A wavelet method for reducing the computational cost of BE-based homogenization analysis

Engineering Analysis with Boundary Elements

Volumn 27, Issue 5, 2003, Pages 439-454

  Koro, Kazuhiro ^a   Abe, Kazuhisa ^a  

^a NIIGATA UNIVERSITY   (Japan)

Author keywords

Effective elastic modulus; Haar wavelets; Homogenization method; Unidirectional composites; Wavelet BEM

Indexed keywords

ADAPTIVE ALGORITHMS; BOUNDARY ELEMENT METHOD; COMPOSITE MATERIALS; DEGREES OF FREEDOM (MECHANICS); ELASTIC MODULI; FINITE ELEMENT METHOD; MATRIX ALGEBRA; MICROSTRUCTURE;

HOMOGENIZATION ANALYSIS;

WAVELET TRANSFORMS;

EID: 0037738927     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(02)00154-6     Document Type: Article

References (24)

1. Hashin Z. Analysis of composite materials - a survey. J Appl Mech ASME. 50:1983;480-505.
2. Hollister S.J., Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech. 10:1992;73-95.
3. Guedes J.M., Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Meth Appl Mech Engng. 83:1990;143-198.
4. Michel J.C., Moulinec H., Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Comput Meth Appl Mech Engng. 172:1999;109-143.
5. Terada K., Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media. Comput Meth Appl Mech Engng. 190:2001;5427-5464.
6. Okada H., Fukui Y., Kumazawa N. Homogenization method for heterogeneous material based on boundary element method. Comput Struct. 79:2001;1987-2007.
7. Kamiński M. Boundary element method homogenization of the periodic linear elastic fiber composites. Engng Anal Bound Elem. 23:1999;815-823.
8. Procházka P. Shape optimization of composites using the BEM. Chen C.S., Brebbia C.A., Pepper D.W. Boundary element technology XIII. 1999;89-98 WIT Press, Southampton.
9. Procházka P. Homogenization of linear and of debonding composites using the BEM. Engng Anal Bound Elem. 25:2001;753-769.
10. Dahmen W., Pröosdorf S., Schneider R. Wavelet approximation methods for pseudodifferential equations. II. Matrix compression and fast solution. Adv Comput Math. 1:1993;259-335.
11. Beylkin G., Coifman R., Rokhlin V. Fast wavelet transforms and numerical algorithms I. Commun Pure Appl Math. 44:1991;141-183.
12. Goswami J.C., Chan A.K., Chui C.K. On solving first-kind integral equations using wavelets on a bounded interval. IEEE Trans Antenna Propag. 43:(6):1995;614-622.
13. von Petersdorff T., Schwab C. Wavelet approximations for first kind boundary integral equations on polygons. Numerische Mathematik. 74:1996;479-519.
14. Wang G. Application of wavelets on the interval to numerical analysis of integral equations in electromagnetic scattering problems. Int J Numer Meth Engng. 40:1997;1-13.
15. Rathsfeld A. A wavelet algorithm for the boundary element solution of a geodetic boundary value problem. Comput Meth Appl Mech Engng. 157:1998;267-287.
16. Lage C., Schwab C. Wavelet Galerkin algorithms for boundary integral equations. SIAM J Sci Comput. 20:(6):1999;2195-2222.
17. Koro K., Abe K. Non-orthogonal spline wavelets for boundary element analysis. Engng Anal Bound Elem. 25:2001;149-164.
18. Koro K., Abe K. Determination of optimal threshold for matrix compression in wavelet BEM. Bescos D.E., Brebbia C.A., Katsikadelis J.T., Manolis G.D. Boundary Elements XXIII. 2001;475-484 WIT Press, Southampton.
19. Abe K., Koro K. Gauss quadrature method using wavelet basis as a weighting function for boundary element analysis. Bescos D.E., Brebbia C.A., Katsikadelis J.T., Manolis G.D. Boundary elements XXIII. 2001;455-464 WIT Press, Southampton.
20. Parreira P., Guiggiani M. On the implementation of the Galerkin approach in the boundary element method. Comput Struct. 33:(1):1989;269-279.
21. Guiggiani M., Gigante A. A general algorithm for multi-dimensional Cauchy principal value integrals in the boundary element method. J Appl Mech ASME. 57:1990;906-915.
22. Lachat J.C., Watson J.O. Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics. Int J Numer Meth Engng. 10:1976;991-1005.
23. Telles J.C.F. A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer Meth Engng. 24:1987;959-973.
24. Saad Y., Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear system. SIAM J Sci Stat Comput. 7:(3):1986;856-869.