Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 43, 2003 - Issue 4
57
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

MULTIDIMENSIONAL SUPERCOMPACT WAVELETS FOR FLUID DYNAMICS

Pages 307-329 | Published online: 02 Feb 2011

References

  • Engquist , B. , Osher , S. and Zhong , S. 1992 . Fast Wavelets Based Algorithms for Linear Evolutions , ICASE Report .
  • Vasilyev , O. and Paolucci , S. 1996 . A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain . Comput. Phys. , 125 : 498 – 512 .
  • Harten , A. 1995 . Multiresolution Algorithm for the Numerical Solution of Hyperbolic Conservation Laws . Commun. Pure Appl. Math. , 48 : 1305 – 1342 .
  • Gerritsen , M. 1996 . Designing an Efficient Solution Strategy for Fluid Flows, Ph.D. thesis , Stanford, CA : Stanford University .
  • Jameson , L. , Adachi , T. , Ukai , O. and Yuasa , A. 1998 . Wavelet-Based Numerical Methods . Int. J. Comput. Fluid Dynam. , 10 : 267 – 280 .
  • Sweldens , W. 1995 . The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions . Proc. SPIE , 2569 : 68 – 79 .
  • Sweldens , W. and Schroder , P. 1996 . Building Your Own Wavelets at Home . ACM SIGGRAPH Course Note # 13 ,
  • Strang , G. 1989 . Wavelets and Dilation Equations: A Brief Introduction . SIAM Rev , 31 : 614 – 627 .
  • Daubechies , I. 1988 . Orthonormal Basis of Compactly Supported Wavelets . Commun. Pure Appl. Math. , 41 : 909 – 996 .
  • Geronimo , J. , Hardin , D. and Massopust , P. 1994 . Fractal Functions and Wavelet Expansions Based on Several Scaling Functions . Approx. Theory , 78 : 373 – 401 .
  • Strang , G. and Strela , V. 1994 . Orthogonal Multiwavelets with Vanishing Moments . Opt. Eng. , 33 : 2104 – 2107 .
  • Donovan , G. , Geronimo , J. and Hardin , D. 1996 . Interwining Multiresolution Analyses and the Construction of Piecewise Polynomial Wavelets . SIAM J. Math. Anal. , 27 ( 6 ) : 1791 – 1815 .
  • Beam , R. M. and Warming , R. F. 2000 . Discrete Multiresolution Analysis Using Hermite Interpolation: Biorthogonal Multiwavelets . Technical Report, SIAM J. Sd. Comput. , 22 ( 4 ) : 1269 – 1317 .
  • Alpert , B. 1993 . A Class of Bases in l2 for the Sparse Representation of Integral Operators . SIAM J. Math. Anal. , 24 ( 1 ) : 246 – 262 .
  • Beam , R. M. and Warming , R. F. 2000 . Multiresolution Analysis and Supercompact Multiwavelets . SIAM J. Sci. Comput. , 22 ( 4 ) : 1238 – 1268 .
  • Downie , T. R. and Silverman , B. W. 1996 . The Discrete Multiple Wavelet Transform and Thresholding . IEEE Trans. Signal Processing , 46 : 2558 – 2561 .
  • Rogers , S. E. , Kwak , D. and Kiris , C. 1991 . Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations . AIAA J. , 29, no. 4 : 603 – 610 .
  • Rott , N. 1958 . On the Viscous Core of a Line Vortex . J. Appl. Math. and Phys. , 9b ( 5/6 ) : 543 – 553 .
  • Dacles-Mariani , J. , Zilliac , G. G. , Chow , J. S. and Bradshaw , D. 1995 . Numerical/Experimental Study of a Wingtip Vortex in the Near Field . AIAA J. , 33, no. 9 : 1561 – 1568 .
  • Lee , D. February 2000 . Multiresolution with Supercompact Wavelets, 5th High Performance Computing and Communication/Computational Aerosciences (HPCC/CAS) Workshop . NASA Ames Research Center , : 15 – 17 .
  • Lee , D. January 2000 . Supercompact Multi-wavelets for Three Dimensional Flow Field Simulation, AIAA Paper 2000-0396 . 38th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV , : 10 – 13 .
  • Cohen , A. , Daubechies , I. , Jawerth , B. and Vial , P. 1993 . Multiresolution Analysis, Wavelets and Fast Wavelet Transform on an Interval . CRAS Paris, Ser. A , 316 : 417 – 421 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.