domain decomposition technique with moving interfaces for viscous incompressible

¬‚ows, ECCOMAS 96, John Wiley, New York.

Gelb, A.: 1997, The resolution of the Gibbs phenomenon for spherical harmonics, Math.

Comput. 66, 699“717. Applies the Gegenbauer polynomial sequence acceleration of

Gottlieb and Shu to discontinuous functions on the sphere.

BIBLIOGRAPHY

618

Gelb, A. and Gottlieb, D.: 1998, Recovering grid-point values without Gibbs oscillations in

two dimensional domains on the sphere, J. Comput. Phys. Submitted. Gegenbauer

polynomial regularization for rectangular regions or a union of rectancles on the

sphere with meteorological applications.

Gentleman, W. M.: 1972a, Implementing Clenshaw-Curtis quadrature, Communications of

the ACM 15(5), 353“355. Table with complete FORTRAN code including the necesary

cosine-FFT.

Gentleman, W. M.: 1972b, Implementing Clenshaw-Curtis quadrature: I. Methodology

and experience, Communications of the ACM 15(5), 337“342. Careful analysis of perfor-

mance on ¬fty test integrals.

Gentleman, W. M.: 1972c, Implementing Clenshaw-Curtis quadrature: II. Computing the

cosine transformation, Communications of the ACM 15(5), 343“346.

Ghaddar, N. K., Korczak, K. Z., Mikic, B. B. and Patera, A. T.: 1986a, Numerical investiga-

tion of incompressible ¬‚ow in grooved channels, Part 1: Stability and self-sustained

oscillations, Journal of Fluid Mechanics 163, 99“127.

Ghaddar, N. K., Korczak, K. Z., Mikic, B. B. and Patera, A. T.: 1986b, Numerical investi-

gation of incompressible ¬‚ow in grooved channels, Part 2: Resonance and oscillatory

heat transfer, Journal of Fluid Mechanics 168, 541“567.

Ghosh, S., Hossain, M. and Matthaeus, W. H.: 1993, The application of spectral methods

in simulating compressible ¬‚uid and magneto¬‚uid turbulence, Computer Physics Com-

munications 74, 18“40.

Gill, A. W. and Sneddon, G. E.: 1995, Complex mapped matrix methods in hydrodynamic

stability problems, Journal of Computational Physics 122, 13“24. Derive analytic for-

mulas for optimizing Boyd™s mappings to detour around singularities in the complex

plane to calculate eigenvalues for modes with a singularity on or near the real axis, as

occur in linearized hydrodynamic stability and Sturm-Liouville eigenproblems of the

Fourth Kind; illustrated with experiments.

Gill, A. W. and Sneddon, G. E.: 1996, Pseudospectral methods and composite complex

maps for near-boundary critical latitudes, Journal of Computational Physics 129(1), 1“

7. Simple formulas for optimizing a change-of-coordinate to resolve a differential

equation with singularities very close to the boundary; Chebyshev pseudospectral

solution of eigenproblems.

Giraldo, F. X.: 1998, The Lagrange-Galerkin spectral element method on unstructured

quadrilateral grids, J. Comput. Phys. 147(1), 114“146. Semi-Lagrangian spectral ele-

ments for ¬‚uids.

Givi, P. and Madnia, C. K.: 1993, Spectral methods in combustion, in T. J. Chung (ed.), Nu-

merical Modeling in Combustion, Hemisphere, Taylor and Francis, Washington, pp. 409“

452.

Glatzmaier, G. A.: 1984, Numerical simulations of stellar convective dynamos. Part I. The

model and method, Journal of Computational Physics 55, 461“484. Spherical harmonics

in latitude and longitude, Chebyshev polynomials in radius. This model, with re¬ne-

ments, has been used in more than forty successive articles on mantle convection and

stellar ¬‚uid dynamics by Glatzmaier and collaborators.

BIBLIOGRAPHY 619

Glatzmaier, G. A.: 1988, Numerical simulations of mantle convection: Time-dependent

,three-dimensional, compressible spherical shell, Geophysical and Astrophysical Fluid

Dynamics 43, 223“264.

