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

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

001 CPS713 Module on Numerical Simulation of the Collision of two 
    Black Holes as part of Case Study (II) on CFD and Numerical 
    Relativity
002 Abstract of Module on Numerical Simulation of the Collision of two
     Black Holes
003 References for CPS713 Module on Numerical Simulation of the 
    Collision of two Black Holes
004 The Spirit of General Relativity as a Description of Gravitational
     Forces as the Structure of Space-Time
005 General Relativity as a Theory of Distorted Space-Time
006 The Space-Time Structure Created by a Heavy Bowling Ball
007 The Path of a Marble in a Distorted Space-Time
008 Basic Notation for Numerical Formulation of Einstein's Equations
009 The Metric Tensor in Einstein's Formulation of General 
    Relativity-I
010 The Metric Tensor in Einstein's Formulation of General 
    Relativity-II
011 Why Study General Relativity Numerically
012 Some Tests of General Relativity
013 More Tests of General Relativity
014 Equivalence Principle
015 Initial Value Formulation of General Relativity
016 Projection of Einstein's Equations onto Spacial Surfaces
017 Structure of Einstein's Equations in Initial Formulation
018 Linearization of Time Evolution Equations for q ij
019 Structure of Numerical Relativity Equations in terms of 3 by 3 
    matrices q and K
020 Coodinate and Foliation Choices in General Relativity
021 The Lapse and Shift in Gauge Transformations
022 Geometrical Picture for Lapse and Shift Gauge Transformations
023 Notation for Einstein's Equations in Initial Value Formulation
024 The Four Elliptic Constraint Equations in Initial Value 
    Formulation of Einstein's Equations
025 The Twelve Hyperbolic Evolution Equations in Initial Value 
    Formulation of Einstein's Equations
026 A benchmark Numerical Relativity problem
027 Characteristic Surfaces and Key Features of Pittsburgh Approach
028 Numerical Formulation of Three Dimensional Wave Equation in Polar 
    Coordinates
029 Compactification and Computational Variables for Three Dimensional
     Wave Equation
030 Final Computational Formulation of Pittsburgh Benchmark
031 Final Computational Formulation of Pittsburgh Benchmark -- Diagram
032 Discretization of Computational Formulation of 3D Wave Equation
033 Finite Volume Integral Formulation of Differencing Equations
034 Stable Finite Difference Form of Discretized Pittsburgh Wave 
    Equations-I
035 Stable Finite Difference Form of Discretized Pittsburgh 
    WaveEquations-II

Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu