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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
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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
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Basic Motivation of General Relativity and its experimental tests
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Metric Tensor, its derivatives and Einstein's equations
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Initial value formulation and structure of elliptic and hyperbolic equations
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Examination of particular finite difference scheme for the Wave equation in three dimensions -- a study to understand large distances issues in solving numerical relativity
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS713NumRel96master Master Foilset of Detailed Discussion of
Numerical Formulation and Solution of
Collision of two Black Holes
NPACScreenDumps96 Collection of GIF Images for General NPAC
Projects April96-
Numerical Relativity and Solution as set of PDE's
CPS713NumRel96master 001 001 CPS713 Module on Numerical
Simulation of the Collision of two
Black Holes as part of Case Study
(II) on CFD and Numerical Relativity
CPS713NumRel96master 002 002 Abstract of Module on Numerical
Simulation of the Collision of two
Black Holes
CPS713NumRel96master 003 003 References for CPS713 Module on
Numerical Simulation of the
Collision of two Black Holes
CPS713NumRel96master 004 004 The Spirit of General Relativity as
a Description of Gravitational
Forces as the Structure of
Space-Time
CPS713NumRel96master 005 005 General Relativity as a Theory of
Distorted Space-Time
CPS713NumRel96master 006 006 The Space-Time Structure Created by
a Heavy Bowling Ball
CPS713NumRel96master 007 007 The Path of a Marble in a Distorted
Space-Time
CPS713NumRel96master 008 008 Basic Notation for Numerical
Formulation of Einstein's Equations
CPS713NumRel96master 009 009 The Metric Tensor in Einstein's
Formulation of General Relativity-I
CPS713NumRel96master 010 010 The Metric Tensor in Einstein's
Formulation of General Relativity-II
CPS713NumRel96master 011 011 Why Study General Relativity
Numerically
NPACScreenDumps96 002 012 An Example of Gravitational
Waveforms
NPACScreenDumps96 003 013 Two Polarizations of Gravitational
Waveforms
NPACScreenDumps96 004 014 A schematic view of a LIGO
Interferometer
NPACScreenDumps96 005 015 Schematic Layout of the Initial LIGO
facilities
NPACScreenDumps96 006 016 Expected Total Noise in each of
LIGO's first 4km interferometers
NPACScreenDumps96 007 017 Expected Signal versus Noise in
Gravitational Wave Detectors
CPS713NumRel96master 012 018 Some Tests of General Relativity
CPS713NumRel96master 013 019 More Tests of General Relativity
CPS713NumRel96master 014 020 Equivalence Principle
CPS713NumRel96master 015 021 Initial Value Formulation of General
Relativity
CPS713NumRel96master 016 022 Projection of Einstein's Equations
onto Spacial Surfaces
CPS713NumRel96master 017 023 Structure of Einstein's Equations in
Initial Formulation
CPS713NumRel96master 018 024 Linearization of Time Evolution
Equations for q ij
CPS713NumRel96master 019 025 Structure of Numerical Relativity
Equations in terms of 3 by 3
matrices q and K
CPS713NumRel96master 020 026 Coodinate and Foliation Choices in
General Relativity
CPS713NumRel96master 021 027 The Lapse and Shift in Gauge
Transformations
CPS713NumRel96master 022 028 Geometrical Picture for Lapse and
Shift Gauge Transformations
CPS713NumRel96master 023 029 Notation for Einstein's Equations in
Initial Value Formulation
CPS713NumRel96master 024 030 The Four Elliptic Constraint
Equations in Initial Value
Formulation of Einstein's Equations
CPS713NumRel96master 025 031 The Twelve Hyperbolic Evolution
Equations in Initial Value
Formulation of Einstein's Equations
Now discuss the Pittsburgh Benchmark
CPS713NumRel96master 026 032 A benchmark Numerical Relativity
problem
CPS713NumRel96master 027 033 Characteristic Surfaces and Key
Features of Pittsburgh Approach
CPS713NumRel96master 028 034 Numerical Formulation of Three
Dimensional Wave Equation in Polar
Coordinates
CPS713NumRel96master 029 035 Compactification and Computational
Variables for Three Dimensional Wave
Equation
CPS713NumRel96master 030 036 Final Computational Formulation of
Pittsburgh Benchmark
CPS713NumRel96master 031 037 Final Computational Formulation of
Pittsburgh Benchmark -- Diagram
CPS713NumRel96master 032 038 Discretization of Computational
Formulation of 3D Wave Equation
CPS713NumRel96master 033 039 Finite Volume Integral Formulation
of Differencing Equations
CPS713NumRel96master 034 040 Stable Finite Difference Form of
Discretized Pittsburgh Wave
Equations-I
CPS713NumRel96master 035 041 Stable Finite Difference Form of
Discretized Pittsburgh
WaveEquations-II
List of Foils Used as they occur
CPS713NumRel96master Master Foilset of Detailed Discussion of
Numerical Formulation and Solution of
Collision of two Black Holes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
NPACScreenDumps96 Collection of GIF Images for General NPAC
Projects April96-
2 3 4 5 6 7
Sorted List of Foils Used
CPS713NumRel96master Master Foilset of Detailed Discussion of
Numerical Formulation and Solution of
Collision of two Black Holes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
NPACScreenDumps96 Collection of GIF Images for General NPAC
Projects April96-
2 3 4 5 6 7
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