# Parallel Spectral Numerical Methods/Bibliography

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{AllCah79} S.M. Allen, and J.W. Cahn, A microscopic theory for antiphase boundary motion and its applications to antiphase domain coarsening, Acta Metallurgica 27, 1085-1095, (1979).
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{BirRot89} G. Birkhoff, and G.C., Rota, Ordinary Differential Equations (4th ed.), Wiley, (1989).
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{BlaCasChaMur12} S. Blanes, F. Casas, P. Chartier and A. Murua, Splitting methods with complex coefficients for some classes of evolution equations, Mathematics of Computation (forthcoming) http://arxiv.org/abs/1102.1622
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{Bra06} B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson, (2006).
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{BofEck12} G. Boffetta and R.E. Ecke, Two-Dimensional Turbulence, Annual Review of Fluid Mechanics 44, 427-451, (2012).
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{BoyDip10} W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, (2010).
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{Boy01} J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, (2001). http://www-personal.umich.edu/~jpboyd/
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{CHQZ06} C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, (2006).
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{CHQZ07} C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer, (2007).
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{CloMuiRig12} B. Cloutier, B.K. Muite and P. Rigge, Performance of FORTRAN and C GPU Extensions for a Benchmark Suite of Fourier Pseudospectral Algorithms Forthcoming Proceedings of the Symposium on Application Accelerators in High Performancs computing (2012) http://arxiv.org/abs/1206.3215
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{CooTuk65} J.W. Cooley and J.W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation 19, 297-301, (1965).
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Courant, R.; John, F. (1999). Introduction to Calculus and Analysis. Vol. II. Springer.
{CouJoh98} R. Courant and F. John, Introduction to Calculus and Analysis I, II Springer (1998,1999)
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{DonSch11} R. Donninger and W. Schlag, Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation, Nonlinearity 24, 2547-2562, (2011).
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{DoeGib95} C.R. Doering and J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, (1995).
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{EliShu09} B. Eliasson and P. K. Shukla Nonlinear aspects of quantum plasma physics: Nanoplasmonics and nanostructures in dense plasmas Plasma and Fusion Research: Review Articles, 4, 32 (2009).
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{Eva10} L.C. Evans, Partial Differential Equations, American Mathematical Society, (2010).
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{For77} B. Fornberg, A numerical study of 2-D turbulence, Journal of Computational Physics 25, 1-31, (1977).
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{Gal02} G. Gallavotti, Foundations of Fluid Dynamics, Springer, (2002).
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{GotOrs77} D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, (1977).
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{Gre94} W. Grenier, Relativistic Quantum Mechanics, Springer, (1994)
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{GroLusSkj99} W. Gropp, E. Lusk and A. Skjellum, Using MPI, MIT Press, (1999).
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{GroLusTha99} W. Gropp, E. Lusk and R. Thakur, Using MPI-2, MIT Press, (1999).
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{HeiJohBur84} M.T. Heideman, D.H. Johnson and C.S. Burrus, Gauss and the History of the Fast Fourier Transform, IEEE ASSP Magazine 1(4), 1421, (1984).
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{HesGotGot07} J.S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral Methods for Time-Dependent Problems, Cambridge University Press, (2007).
Hughes-Hallett, D. (2008). Calculus, Single and Multivariable (5th ed.). Wiley. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
{HugEtAl08} D. Hughes-Hallett, A.M. Gleason, D.E. Flath, P.F. Lock, D.O. Lomen, D. Lovelock, W.G. MacCallum, D. Mumford, B. G. Osgood, D. Quinney, K. Rhea, J. Tecosky-Feldman, T.W. Tucker, and O.K. Bretscher, A. Iovita, W. Raskind, S.P. Gordon, A. Pasquale, J.B. Thrash, Calculus, Single and Multivariable, 5th ed. Wiley, (2008)
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{HolKarLieRis10} H. Holden, K.H. Karlsen, K.-A. Lie and N.H. Risebro, Splitting Methods for Partial Differential Equations with Rough Solutions, European Mathematical Society Publishing House, Zurich, (2010).