Glatzmaier, G. A. and Roberts, P. H.: 1997, Simulating the geodynamo, Contemp. Phys.

38(4), 269“288. C.

Glowinski, R., Keller, H. B. and Reinhart, L.: 1985, Continuation conjugate gradient meth-

ods for the least squares solution of nonlinear boundary value problems, SIAM Journal

of Scienti¬c and Statistical Computing 6, 793“832.

Godon, P.: 1995, The propagation of acoustic waves and quasi-periodic oscillations in ac-

cretion disc boundary layers, Monthly Notices of the Royal Astronomical Society 274, 61“

74. Polar coordinates in a two-dimensional plane; Fourier-Chebyshev with 4th order

Runge-Kutta. Application.

Godon, P.: 1996a, Accretion disc boundary layers around pre-main-sequence stars, Monthly

Notices of the Royal Astronomical Society 279(4), 1071“1082. Polar coordinates in a two-

dimensional plane; Fourier-Chebyshev with 4th order Runge-Kutta. Application.

Godon, P.: 1996b, Accretion disk boundary layers in classical t tauri stars, Astrophysical Jour-

nal 463(2), 674“680. Polar coordinates in a two-dimensional plane; Fourier-Chebyshev

with 4th order Runge-Kutta. Kosloff/Tal-Ezer mapping.

Godon, P.: 1997a, Advection in accretion disk boundary layers, Astrophysical Journal

483(1), 882“886. Polar coordinates in a two-dimensional plane through the center of

an accretion disk around a star: Chebyshev in radius and Fourier in the polar angle.

Godon, P.: 1997b, Numerical modeling of tidal effects in polytropic accretion disks, Astro-

physical Journal 480(1), 329“343. Polar coordinates in a two-dimensional plane through

the center of an accretion disk around a star: Chebyshev in radius and Fourier in the

polar angle. Kosloff-Tal-Ezer mapping.

Godon, P., , Regev, O. and Shaviv, G.: 1995, One-dimensional time-dependent numerical

modeling of accretion disc boundary-layers, Monthly Notices of the Royal Astronomical

Society 275(4), 1093“1101. Chebyshev-Fourier polar coordinate model with 4th order

Runge-Kutta time-marching.

Godon, P. and Shaviv, G.: 1993, A two-dimensional time-dependent Chebyshev method

of collocation for the study of astrophysical ¬‚ows, Comput. Meths. Appl. Mech. Engin.

110(1“2), 171“194. Chebyshev-Fourier polar coordinate model with 4th order Runge-

Kutta time-marching.

Godon, P. and Shaviv, G.: 1995, The dynamics of two-dimensional local and ¬nite

perturbations in envelopes of rotating dwarf stars, Astrophysical Journal 447, 797“

806. Chebyshev-Fourier polar coordinate model with 4th order Runge-Kutta time-

marching.

Goldhirsch, I., Orszag, S. A. and Maulik, B. K.: 1987, An ef¬cient method for computing

leading eigenvalues and eigenvectors of large asymmetric matrices, Journal of Scienti¬c

Computing 2, 33“58.

Gordon, C. T. and Stern, W. F.: 1982, A description of the GFDL global spectral model,

Monthly Weather Review 110, 625“644.

BIBLIOGRAPHY

620

Gottlieb, D.: 1981, The stability of pseudospectral Chebyshev methods, Mathematics of Com-

putation 36, 107“118.

Gottlieb, D.: 1984, Spectral methods for compressible ¬‚ow problems, in Soubbaramayer

and J. P. Boujot (eds), Proceedings of the 9th International Conference on Numerical Methods

in Fluid Dynamics, Saclay, France, number 218 in Lecture Notes in Physics, Springer-

Verlag, New York, pp. 48“61.

Gottlieb, D. and Hirsh, R. S.: 1989, Parallel pseudospectral domain decomposition tech-

niques, Journal of Scienti¬c Computing 4(1), 309“326.

Gottlieb, D. and Lustman, L.: 1983a, The Dufort-Frankel Chebyshev method for parabolic

initial value problems, Computers and Fluids 11, 107“120.

