# Parallel Spectral Numerical Methods/Bibliography

Allen, S.M.; Cahn, J.W. (1979), "A microscopic theory for antiphase boundary motion and its applications to antiphase domain coarsening", Acta Metallurgica 27: 1085-1095

{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. (1989). Ordinary Differential Equations (4 ed.). Wiley.

{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.

{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. (2006). A Friendly Introduction to Numerical Analysis. Pearson.

{Bra06} B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson, (2006).

Boffetta, G.; Ecke, R.E. (2012). "Two-Dimensional Turbulence". Annual Review of Fluid Mechanics 44: 427-451.

{BofEck12} G. Boffetta and R.E. Ecke, Two-Dimensional Turbulence, Annual Review of Fluid Mechanics 44, 427-451, (2012).

DiPrima, R.C. (2010). Elementary Differential Equations and Boundary Value Problems. Wiley.

{BoyDip10} W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, (2010).

Boyd, J.P. (2001). Chebyshev and Fourier Spectral Methods. Dover.

{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. (2006). Spectral Methods: Fundamentals in Single Domains. Springer.

{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. (2007). Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer.

{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. (2005). "Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows". Fluid Dynamics Research 36: 239-248.

{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).

P., Rigge. "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.

{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. (1965). "An algorithm for the machine calculation of complex Fourier series". Mathematics of Computation 19: 297-301.

{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. (1998). Introduction to Calculus and Analysis. I. Springer.

Courant, R.; John, F. (1999). Introduction to Calculus and Analysis. II. Springer.

{CouJoh98} R. Courant and F. John, Introduction to Calculus and Analysis I, II Springer (1998,1999)

Donninger, R.; Schlag, W. (2011). "Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation". Nonlinearity 24: 2547-2562.

{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. (1995). Applied Analysis of the Navier-Stokes Equations. Cambridge University Press.

{DoeGib95} C.R. Doering and J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, (1995).

Shukla, P.K. (2009). "Nonlinear aspects of quantum plasma physics: Nanoplasmonics and nanostructures in dense plasmas". Plasma and Fusion Research: Review Articles 4: 32.

{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. (2010). Partial Differential Equations. American Mathematical Society.

{Eva10} L.C. Evans, Partial Differential Equations, American Mathematical Society, (2010).

Fornberg, B. (1977). "A numerical study of 2-D turbulence". Journal of Computational Physics 25: 1-31.

{For77} B. Fornberg, A numerical study of 2-D turbulence, Journal of Computational Physics 25, 1-31, (1977).

Gallavotti, G. (2002). Foundations of Fluid Dynamics. Springer.

{Gal02} G. Gallavotti, Foundations of Fluid Dynamics, Springer, (2002).

```http://www.math.rutgers.edu/~giovanni/glib.html#E
```

Gottlieb, D.; Orszag, S.A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.

{GotOrs77} D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, (1977).

Grenier, W. (1994). Relativistic Quantum Mechanics. Springer.

{Gre94} W. Grenier, Relativistic Quantum Mechanics, Springer, (1994)

Skjellum, A. (1999). Using MPI. MIT Press.

{GroLusSkj99} W. Gropp, E. Lusk and A. Skjellum, Using MPI, MIT Press, (1999).

Gropp, W.; Lusk, E.; Thakur, R. (1999). Using MPI-2. MIT Press.

{GroLusTha99} W. Gropp, E. Lusk and R. Thakur, Using MPI-2, MIT Press, (1999).

Burrus, C.S. (1984). "Gauss and the History of the Fast Fourier Transform". IEEE ASSP Magazine 1 (4): 1421.

{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).

Gottlieb, D. (2007). Spectral Methods for Time-Dependent Problems. Cambridge University Press.

{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 (2008). Calculus, Single and Multivariable (5th ed.). Wiley.

{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).

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).

Iserles, A. (2009). A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press.

{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. (2008). "Fourth order time-stepping for low dispersion Korteweg-De Vries and nonlinear Schrödinger equations". Electronic Transactions on Numerical Analysis 29: 116-135.

{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).

{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).

```http://arxiv.org/abs/1108.3345
```

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 ${\displaystyle O(10^{5})}$ 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 ${\displaystyle O(10^{5})}$ computational cores, International Journal of Numerical Methods in Fluids 67, 1735-1757, (2011).

Landau, R.H. (1996). Quantum Mechanics II. Wiley.

{Lan96} R. H. Landau, Quantum Mechanics II, Wiley, (1996).

Lax, A. (1976). Calculus with Applications and Computing. 1. Springer.

{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
```

Loss, M. (2003). Analysis. American Mathematical Society.

{LieLos03} E.H. Lieb and M. Loss, Analysis, American Mathematical Society, (2003).

Ponce, G. (2009). Introduction to Nonlinear Dispersive Equations. Springer.

{LinPon09} F. Linares and G. Ponce, Introduction to Nonlinear Dispersive Equations, Springer, (2009).

Wagenbreth, G. (2011). High Performance Computing: Programming and Applications. CRC Press.

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

Bertozzi, A.L. (2002). Vorticity and Incompressible Flow. Cambridge University Press.

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

McLachlan, R.I.; Quispel, G.R.W. (2002). "Splitting Methods". Acta Numerica 11: 341-434.

{McLQui02} R.I. McLachlan and G.R.W. Quispel, Splitting Methods, Acta Numerica 11, 341-434, (2002).

Cohen, M. (2011). Modern Fortran Explained. Oxford University Press.

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

Schlag, W. (2011). Invariant Manifolds and Dispersive Hamiltonian Evolution Equations. European Mathematical Society.

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

Olver, P.J. (2010). "Dispersive Quantization". American Mathematical Monthly 117: 599-610.

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

Shakiban, C. (2006). Applied Linear Algebra. Prentice Hall.

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

Orszag, S.A.; Patterson Jr., G.S. (1979). Physical Review Letters 28 (2): 76-79.

{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).

Rogers, R.C. (2004). An Introduction to Partial Differential Equations. Springer.

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

Shapiro, A (1993). "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.

{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).

Wang, L.-L. (2011). Spectral Methods: Algorithms, Analysis and Applications. Springer.

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

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

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

Temam, R. (2001). Navier-Stokes Equations (Third ed.). American Mathematical Society.

{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. (2000). Spectral Methods in Matlab. SIAM.

{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. (1988). Physical Fluid Dynamics. Clarendon Press.

{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. (1986). "Split-step methods for the solution of the nonlinear Schrödinger equation". SIAM Journal on Numerical Analysis (SIAM) 23 (3): 485-507.

{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. (2010). Nonlinear Waves in Integrable and Nonintegrable Systems. SIAM.

{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
```