Parallel Spectral Numerical Methods/Bibliography: Difference between revisions

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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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{CicBra05} C. Cichowlas and M.-E. Brachet, Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows, Fluid Dynamics Research 36, 239-248, (2005).

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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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{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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{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).

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{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).

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{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).

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{KleMuiRoi11} C. Klein, B.K. Muite and K. Roidot, Numerical Study of Blowup in the Davey-Stewartson System, http://arxiv.org/abs/1112.4043

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{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).

http://arxiv.org/abs/1108.3345 

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{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).

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{LaiLi11} S. Laizet and N. Li, Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) 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).

{LiLai10} N. Li and S. Laizet, 2DECOMP&FFT - A highly scalable 2D decomposition library and FFT interface, Proc. Cray User Group 2010 Conference.

http://web.archive.org/web/20130814233258/http://www.2decomp.org/pdf/17B-CUG2010-paper-Ning_LI.pdf 

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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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{LevWag11} J. Levesque and G. Wagenbreth, High Performance Computing: Programming and Applications, CRC Press, (2011).

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{MajBer02} A.J. Majda and A.L. Bertozzi, Vorticity and Incompressible Flow, Cambridge University Press, (2002).

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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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{MetReiCoh11} M. Metcalf, J. Reid and M. Cohen, Modern Fortran Explained, Oxford University Press, (2011).

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{NakSch11} K. Nakanishi and W. Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Equations, European Mathematical Society, (2011).

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{Olv10} P.J. Olver, Dispersive Quantization, American Mathematical Monthly, 117, 599-610, (2010).

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{OlvSha06} P.J. Olver and C. Shakiban, Applied Linear Algebra, Prentice Hall, (2006).

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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).

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{Pey02} R. Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, (2002).

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{RenRog04} R. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations, Springer, (2004).

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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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{SheTanWan11} J. Shen, T. Tang and L.-L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, (2011).

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{SulSul99} C. Sulem and P.L. Sulem, The Nonlinear Schrodinger equation: Self-Focusing and Wave Collapse, Springer, (1999).

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{Tem01} R. Temam, Navier-Stokes Equations, Third revised edition, AMS, (2001).

{Tha08} M. Thalhammer, Time-Splitting Spectral Methods for Nonlinear Schrodinger Equations, Unpublished manuscript, (2008).

http://techmath.uibk.ac.at/mecht/research/SpringSchool/manuscript_Thalhammer.pdf 

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{Tre00} L. N. Trefethen, Spectral Methods in Matlab, SIAM, (2000).

{TreEmb01} L. N. Trefethen and K. Embree (Ed.), The (Unfninished) PDE coffee table book. Unpublished notes available online

http://people.maths.ox.ac.uk/trefethen/pdectb.html 

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{Tri88} D.J. Tritton, Physical Fluid Dynamics, Clarendon Press, (1988).

{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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{WeiHer86} J.A.C. Weideman and B.M. Herbst, Split-step methods for the solution of the nonlinear Schrödinger equation, SIAM Journal on Numerical Analysis 23(3), 485-507, (1986).

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{Yan10} J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, SIAM, (2010).

{Yan06} L. Yang, Numerical studies of the Klein-Gordon-Schrodinger equations, Masters Thesis, National University of Singapore

http://scholarbank.nus.edu.sg/handle/10635/15515

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