Gottlieb, D. and Lustman, L.: 1983b, The spectrum of the Chebyshev collocation operator

for the heat equation, SIAM Journal of Numerical Analysis 20, 909“921. Global and

subdomain cases are analyzed with numerical results for the potential equation of

airfoil theory.

Gottlieb, D. and Orszag, S. A.: 1977, Numerical Analysis of Spectral Methods, SIAM, Philadel-

phia, PA. 200 pp.

Gottlieb, D. and Orszag, S. A.: 1980, High resolution spectral calculations of inviscid com-

pressible ¬‚ows, in (ed.), Approximation Methods for Navier-Stokes Problems, Springer-

Verlag, New York, pp. 381“398.

Gottlieb, D. and Shu, C.-W.: 1994, Resolution properties of the Fourier method for discon-

tinuous waves, in C. Bernardi and Y. Maday (eds), Analysis, Algorithms and Applications

of Spectral and High Order Methods for Partial Differential Equations, Selected Papers from

the International Conference on Spectral and High Order Methods (ICOSAHOM ™92),

Le Corum, Montpellier, France, 22-26 June 1992, North-Holland, Amsterdam, pp. 27“

38. Also in Comput. Meths. Appl. Mech. Engrg., vol. 116.

Gottlieb, D. and Shu, C.-W.: 1995a, On the Gibbs phenomenon IV: Recovering exponen-

tial accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic

function, Mathematics of Computation 64, 1081“1095.

Gottlieb, D. and Shu, C.-W.: 1995b, On the Gibbs phenomenon V: Recovering exponential

accuracy from collocation point values of a piecewise analytic function, Numerische

Mathematik 71, 511“526.

Gottlieb, D. and Streett, C. L.: 1990, Quadrature imposition of compatibility conditions in

Chebyshev methods, Journal of Scienti¬c Computing 5(3), 223“240.

Gottlieb, D. and Tadmor, E.: 1985, Recovering pointwise values of discontinuous data

within spectral accuracy, in E. M. Murman and S. S. Abarbanel (eds), Progress and

Supercomputing in Computational Fluid Dynamics, Birkh¨ user, Boston, pp. 357“375.

a

Gottlieb, D. and Tadmor, E.: 1991, The CFL condition for spectral approximation to hyper-

bolic BVPs, Mathematics of Computation 56, 565“588.

Gottlieb, D. and T´ mam, R.: 1993, Implementation of the Nonlinear Galerkin method with

e

pseudospectral (collocation) discretizations, Applied Numerical Mathematics 12, 119“

134.

BIBLIOGRAPHY 621

Gottlieb, D. and Turkel, E.: 1980, On time discretization for spectral methods, Studies in

Applied Mathematics 63, 67“86.

Gottlieb, D. and Turkel, E.: 1985, Topics in spectral methods for time dependent problems,

in F. Brezzi (ed.), Numerical Methods In Fluid Dynamics, Springer-Verlag, New York,

pp. 115“155.

Gottlieb, D., Hussaini, M. Y. and Orszag, S. A.: 1984a, Theory and application of spectral

methods, in R. G. Voigt, D. Gottlieb and M. Y. Hussaini (eds), Spectral Methods for

Partial Differential Equations, SIAM, Philadelphia, pp. 1“54.

Gottlieb, D., Lustman, L. and Orszag, S. A.: 1981a, Spectral calculations of one-dimensional

inviscid compressible ¬‚ow, SIAM Journal of Scienti¬c and Statistical Computing 2, 296“

310.

Gottlieb, D., Lustman, L. and Streett, C. L.: 1984b, Spectral methods for two-dimensional

shocks, in R. G. Voigt, D. Gottlieb and M. Y. Hussaini (eds), Spectral Methods for Partial

Differential Equations, SIAM, Philadelphia, pp. 79“96.

Gottlieb, D., Lustman, L. and Tadmor, E.: 1987a, Stability analysis of spectral methods for

hyperbolic initial-value problems, SIAM Journal of Numerical Analysis 24, 241“258.

