Marble in a Distorted Space-Time
8 Basic Notation for Numerical Formulation of Einstein's Equations
9 The Metric Tensor in Einstein's Formulation of General Relativity-I
10 The Metric Tensor in Einstein's Formulation of General Relativity-II
11 Why Study General Relativity Numerically
12 An Example of Gravitational Waveforms
13 Two Polarizations of Gravitational Waveforms
14 A schematic view of a LIGO Interferometer
15 Schematic Layout of the Initial LIGO facilities
16 Expected Total Noise in each of LIGO's first 4km interferometers
17 Expected Signal versus Noise in Gravitational Wave Detectors
18 Some Tests of General Relativity
19 More Tests of General Relativity
20 Equivalence Principle
21 Initial Value Formulation of General Relativity
22 Projection of Einstein's Equations onto Spacial Surfaces
23 Structure of Einstein's Equations in Initial Formulation
24 Linearization of Time Evolution Equations for q ij
25 Structure of Numerical Relativity Equations in terms of 3 by 3 matrices q and K
26 Coodinate and Foliation Choices in General Relativity
27 The Lapse and Shift in Gauge Transformations
28 Geometrical Picture for Lapse and Shift Gauge Transformations
29 Notation for Einstein's Equations in Initial Value Formulation
30 The Four Elliptic Constraint Equations in Initial Value Formulation of Einstein's Equations
31 The Twelve Hyperbolic Evolution Equations in Initial Value Formulation of Einstein's Equations
Now discuss the Pittsburgh Benchmark
32 A benchmark Numerical Relativity problem
33 Characteristic Surfaces and Key Features of Pittsburgh Approach
34 Numerical Formulation of Three Dimensional Wave Equation in Polar Coordinates
35 Compactification and Computational Variables for Three Dimensional Wave Equation
36 Final Computational Formulation of Pittsburgh Benchmark
37 Final Computational Formulation of Pittsburgh Benchmark -- Diagram
38 Discretization of Computational Formulation of 3D Wave Equation
39 Finite Volume Integral Formulation of Differencing Equations
40 Stable Finite Difference Form of Discretized Pittsburgh Wave Equations-I
41 Stable Finite Difference Form of Discretized Pittsburgh WaveEquations-II
Full WebWisdom URL and this Foilset Search
This contains all WebWisdom links preceded by those referenced in this foilset

List of WebWisdom URL's Used in this Foilset


key millerintro680 URL http://www.npac.syr.edu/techreports/html/0650/abs-0680.html * Introduction to Relativity for Computer Scientist by gcf on April 14,1996
Times 1 Foils referenced Script
key nratnpac URL http://www.npac.syr.edu/projects/bbh/more.html * Numerical Relativity Resources at NPAC by gcf on April 14,1996
Times 1 Foils referenced Script
key pittsbasef90 URL http://www.npac.syr.edu/projects/bbh/PITT_CODES/pitt_f90base.html * Fortran90 Implementation of Pittsburgh Code by gcf on April 14,1996
Times 1 Foils referenced Script
key pittsf77 URL http://www.npac.syr.edu/projects/bbh/PITT_CODES/pitt_f77.html * Pittsburgh's Original Fortran77 Code by gcf on April 14,1996
Times 1 Foils referenced Script
key pittshpf URL http://www.npac.syr.edu/projects/bbh/PITT_CODES/pitt_hpf.html * HPF Implementation of Pittsburgh Code by gcf on April 14,1996
Times 1 Foils referenced Script
key pittsintro681 URL http://www.npac.syr.edu/techreports/html/0650/abs-0681.html * Introduction to Pittsburgh Wave Evolution Code for Computer Scientist by gcf on April 14,1996
Times 1 Foils referenced Script
key pittsoriginal URL http://www.npac.syr.edu/projects/bbh/PITT_CODES/pitt.ps * Pittsburgh's Original Description of Their Wave Equation Evolution by gcf on April 14,1996
Times 1 Foils referenced Script
key slitex/bbhklasky URL http://pcwebwisdom/cdrom/foilsets/bbhklasky/index.html * Slitex Scott Klasky Presentation on Binary Black Hole Collision by gcf on Mon Feb 17 1997
Times 1 Foils referenced Script
© Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu

If you have any comments about this server, send e-mail to webmaster@npac.syr.edu.

Page produced by wwwfoil on Sun Feb 22 1998