Tao, T. (2011). "Operator splitting for the KdV equation". Mathematics of Computation. 80: 821–846.
{HolKarRisTao11} H. Holden, K.H. Karlsen, N.H. Risebro and T. Tao, Operator splitting for the KdV equation, Mathematics of Computation 80, 821-846, (2011).
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{Ise09} A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, (2009).
{Joh12} R. Johnstone, Improved Scaling for Direct Numerical Simulations of Turbulence, HECTOR distributed Computational Science and Engineering Report, http://www.hector.ac.uk/cse/distributedcse/reports/ss3f-swt/
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{Kle08} C. Klein, Fourth order time-stepping for low dispersion Korteweg-De Vries and nonlinear Schrödinger equations, Electronic Transactions on Numerical Analysis 29, 116-135, (2008).
Roidot, K. (2011). "Numerical Study of Blowup in the Davey-Stewartson System". {{cite journal}}: Cite journal requires |journal= (help)
{KleMuiRoi11} C. Klein, B.K. Muite and K. Roidot, Numerical Study of Blowup in the Davey-Stewartson System, http://arxiv.org/abs/1112.4043
Klein, C.; Roidot, K. (2011). "Fourth order time-stepping for Kadomstev-Petviashvili and Davey-Stewartson Equations". SIAM Journal on Scientific Computation. 33: 3333–3356.
{KleRoi11} C. Klein and K. Roidot, Fourth order time-stepping for Kadomstev-Petviashvili and Davey-Stewartson Equations, SIAM Journal on Scientific Computation 33, 3333-3356, (2011).
Laizet, S.; Lamballais, E. (2009). "High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy". Journal of Computational Physics. 238: 5989–6015.
{LaiLam09} S. Laizet and E. Lamballais, High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy, Journal of Computational Physics 228, 5989-6015, (2009).
Li, N. (2011). "Incompact3d: A powerful tool to tackle turbulence problems with up to $O(10^{5})$ computational cores". International Journal of Numerical Methods in Fluids. 67: 1735–1757.
{LaiLi11} S. Laizet and N. Li, Incompact3d: A powerful tool to tackle turbulence problems with up to $O(10^{5})$ computational cores, International Journal of Numerical Methods in Fluids 67, 1735-1757, (2011).
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{Lan96} R. H. Landau, Quantum Mechanics II, Wiley, (1996).
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{LaxBurLax76} P. Lax, S. Burstein and A. Lax, Calculus with Applications and Computing, Vol. 1, Springer, (1976).
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{LieLos03} E.H. Lieb and M. Loss, Analysis, American Mathematical Society, (2003).
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{LinPon09} F. Linares and G. Ponce, Introduction to Nonlinear Dispersive Equations, Springer, (2009).
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{McLQui02} R.I. McLachlan and G.R.W. Quispel, Splitting Methods, Acta Numerica 11, 341-434, (2002).
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Olver, P.J. (2010). "Dispersive Quantization". American Mathematical Monthly. 117: 599–610. {{cite journal}}: Cite has empty unknown parameter: |coauthors= (help)
{Olv10} P.J. Olver, Dispersive Quantization, American Mathematical Monthly, 117, 599-610, (2010).
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{OrsPat72} S.A. Orszag and G.S. Patterson Jr., Numerical simulation of three-dimensional homogeneous isotropic turbulence, Physical Review Letters 28(2), 76-79, (1972).
Peyret, R. (2002). Spectral Methods for Incompressible Viscous Flow. Springer.
{Pey02} R. Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, (2002).
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{Sha93} A. Shapiro The use of an exact solution of the Navier-Stokes equations in a validation test of a three-dimensional nonhydrostatic numerical model, Monthly Weather Review 121, 2420-2425, (1993).
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{Uec09} H. Uecker, A short ad hoc introduction to spectral for parabolic PDE and the Navier-Stokes equations, Lecture notes from the 2009 International Summer School on Modern Computational Science
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{Yan06} L. Yang, Numerical studies of the Klein-Gordon-Schrodinger equations, Masters Thesis, National University of Singapore