On the Construction and Use of Two-Dimensional Wavelet-Like Basis
Keywords:
On the Construction and Use of Two-Dimensional Wavelet-Like BasisAbstract
An alternative method for generating higher dimensional wavelet-like basis functions is proposed in this paper. One method that has been used was to derive the two-dimensional wavelet-like basis from the two-dimensional traditional finite element basis. However, in this paper, products of one-dimensional wavelet-like functions are used as two-dimensional waveletlike basis functions. The generation of linear wavelet-like functions is discussed in detail and the use of linear and higher order wavelet-like functions is also investigated. The advantages and disadvantages of this technique for deriving wavelet-like basis functions will be discussed.
Downloads
References
M. Krumpholz and L. P. B. Katehi,
"MRTD: New Time Domain Schemes
Based on Multiresolution Analysis," IEEE
Transactions on Microwave Theory and
Techniques, Vol. 44, No. 4, pp. 555-571,
April 1996.
Richard K. Gordon, "On the use of
wavelet-like basis functions in the finite
element analysis of elliptic problems,"
Proceedings of the Eleventh Annual
Review of Progress in Applied
Computational Electromagnetics, pp. 559-
, Monterey, CA, March 1995.
W. Elliott Hutchcraft, Richard K. Gordon,
and Jin-Fa Lee, “A Finite Element Time
Domain Method Using Wavelet-Like Basis
Functions”, Proceedings of The Thirty-First
Southeastern Symposium on System
Theory, pp. 310-314, Vol. 1, March 1999.
Stephane Jaffard, "Wavelet methods for
fast resolution of elliptic problems," SIAM
Journal on Numerical Analysis, vol. 29,
num. 4, pp. 965-986, August 1992.
I. Daubechies, “Orthonormal bases of
compactly supported wavelets,” Commun.
Pure Appl. Math., vol. 41, pp. 909-996,
November 1988.
W. Elliott Hutchcraft and Richard K.
Gordon, “On the Generation of Two-
dimensional Wavelet-Like Basis
Functions”, Proceedings of The Thirty-
Third Southeastern Symposium on System
Theory, pp. 387-390, March 2001.
W. Elliott Hutchcraft and Richard K.
Gordon, “Higher Order Wavelet-Like Basis
Functions in the Numerical Solution of
Partial Differential Equations using the
Finite Element Method”, Proceedings of
The Thirty-Third Southeastern Symposium
on System Theory, pp. 391-394, March
Y.W. Cheong, Y. M. Lee, and K. H. Ra et.
al., “Wavelet-Galerkin scheme of time-
dependent inhomogeneous electromagnetic
problems,” IEEE Microwave Guided Wave
Lett., vol 9, pp. 297-299, August 1999.
Ben Zion Steinberg and Yehuda Leviatan,
“On the use of wavelet expansions in the
method of moments,” IEEE Transactions
on Antennas and Propagation, vol. 4 1, no.
, pp. 610-619, May 1993.
T. K. Sarkar, L. E. Garcia-Castillo, and M.
S. Salazar-Palma, “Utilization of wavelet
concepts in finite elements for efficient
solution of Maxwell's equation,” 1994
Digest of the IEEE Antennas and
Propagation Society International
Symposium, vol. 1, p. 7, June 1994.
H. C. Schweinler and E. P. Wigner,
“Orthogonalization methods,” Journal of
Mathematical Physics, pp. 1693-1694, May
Gene H. Golub and Charles F. Van Loan,
Matrix Computations, Second Edition, p.
, The Johns Hopkins University Press,
