Parallel Spectral Numerical Methods/Bibliography

Allen S.M. Cahn J.W. A microscopic theory for antiphase boundary motion and its applications to antiphase domain coarsening Acta Metallurgica 27 1085-1095 1979 {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). Birkhoff G Rota G.C. Ordinary Differential Equations Wiley 4 1989 {BirRot89} G. Birkhoff, and G.{}C., Rota, Ordinary Differential Equations (4th ed.), Wiley, (1989). Blanes S. Casas F. Chartier P. Murua A. Splitting methods with complex coefficients for some classes of evolution equations Mathematics of Computation http://arxiv.org/abs/1102.1622 {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 Bradie B. A Friendly Introduction to Numerical Analysis Pearson 2006 {Bra06} B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson, (2006). Boffetta G. Ecke R.E. Two-Dimensional Turbulence Annual Review of Fluid Mechanics 44 427-451 2012 {BofEck12} G. Boffetta and R.E. Ecke, Two-Dimensional Turbulence, Annual Review of Fluid Mechanics 44, 427-451, (2012). Boyce W.E. DiPrima R.C. Elementary Differential Equations and Boundary Value Problems Wiley 2010 {BoyDip10} W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, (2010). Boyd J.P. Chebyshev and Fourier Spectral Methods Dover 2001 http://www-personal.umich.edu/~jpboyd/ {Boy01} J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, (2001). http://www-personal.umich.edu/~jpboyd/ Canuto C. Hussaini M.Y. Quarteroni A. Zang T.A. Spectral Methods: Fundamentals in Single Domains Springer 2006 {CHQZ06} C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, (2006). Canuto C. Hussaini M.Y. Quarteroni A. Zang T.A. Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics Springer 2007 {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). Cichowlas C. Brachet M.-E. Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows Fluid Dynamics Research 36 239-248 2005 {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). Cloutier B. Muite B.K. Rigge P. Performance of FORTRAN and C GPU Extensions for a Benchmark Suite of Fourier Pseudospectral Algorithms Proceedings of the Symposium on Application Accelerators in High Performance computing IEEE http://arxiv.org/abs/1206.3215 {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 Cooley J.W. Tukey J.W. An algorithm for the machine calculation of complex Fourier series Mathematics of Computation 19 297-301 1965 {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). Courant R. John F. Introduction to Calculus and Analysis Springer I 1998 Courant R. John F. Introduction to Calculus and Analysis Springer II 1999 {CouJoh98} R. Courant and F. John, Introduction to Calculus and Analysis I, II Springer (1998,1999) Donninger R. Schlag W. Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation Nonlinearity 24 2547-2562 2011 {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). Doering C.R. Gibbon J.D. Applied Analysis of the Navier-Stokes Equations Cambridge University Press 1995 {DoeGib95} C.R. Doering and J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, (1995). Eliasson B. Shukla P.K. Nonlinear aspects of quantum plasma physics: Nanoplasmonics and nanostructures in dense plasmas Plasma and Fusion Research: Review Articles 4 32 2009 {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). Evans L.C. Partial Differential Equations American Mathematical Society 2010 {Eva10} L.C. Evans, Partial Differential Equations, American Mathematical Society, (2010). Fornberg B. A numerical study of 2-D turbulence Journal of Computational Physics 25 1-31 1977 {For77} B. Fornberg, A numerical study of 2-D turbulence, Journal of Computational Physics 25, 1-31, (1977). Gallavotti G. Foundations of Fluid Dynamics Springer 2002 http://www.math.rutgers.edu/~giovanni/glib.html#E {Gal02} G. Gallavotti, Foundations of Fluid Dynamics, Springer, (2002). http://www.math.rutgers.edu/~giovanni/glib.html#E Gottlieb D. Orszag S.A. Numerical Analysis of Spectral Methods: Theory and Applications SIAM 1977 {GotOrs77} D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, (1977). Grenier W. Relativistic Quantum Mechanics Springer 1994 {Gre94} W. Grenier, Relativistic Quantum Mechanics, Springer, (1994) Gropp W. Lusk E. Skjellum A. Using MPI MIT Press 1999 {GroLusSkj99} W. Gropp, E. Lusk and A. Skjellum, Using MPI, MIT Press, (1999). Gropp W. Lusk E. Thakur R. Using MPI-2 MIT Press 1999 {GroLusTha99} W. Gropp, E. Lusk and R. Thakur, Using MPI-2, MIT Press, (1999). Heideman H.T. Johnson D.H. Burrus C.S. Gauss and the History of the Fast Fourier Transform IEEE ASSP Magazine 1 4 1421 1984 {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). Hesthaven J.S. Gottlieb S. Gottlieb D. Spectral Methods for Time-Dependent Problems Cambridge University Press 2007 {HesGotGot07} J.S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral Methods for Time-Dependent Problems, Cambridge University Press, (2007). Hughes-Hallett D. 