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We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell.
Note on the Bondi-Metzner-Sachs group,
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Tensor and spinor spherical harmonics and the spin-s harmonics y-s-lm(theta, phi),
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The pseudospectral approximation applied to the shallow water equations on the sphere,
P. E. Merilees, · 1973
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C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco, 1973
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Kinematics and dynamics of general relativity,
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B. Fornberg, · 1995
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Spectral methods in general relativity – toward the simulation of 3D-gravitational collapse of neutron stars,
S. Bonazzola, J. Frieben, E. Gourgoulhon, J.-A. Marck, · 1996
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Fast shallow-water equation solvers in latitude-longitude coordinates,
W. F. Spotz, M. A. Taylor, P. N. Swarztrauber, · 1998
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B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1998
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Binary black hole mergers in 3D numerical relativity,
B. Brügmann, · 1999
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Double Fourier series on a sphere: applications to elliptic and vorticity equations,
H.-B. Cheong, · 2000
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Generalized discrete spherical harmonic transforms,
P. N. Swarztrauber, W. F. Spotz, · 2000
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L. N. Trefethen, Spectral methods in MATLAB, Society for Industrial and Applied Mathematics, 2000
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A MATLAB differentiation matrix suite,
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Computational harmonic analysis for tensor fields on the two-sphere,
P. Kostelec, D. K. Maslen, D. Rockmore, D. Healy, · 2000
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J. P. Boyd, Chebyshev and Fourier Spectral Methods (Second Edition, Revised), Dover Publications, New York, 2001
2001
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Simple excision of a black hole in 3+1 numerical relativity,
M. Alcubierre, B. Brügmann, · 2001
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A performance comparison of associated legendre projections,
W. F. Spotz, P. N. Swarztrauber, · 2001
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First-order symmetrizable hyperbolic formulations of Einstein’s equations including lapse and shift as dynamical fields,
K. Alvi, · 2002
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Harmonic coordinate method for simulating generic singularities,
D. Garfinkle, · 2002
Simulation of binary black hole spacetimes with a harmonic evolution scheme,
F. Pretorius, · 2006
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J. S. Hesthaven, S. Gottlieb, D. Gottlieb, Spectral Methods for Time-Dependent Problems, Cambridge University Press, Cambridge, 2007
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Fast spin +-2 spherical harmonics transforms,
Y. Wiaux, L. Jacques, P. Vandergheynst, · 2007
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Outer boundary conditions for einstein’s field equations in harmonic coordinates,
M. Ruiz, O. Rinne, O. Sarbach, · 2007
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Testing outer boundary treatments for the Einstein equations,
O. Rinne, L. Lindblom, M. A. Scheel, · 2007
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An explicit harmonic code for black-hole evolution using excision,
B. Szilágyi, D. Pollney, L. Rezzolla, J. Thornburg, J. Winicour, · 2007
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Cited alongside, same era.
Spherical harmonic projectors,
P. N. Swarztrauber, W. F. Spotz, · 2003
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A. Ben-Israel, T. Greville, Generalized inverses, Springer-Verlag, New York, 2003
2003
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General-covariant evolution formalism for numerical relativity,
C. Bona, T. Ledvinka, C. Palenzuela, M. Žáček, · 2003
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Numerical simulation of orbiting black holes,
B. Brügmann, W. Tichy, N. Jansen, · 2004
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Boundary conditions for the Einstein evolution system,
L. E. Kidder, L. Lindblom, M. A. Scheel, L. T. Buchman, H. P. Pfeiffer, · 2005
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Constraint damping in the Z4 formulation and harmonic gauge,
C. Gundlach, J. M. Martin-Garcia, G. Calabrese, I. Hinder, · 2005
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Calibration of Moving Puncture Simulations,
B. Brügmann, J. A. González, M. Hannam, S. Husa, U. Sperhake, W. Tichy, · 2008
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Spectral methods for numerical relativity,
P. Grandclément, J. Novak, · 2009
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Long term black hole evolution with the BSSN system by pseudo-spectral methods,
W. Tichy, · 2009
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M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi, GNU Scientific Library Reference Manual, Network Theory Ltd., 3rd edition edition, 2009
2009
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Implementation of higher-order absorbing boundary conditions for the Einstein equations,
O. Rinne, L. T. Buchman, M. A. Scheel, H. P. Pfeiffer, · 2009
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A spectral method for the wave equation of divergence-free vectors and symmetric tensors inside a sphere,
J. Novak, J.-L. Cornou, N. Vasset, · 2010
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An improved magma gemm for fermi graphics processing units,
R. Nath, S. Tomov, J. Dongarra, · 2010
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CUDA, NVIDIA, 2011. http://www.nvidia.com/object/cuda_home.html
2011
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The present work identified and reported an issue with the CUDA/CUBLAS 3.2 implementation of dgemm for the product of small matrices with matrices with one small and one large dimension. This was fixed in CUDA 4.0rc, 2011
2011
Closest in time.