"Spectral Methods for Numerical Relativity"
by
Philippe Grandclément and Jérôme Novak
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Abstract
1
Introduction
1.1
About spectral methods
1.2
Spectral methods in physics
1.3
A simple example
2
Concepts in One Dimension
2.1
Best polynomial approximation
2.2
Interpolation on a grid
2.3
Polynomial interpolation
2.4
Usual polynomials
2.5
Spectral methods for ODEs
2.6
Multidomain techniques for ODEs
3
Multidimensional Cases
3.1
Spatial coordinate systems
3.2
Spherical coordinates and harmonics
3.3
Going further
4
Time-Dependent Problems
4.1
Time discretization
4.2
Imposition of boundary conditions
4.3
Discretization in space: stability and convergence
4.4
Fully-discrete analysis
4.5
Going further: High-order time schemes
5
Stationary Computations and Initial Data
5.1
Introduction
5.2
Single compact stars
5.3
Single black holes
5.4
Rings around black holes
5.5
Compact star binaries
5.6
Black-hole–binary systems
5.7
Black-hole–neutron-star binaries
5.8
Spacetimes with waves
5.9
Hyperboloidal initial data
6
Dynamic Evolution of Relativistic Systems
6.1
Single Stars
6.2
Vacuum and black hole evolutions
6.3
Binary systems
7
Conclusions
7.1
Strengths and weaknesses
7.2
Combination with other methods
7.3
Future developments
References
Footnotes
Updates
Figures