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  Contents
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- 1
- Y.Abdelatif, M. An, N. Anupindi,
G. Kechriotis, C. Lu, R. Tolimieri,
Group Invariant Fourier Transform Algorithms,
Advances in Electronics and Electron Physics,
93, Academic Press, 1995.
- 2
- M. An, I. Gertner, M. Rofheart and R. Tolimieri,
``Discrete Fast Fourier Transform Algorithms: A Tutorial Survey,"
Advances in Electronics and Electron Physics,
80 Academic Press, 1991.
- 3
- Myoung An, Chao Lu and R. Tolimieri,
Algorithms for Discrete Fourier Transforms and Convolution,
Springer-Verlag, New York, (1989).
- 4
- H. Aref, The numerical experiment in
fluid mechanics, J. Fluid Mech. 173, 15-41, (1986)
- 5
- N. Aubry, P. Holmes, J.L. Lumley and E. Stone,
The Dynamics of Coherent Structures in the Wall Region of a
Turbulent Boundary Layer,
J. Fluid Mech. 192, 115-173, (1988)
- 6
- G. Belykin, R. Coifman and V. Rokhlin,
Fast Wavelet Transforms and Numerical Algorithms I,
CPAM XLIV, 141-183, (1991)
- 7
- M. Brachet, M. Meneguzzi, H. Politano and P. Sulem,
The dynamics of freely decaying two-dimensional turbulence,
J Fluid Mech 194 (1988), 333-349.
- 8
- M. Brachet, M. Meneguzzi, A. Vincent,
H. Politano and P. Sulem,
Can three-dimensional ideal flows become singular
in a finite time ?,
Singularities in Fluids, Plasmas and Optics Eds,
R.E. Caflisch and G.C. Papanicolaou. 39-51, Kluwer Academic Pub.
Amsterdam (1993).
- 9
- B.L. Buzbee and F.W. Dorr,
The Direct Solution of the Biharmonic Equation on
Rectangular Regions and the Poisson Equation on Irregular
Regions, SIAM J Numer Anal 11 (1974) p. 753
- 10
- C. Canuto, M.Y. Hussaini, A. Quarteroni and
T.A. Zang, Spectral Methods in Fluid Dynamics,
Springer Series in Computational Physics, Springer-Verlag,
Berlin-Heidelberg (1988).
- 11
- G.F. Carnevale and G.K. Vallis,
Pseudo-advective relaxation to stable states of inviscid
two-dimensional fluids J. Fluid Mech., 213, 549-571, (1990)
- 12
- R.R. Coifman and M.V. Wickerhauser,
Entropy-Based Algorithms for Best-Basis Selection,
IEEE Transactions on Information Theory 38, 713-718 (1992).
- 13
- Y. Couder and C. Basdevant, Experimental and
numerical study of vortex couples in two-dimensional flows,
J. Fluid Mech. 173, 225-251, (1986)
- 14
- P.F. Cummins and L.A. Mysak,
A Quasi-Geostrophic Circulation Model of the Northeast Pacific.
Part I: A Preliminary Numerical Experiment
J. Physical Oceanography 18, 1261-1286, (1988)
- 15
- I. Daubechies,
Orthonormal bases of compactly supported wavelets,
Comm. Pure Appl. Math 41, (1988), 906-966.
- 16
- P.J. Davis,
Circulant Matrices,
John Wiley, New York (1979).
- 17
- E.J. Dean, R. Glowinski and O. Pironneau,
Iterative solution of the Stream Function-Vorticity
Formulation of the Stokes Problem. Applications to the
Numerical Simulation of Incompressible Viscous Flow.,
University of Houston Tech Report.
- 18
- R.J. DiPerna,
Convergence of the Viscosity Method for Isentropic Gas Dynamics,
Commun. Math. Phys. 91, 1-30, (1983)
- 19
- B. Engquist and T.Y. Hou,
Computation of Oscillatory Solutions to Hyperbolic
Differential Equations using Particle Methods,
UCLA Dept of Math Preprint (1989)
- 20
- C.A.J. Fletcher,
Computational Techniques for Fluid Dynamics, Vol. II,
Springer Series in Computational Physics, Springer Verlag,
New York (1988)
- 21
-
I. Gertner.
A New Efficient Algorithm to compute the Two-Dimensional
Discrete Fourier Transform.
