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LOCAL foilset Master Foilset of Detailed Discussion of Numerical Formulation and Solution of Collision of two Black Holes

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


Table of Contents for Master Foilset of Detailed Discussion of Numerical Formulation and Solution of Collision of two Black Holes


1 Separate IMAGE * Separate HTML CPS713 Module on Numerical Simulation of the Collision of two Black Holes as part of Case Study (II) on CFD and Numerical Relativity
2 Separate IMAGE * Separate HTML Abstract of Module on Numerical Simulation of the Collision of two Black Holes
3 Separate IMAGE * Separate HTML References for CPS713 Module on Numerical Simulation of the Collision of two Black Holes
4 Separate IMAGE * Separate HTML The Spirit of General Relativity as a Description of Gravitational Forces as the Structure of Space-Time
5 Separate IMAGE * Separate HTML General Relativity as a Theory of Distorted Space-Time
6 Separate IMAGE * Separate HTML The Space-Time Structure Created by a Heavy Bowling Ball
7 Separate IMAGE * Separate HTML The Path of a Marble in a Distorted Space-Time
8 Separate IMAGE * Separate HTML Basic Notation for Numerical Formulation of Einstein's Equations
9 Separate IMAGE * Separate HTML The Metric Tensor in Einstein's Formulation of General Relativity-I
10 Separate IMAGE * Separate HTML The Metric Tensor in Einstein's Formulation of General Relativity-II
11 Separate IMAGE * Separate HTML Why Study General Relativity Numerically
12 Separate IMAGE * Separate HTML Some Tests of General Relativity
13 Separate IMAGE * Separate HTML More Tests of General Relativity
14 Separate IMAGE * Separate HTML Equivalence Principle
15 Separate IMAGE * Separate HTML Initial Value Formulation of General Relativity
16 Separate IMAGE * Separate HTML Projection of Einstein's Equations onto Spacial Surfaces
17 Separate IMAGE * Separate HTML Structure of Einstein's Equations in Initial Formulation
18 Separate IMAGE * Separate HTML Linearization of Time Evolution Equations for q ij
19 Separate IMAGE * Separate HTML Structure of Numerical Relativity Equations in terms of 3 by 3 matrices q and K
20 Separate IMAGE * Separate HTML Coodinate and Foliation Choices in General Relativity
21 Separate IMAGE * Separate HTML The Lapse and Shift in Gauge Transformations
22 Separate IMAGE * Separate HTML Geometrical Picture for Lapse and Shift Gauge Transformations
23 Separate IMAGE * Separate HTML Notation for Einstein's Equations in Initial Value Formulation
24 Separate IMAGE * Separate HTML The Four Elliptic Constraint Equations in Initial Value Formulation of Einstein's Equations
25 Separate IMAGE * Separate HTML The Twelve Hyperbolic Evolution Equations in Initial Value Formulation of Einstein's Equations
26 Separate IMAGE * Separate HTML A benchmark Numerical Relativity problem
27 Separate IMAGE * Separate HTML Characteristic Surfaces and Key Features of Pittsburgh Approach
28 Separate IMAGE * Separate HTML Numerical Formulation of Three Dimensional Wave Equation in Polar Coordinates
29 Separate IMAGE * Separate HTML Compactification and Computational Variables for Three Dimensional Wave Equation
30 Separate IMAGE * Separate HTML Final Computational Formulation of Pittsburgh Benchmark
31 Separate IMAGE * Separate HTML Final Computational Formulation of Pittsburgh Benchmark -- Diagram
32 Separate IMAGE * Separate HTML Discretization of Computational Formulation of 3D Wave Equation
33 Separate IMAGE * Separate HTML Finite Volume Integral Formulation of Differencing Equations
34 Separate IMAGE * Separate HTML Stable Finite Difference Form of Discretized Pittsburgh Wave Equations-I
35 Separate IMAGE * Separate HTML Stable Finite Difference Form of Discretized Pittsburgh WaveEquations-II

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