Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

A Study on the Comparison Between Full-3D and Quasi-1D Supercompact Multiwavelets

Full-3D와 Quasi-1D Supercompact Multiwavelets의 비교 연구

  • 박준표 (한양대학교 대학원 기계공학과) ;
  • 이도형 (한양대학교 기계정보경영공학부) ;
  • 권도훈 (한양대학교 대학원 기계공학과)
  • Published : 2004.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

CFD data compression methods based on Full-3D and Quasi-1D supercompact multiwavelets are presented. Supercompact wavelets method provide advantageous benefit that it allows higher order accurate representation with compact support. Therefore it avoids unnecessary interaction with remotely located data across singularities such as shock. Full-3D wavelets entails appropriate cross-derivative scaling function & wavelets, hence it can allow highly accurate multi-spatial data representation. Quasi-1D method adopt 1D multiresolution by alternating the directions rather than solving huge transformation matrix in Full-3D method. Hence efficient and relatively handy data processing can be conducted. Several numerical tests show swift data processing as well as high data compression ratio for CFD simulation data.

Keywords

References

  1. Brani Vidakovic and Peter Mueller, 1991, 'Wavelets for Kids: A Tutorial Introduction,' Duke University
  2. Michel Misiti, Yves Misiti, Georges Oppenheim and Jean-Michel Poggi, 1996, 'Wavelet TOOLBOX,' The Math Works, Inc.
  3. Richard M. Beam and Robert F. Warming, 2000, 'Multiresolution Analysis and Supercompact Multiwavelets,' SIAM journal on scientific computing, Vol. 22, No. 4, pp. 1238-1268 https://doi.org/10.1137/S1064827596311906
  4. Alpert, B., 1993, 'A Class of Bases in for the Sparse Representation of Integral Operators,' SIAM Journal on Mathematical Analysis, Vol. 24, pp. 246-262 https://doi.org/10.1137/0524016
  5. Dohyung Lee, 2000, 'Supercompact Multiwavelets for Three Dimensional Flow Field Simulation,' 38th AIAA Aerospace Meeting & Exhibit
  6. Dohyung Lee, Richard M. Beam and Robert F. Wanning, 2001, 'Supercompact Multiwavelets for Flow Field Simulation,' Computers & Fluids, Vol. 30, pp. 783-805 https://doi.org/10.1016/S0045-7930(01)00029-9
  7. Dohyung Lee, 2003, 'MultiDimensional Supercompact Wavelets For Fluid Dynamics,' Numerical Heat Transfer, Part B, Vol. 43, pp. 307-329 https://doi.org/10.1080/713836221
  8. Hyungmin Kang, Dongho Lee and Dohyung Lee, 2003, 'A Study on CFD Data Compression Using Hybrid Supercompact Wavelets,' KSME International Journal, Vol. 17, No. 11, pp. 1784-1792
  9. Sweldens, W., 1995, 'The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions,' Proc. SPIE, Vol. 2569, pp. 68-79 https://doi.org/10.1117/12.217619
  10. Sweldens, W. and Schroder, P., 1996, 'Building Your Own Wavelets at Home,' ACM SIGGRAPH Course Note #13
  11. David L. Donoho and Iain M. Johnstone, 1993, 'Ideal Spatial Adaptation via Wavelet Shrinkage,' Stanford University
  12. Donoho D.L., 'De-Noising by soft-thresholding', IEEE, Vol.41, pp.613-627, 1995 https://doi.org/10.1109/18.382009
  13. T.R. Downie and B. W. Silverman, 'The discrete multiple wavelet transform and thresholding methods', IEEE, Vol.46, pp.2558-2561, Sept., 1998 https://doi.org/10.1109/78.709546
  14. Rott, N., 1958, 'On the Viscous Core of a Line Vortex,' J Appl Math Phys, Vol. 9b(5/6), pp. 543-553 https://doi.org/10.1007/BF02424773