IEEE Transactions on ASSP, 36:1036-1050, July 1988.
- 22
- R. Glowinski, W. M. Lawton, M. Ravachol and
E. Tenenbaum,
Wavelet solution of linear and nonlinear elliptic,
parabolic and hyperbolic problems in one space dimension,
Proceedings of the
9th International Conference on Numerical Methods in Applied
Sciences and Engineering SIAM, Philadelphia, (1990).
- 23
- R. Glowinski, J.F. Bourgat, P. LeTallec and M. Vidrascu,
Variational formulation and algorithm for trace operator in domain
decomposition calculations, in Domain Decomposition Methods, SIAM (1989)
- 24
- W. Gautschi,
Attenuation Factors in Practical Fourier Analysis,
Numer. Math. 18, 373-400 (1972)
- 25
- G. H. Golub and C.F. Van Loan,
Matrix Computations, The John Hopkins University Press,
Baltimore (1983).
- 26
- J. Goodman and P.D. Lax,
On Dispersive Difference Schemes. I,
Commun Pure and Appl. Math 41, 591-613 (1988)
- 27
- T, Hou and P.D. Lax,
Dispersive Approximations in Fluid Dynamics,
Courant Institute, NYU, Preprint (1989)
- 28
- P.D. Lax,
Oscillatory Solutions of Partial Differential Equations,
Mathematics Applied to Science, Academic Press (1988)
- 29
- E.W. Larsen,
Two Types of Homogenization,
SIAM J Math 36, 26-33, (1979)
- 30
- A. Latto, H. L. Resnikoff and E. Tenenbaum,
The evaluation of connection coefficients of
compactly supportes wavelets, Aware Technical Report
AD910708 (July 1991) and the Proceedings of the French - USA
Workshop on Wavelets and Turbulence, Princeton University,
June 1991, Editor, Y. Maday, Springer - Verlag (1992).
- 31
- A. Latto and E. Tenenbaum,
Les ondelettes à support compact et la solution
numérique de l'équation de Burgers,
C. R. Acad. Sci. Paris 311 pp 903-909 (1990).
- 32
- W. Lawton, W. Morrell, E. Tenenbaum and
J. Weiss,
The Wavelet-Galerkin Method for Partial Differential Equations,
Aware Technical Report AD901220 (1990)
- 33
- C. Lu, Z. Qian and R. Tolimieri,
Small FFT Module Implementation on the i860 Processor,
to appear, Proceedings of the International Conference on Signal
Processing Applications and Technology, Nov 1992, Cambridge, MA.
- 34
- C. Lu, M. An, Z. Qian and R. Tolimieri,
Parallel M-D FFT Algorithms and their Implementation on
Distributed Computing Systems, to appear, Proceedings
of the 13th International Conference on Distributed Computing Systems,
May 25-28, 1993, Pittsburgh, PA.
- 35
- J.L. Lumley, ed.,
Whither Turbulence? Turbulence at the Crossroads,
Lecture Notes in Physics 357, Springer-Verlag (1989)
- 36
- S. Mallat, A theory for multiresolution signal
decomposition: the wavelet transform,
Trans. Amer. Math. Soc. 315, 68-87 (1989).
- 37
- S. Mallat and S. Zhou,
Wavelet Transform Maxima and Multiscale Edges,
in Wavelets and Their Applications ed. M.B. Ruskai
Jones and Bartlett, Boston (1992).
- 38
- D.W. McLaughlin, G.C. Papanicolaou, and O.R.
Pironneau,
Convection of Microstructure and Related Problems,
SIAM J Appl Math 45, 780-797, (1985)
- 39
- B. Nicolaenko, C. Foias and R. Temam, eds.,
The Connection between Infinite Dimensional and Finite
Dimensional Dynamical Systems,
AMS Contemporary Mathematics 99, Amer. Math. Soc. (1987).
- 40
- L. Onsager,
Statistical hydrodynamics,
Nuovo Cimento Suppl. 6, 279-287 (1949).