Gottlieb, D., Lustman, L. and Tadmor, E.: 1987b, Convergence of spectral methods for

hyperbolic initial-value problems, SIAM Journal of Numerical Analysis 24, 532“537.

Gottlieb, D., Orszag, S. A. and Turkel, E.: 1981b, Stability of pseudospectral and ¬nite dif-

ference methods for variable coef¬cient problems, Mathematics of Computation 37, 293“

305.

Gottlieb, D., Shu, C.-W., Solomonoff, A. and Vandeven, H.: 1992, On the Gibbs phe-

nomenon I: recovering exponential accuracy from the Fourier partial sum of a non-

periodic analytic function, Journal of Computational and Applied Mathematics 43, 81“98.

Grant, F. C. and Feix, M. R.: 1967, Fourier-Hermite solutions of the Vlasov equations in

the linearized limit, The Physics of Fluids 10(4), 696“702. Damping term is added to

improve the otherwise slow convergence of the Hermite series for the velocity coor-

dinate.

Gravel, S. and Staniforth, A.: 1994, A mass-conserving semi-Lagrangian scheme for

shallow-water equations, Monthly Weather Review 122, 243“248.

ˆe

Gravel, S., Staniforth, A. and Cot´ , J.: 1993, A stability analysis of a family of baroclinic

semi-Lagrangian forecast models, Monthly Weather Review 121, 815“824.

Greengard, L. and Strain, J.: 1991, The fast Gauss transform, SIAM J. Scient. Stat. Comput.

12, 79“94. Sum of N Gaussians at N points in space; not a generalized FFT but a close

cousin.

Gresho, P. M., Gartling, D. K., Torczynski, J. R., Cliffe, K. A., Winters, K. H., Garratt,

T. J., Spence, A. and Goodrich, J. W.: 1993, Is the steady visous incompressible two-

dimensional ¬‚ow over a backward- facing step at Re=800 stable?, International Journal

for Numerical Methods in Fluids 17, 501“541. Shows, by applying several different al-

gorithms to a classical benchmark, that a published spectral element calculation was

in error because of insuf¬cient convergence tests. See also Kaiktsis, Karniadakis and

Orszag(1991, 1996).

BIBLIOGRAPHY

622

Grosch, C. E. and Orszag, S. A.: 1977, Numerical solution of problems in unbounded re-

gions: coordinate transforms, Journal of Computational Physics 25, 273“296.

Guillard, H. and Desideri, J. A.: 1990, Iterative methods with spectral preconditioning for

elliptic equations, Comput. Meths. Appl. Mech. Engrg. 80(1“3), 305“312.

Guillard, H. and Peyret, R.: 1988, On the use of spectral methods for the numerical solution

of stiff problems, Computer Methods in Applied Mechanics and Engineering 66, 17“43.

Flame propagation problems and Burgers™ equation.

Guo, B.-Y.: 1998, Spectral Methods and Their Applications, World Scienti¬c, Singapore. 360

pp. Emphasizes proofs rather than numerical examples.

Guo, B.-Y. and Manoranjan, V. S.: 1985, A spectral method for solving the RLW equation,

IMA Journal of Numerical Analysis 5, 307“318.

Gustafsson, N. and McDonald, A.: 1996, A comparison of the HIRLAM gridpoint and spec-

tral semi-Lagrangian models, Monthly Weather Review 124(9), 2008“2022. Both models

work well and at comparable cost; semi-Lagrangian advection is more accurate than

the alternatives.

Gwynllyw, D. R., Davies, A. R. and Phillips, T. N.: 1996, A moving spectral element ap-

proach to the dynamically loaded journal bearing problem, Journal of Computational

Physics 123, 476“494.

Haidvogel, D. B.: 1977, Quasigeostrophic regional and general circulation modelling: an

ef¬cient pseudospectral aproximation technique, in R. P. Shaw (ed.), Computing Meth-

ods in Geophysical Mechanics, Volume 25, ASME, New York. REVIEW.

Haidvogel, D. B.: 1983, Periodic and regional models, in A. P. Robinson (ed.), Eddies in