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These lecture notes accompany two classes given at the NRHEP2 school.
Über matrizen die beschränkte halbgruppen erzeugen
Heinz-Otto Kreiss · 1959
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Local boundary conditions for dissipative symmetric linear differential operators
P. D. Lax and R. S. Phillips · 1960
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Lectures on quantum mechanics
Paul A. M. Dirac · 1964
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Initial boundary value problems for hyperbolic systems
Heinz-Otto Kreiss · 1970
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Theorem on matrices depending on parameters and its applications to hyperbolic systems
M. S. Agranovich · 1972
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Perturbations of a rotating black hole. I. fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations
Saul A. Teukolsky · 1973
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Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary
A. Majda and S. Osher · 1975
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Pseudodifferential operators / Michael E. Taylor
Michael E. Taylor · 1981
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Symmetric positive systems with boundary characteristics of constant multiplicity
J. Rauch · 1985
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General relativistic collapse to black holes and gravitational waves from black holes
Takashi Nakamura, Ken-ichi Oohara, and Yasufumi Kojima · 1987
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Initial-boundary value problems and the Navier-Stokes equations
Heinz Otto Kreiss and J. Lorenz · 1989
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Time dependent problems and difference methods
Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger · 1995
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Evolution of three-dimensional gravitational waves: Harmonic slicing case
M. Shibata and T. Nakamura · 1995
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The initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity
Paolo Secchi · 1996
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On the Numerical integration of Einstein’s field equations
T. W. Baumgarte and S. L. Shapiro · 1998
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The Cauchy problem and the initial boundary value problem in numerical relativity
J.M.Stewart · 1998
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Characteristic evolution and matching
Jeffrey Winicour · 1998
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Classical Electrodynamics
John David Jackson · 1999
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Einstein’s equations with asymptotically stable constraint propagation
O. Brodbeck, S. Frittelli, P. Hübner, and O. A. Reula · 1999
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The block structure condition for symmetric hyperbolic systems
Guy Métivier · 2000
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Illustrating stability properties of numerical relativity in electrodynamics
A. M. Knapp, E. J. Walker, and Thomas W. Baumgarte · 2002
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Detecting ill posed boundary conditions in general relativity
Gioel Calabrese and Olivier Sarbach · 2003
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Controlling the growth of constraints in hyperbolic evolution systems
Lee Lindblom, Mark A. Scheel, Lawrence E. Kidder, Harald P. Pfeiffer, Deirdre Shoemaker, and Saul A. Teukolsky · 2004
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Strongly hyperbolic systems in general relativity
Oscar A. Reula · 2004
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Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints
Carsten Gundlach and Jose M. Martin-Garcia · 2004
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Strongly hyperbolic second order Einstein’s evolution equations
G. Nagy, O. E. Ortiz, and O. A. Reula · 2004
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Conformal infinity
Jörg Frauendiener · 2004
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A Model problem for the initial-boundary value formulation of Einstein’s field equations
Oscar Reula and Olivier Sarbach · 2005
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Constraint damping in the Z4 formulation and harmonic gauge
Carsten Gundlach, Jose M. Martin-Garcia, G. Calabrese, and I. Hinder · 2005
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Hyperbolicity of second-order in space systems of evolution equations
Carsten Gundlach and Jose M. Martín-García · 2006
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Numerical Relativity: Solving Einstein’s Equations on the Computer
Thomas Baumgarte and Stuart Shapiro · 2010
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The Current Status of Binary Black Hole Simulations in Numerical Relativity
Ian Hinder · 2010
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An Introduction to the theory of rotating relativistic stars
Eric Gourgoulhon · 2010
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Initial-boundary value problems for second order systems of partial differential equations
H.-O. Kreiss, O. E. Ortiz, and N. A. Petersson · 2010
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Action principle for Numerical Relativity evolution systems
C. Bona, C. Bona-Casas, and C. Palenzuela · 2010
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Problems which are well-posed in a generalized sense with applications to the Einstein equations
Heinz-Otto Kreiss and Jeffrey Winicour · 2006
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Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
Oliver Rinne · 2006
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Asymptotically null slices in numerical relativity: Mathematical analysis and spherical wave equation tests
Gioel Calabrese, Carsten Gundlach, and David Hilditch · 2006
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3+1 formalism and bases of numerical relativity
Eric Gourgoulhon · 2007
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Constraint Damping in First-Order Evolution Systems for Numerical Relativity
Robert Owen · 2007
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Outer boundary conditions for einstein’s field equations in harmonic coordinates
Milton Ruiz, Oliver Rinne, and Olivier Sarbach · 2007
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An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
Oliver Rinne · 2010
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Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
C. Reisswig, N.T. Bishop, D. Pollney, and B. Szilagyi · 2010
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Hyperbolicity of Hamiltonian formulations in General Relativity
Ronny Richter and David Hilditch · 2011
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Action Principle for the Generalized Harmonic Formulation of General Relativity
J. David Brown · 2011
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Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity
Sebastiano Bernuzzi, Alessandro Nagar, and Anil Zenginoglu · 2011
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Numerical simulations of compact object binaries
Harald P. Pfeiffer · 2012
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Continuum and discrete initial-boundary value problems and einstein’s field equations
Olivier Sarbach and Manuel Tiglio · 2012
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Hyperbolic formulations of General Relativity with Hamiltonian structure
David Hilditch and Ronny Richter · 2012
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Constraint damping for the Z4c formulation of general relativity
Andreas Weyhausen, Sebastiano Bernuzzi, and David Hilditch · 2012
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Numerical relativity in higher dimensions
Ulrich Sperhake · 2013
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Hyperbolicity of Force-Free Electrodynamics
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Hyperbolicity of High Order Systems of Evolution Equations
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Lecture Notes: Numerical Relativity in higher dimensional spacetimes
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Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
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General relativistic null-cone evolutions with a high-order scheme
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The initial boundary value problem of the Z4c formulation of General Relativity
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