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 Wiley 5th 2008 {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) {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). Holden H. Karlsen K.H. Risebro N.H. Tao T. Operator splitting for the KdV equation Mathematics of Computation 80 821-846 2011 {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). Iserles A. A First Course in the Numerical Analysis of Differential Equations Cambridge University Press 2009 {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/ Klein C. Fourth order time-stepping for low dispersion Korteweg-De Vries and nonlinear Schrödinger equations Electronic Transactions on Numerical Analysis 29 116-135 2008 {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). Klein C. Muite B.K. Roidot K. Numerical Study of Blowup in the Davey-Stewartson System 2011 http://arxiv.org/abs/1112.4043 {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. 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 {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 Laizet S. Lamballais E. High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy Journal of Computational Physics 238 5989-6015 2009 {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). Laizet S. Li N. Incompact3d: A powerful tool to tackle turbulence problems with up to computational cores International Journal of Numerical Methods in Fluids 67 1735-1757 2011 {LaiLi11} S. Laizet and N. Li, Incompact3d: A powerful tool to tackle turbulence problems with up to computational cores, International Journal of Numerical Methods in Fluids 67, 1735-1757, (2011). Landau R.H. Quantum Mechanics II Wiley 1996 {Lan96} R. H. Landau, Quantum Mechanics II, Wiley, (1996). Lax P. Burstein S. Lax A. Calculus with Applications and Computing Springer 1 1976 {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 Lieb E.H. Loss M. Analysis American Mathematical Society 2003 {LieLos03} E.H. Lieb and M. Loss, Analysis, American Mathematical Society, (2003). Linares F. Ponce G. Introduction to Nonlinear Dispersive Equations Springer 2009 {LinPon09} F. Linares and G. Ponce, Introduction to Nonlinear Dispersive Equations, Springer, (2009). Levesque J. Wagenbreth G. High Performance Computing: Programming and Applications CRC Press 2011 {LevWag11} J. Levesque and G. Wagenbreth, High Performance Computing: Programming and Applications, CRC Press, (2011). Majda A.J. Bertozzi A.L. Vorticity and Incompressible Flow Cambridge University Press 2002 {MajBer02} A.J. Majda and A.L. Bertozzi, Vorticity and Incompressible Flow, Cambridge University Press, (2002). McLachlan R.I. Quispel G.R.W. Splitting Methods Acta Numerica 11 341-434 2002 {McLQui02} R.I. McLachlan and G.R.W. Quispel, Splitting Methods, Acta Numerica 11, 341-434, (2002). Metcalf M. Reid J. Cohen M. Modern Fortran Explained Oxford University Press 2011 {MetReiCoh11} M. Metcalf, J. Reid and M. Cohen, Modern Fortran Explained, Oxford University Press, (2011). Nakanishi K. Schlag W. Invariant Manifolds and Dispersive Hamiltonian Evolution Equations European Mathematical Society 2011 {NakSch11} K. Nakanishi and W. Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Equations, European Mathematical Society, (2011). Olver P.J. Dispersive Quantization American Mathematical Monthly 117 599-610 2010 {Olv10} P.J. Olver, Dispersive Quantization, American Mathematical Monthly, 117, 599-610, (2010). Olver P.J. Shakiban C. Applied Linear Algebra Prentice Hall 2006 {OlvSha06} P.J. Olver and C. Shakiban, Applied Linear Algebra, Prentice Hall, (2006). Orszag S.A. Patterson Jr. G.S. Physical Review Letters 28 2 76-79 1979 {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. Spectral Methods for Incompressible Viscous Flow Springer 2002 {Pey02} R. Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, (2002). Renardy R. Rogers R.C. An Introduction to Partial Differential Equations Springer 2004 {RenRog04} R. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations, Springer, (2004). Shapiro A 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 {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). Shen J. Tang T. Wang L.-L. Spectral Methods: Algorithms, Analysis and Applications Springer 2011 {SheTanWan11} J. Shen, T. Tang and L.-L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, (2011). Sulem C. Sulem P.L. The Nonlinear Schrodinger equation: Self-Focusing and Wave Collapse Springer 1999 {SulSul99} C. Sulem and P.L. Sulem, The Nonlinear Schrodinger equation: Self-Focusing and Wave Collapse, Springer, (1999). Temam R. Navier-Stokes Equations American Mathematical Society Third 2001 {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 Trefethen L.N. Spectral Methods in Matlab SIAM 2000 {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 Tritton D.J. Physical Fluid Dynamics Clarendon Press 1988 {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 http://www.staff.uni-oldenburg.de/hannes.uecker/hfweb-e.html Weideman J.A.C. Herbst B.M. Split-step methods for the solution of the nonlinear Schrödinger equation SIAM Journal on Numerical Analysis 23 3 485-507 SIAM 1986 {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). Yang J. Nonlinear Waves in Integrable and Nonintegrable Systems SIAM 2010 {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