- 41
- A. Pares-Sierra and G. Vallis,
A Fast Semi-direct Method for the Numerical Solution of
Non-separable Elliptic Equations in Irregular Domains,
J. Comp. Phys. 82 (1989) p. 398
- 42
- F. Pascal and C. Basdevant,
Nonlinear Galerkin Method and Subgrid-Scale Model
for Two Dimensional Turbulent Flows,
Theoret. Comput. Fluid Dynamics, 3 (1992) p. 267.
- 43
- L. Persson, J. Wyller and K. Dysthe,
A Note on Whithams Method and the Homogenization Procedure,
Physica Scripta 38 774-776 (1988)
- 44
- R. Peyret and T.D. Taylor,
Computational Methods for Fluid Flow,
Springer Series in Computational Physics,
Springer-Verlag New York (1983).
- 45
- D. Pollen,
Parameterization of compactly supported wavelets,
Aware Tech Report AD890505 (1989)
- 46
- W. Proskurowski and O. Widlund,
On the Numerical Solution of Helmholtz's Equation
by the Capacitance Matrix Method, Mathematics of Computation
30 (1976) p 433.
- 47
- Z. Qian and J. Weiss,
Wavelets and the Numerical Solution of
Partial Differential Equations,
J. Comp Phys 106 155-175 (1993).
- 48
- Z. Qian and J. Weiss,
Wavelets and the Numerical Solution of Boundary
Value Problems,
Applied Mathematics Letters 6 47-52, (1993).
- 49
- R. Sadourny and C. Basdevant,
Parameterization of subgrid scale baratropic and
baroclinic eddies in quasi-geostrophic models: Anticipated
Potential Vorticity Method, J. Atmos. Sci 42
1353-1363 (1985).
- 50
- E.P. Simoncelli, W.T. Freeman, E.H. Anderson,
and D.J. Heeger,
Shiftable Multiscale Transforms,
IEEE Trans on Information Theory, 38, p 587-607 (1992).
- 51
- G. Strang,
Wavelets and dilation equations: A brief introduction,
SIAM Review 31 (1989), 614-627.
- 52
- L. Tartar,
The Compensated Compactness Method Applied to Systems of
Conservation Laws,
Systems of Nonlinear Partial Differential Equations,
Ed. J.M. Ball, 263-285, D. Reidel Pub Co. (1983).
- 53
- R. Tolimieri,
Efficient and Flexible Algorithms for Digital Signal Processing
on Multiple Independent Node Parallel Computers,
Three year AFOSR Grant F499620-91-C-0098. Start date: Oct. 1991
- 54
- R. Tolimieri, M. An and C. Lu,
Mathematics of Multidimensional Fourier Transform Algorithms,
Springer-Verlag, New York, 1993.
- 55
- E. Van Groesen,
Time-Asymptotics and the Self-Organization Hypothesis for
2D Navier-Stokes Equations,
Physica 148A 312-330 (1988).
- 56
- Weinan E and Huanan Yang,
Numerical Study of Oscillatory Solutions of the
Gas-Dynamic Equations,
Stud Appl Math 85, 29-52, (1991)
- 57
- J. Weiss,
The dynamics of enstrophy transfer in two-dimensional
hydrodynamics, Physica 48D, 273-294, (1991)
- 58
- J. Weiss,
Wavelets and the study of two-dimensional turbulence,
Aware Technical report AD910628, and the Proceedings of the French - USA
Workshop on Wavelets and Turbulence, Princeton University,
June 1991, Editor, Y. Maday, Springer - Verlag (1992).
- 59
- J. Weiss,
``On the formulation of methods of artifical compressibility
for the Navier-Stokes equations'', La Jolla Institute report,
LJI-TN-80-069 June (1980)
- 60
- J. Weiss and Z. Qian,
The long time limit of two-dimensional turbulence in
nonseparable domains,
in preparation (1993).
- 61
- T. Yabe and P. Wang,
Unified Numerical Procedure for Compressible and Incompressible
Fluid,
Journal Phys Soc of Japan 60, 2105-2108, (1991)
- 62
- H.C. Yee, G.H. Klopfer and J-L. Montagne,
High-Resolution Shock-Capturing Schemes for Inviscid and
Viscous Hypersonic Flows,
J Comp Phys 88, 31-61, (1990)
John Edward Weiss
2002-09-30