Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems

George Pan, M. Toupikov, J. Du, B. K. Gilbert

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

The method of moments (MOM) has been used to solve antenna and scattering problems for several decades, due both to its flexibility in handling complex geometric structures and to its numerical accuracy. However, for electrically large problems, the MOM often becomes incapable of achieving solutions due to its requirements for vast amounts of local memory and processor cycles. To overcome this difficulty, orthonormal wavelets have been introduced, which create very sparse moment matrices that can be evaluated by iterative techniques. Nevertheless, the traditional orthonormal wavelets have demonstrated several limitations. The use of intervallic wavelets is presented; they form an orthonormal basis and preserve the same multi-resolution analysis as other unbounded wavelets. In contrast to periodic wavelets, endpoint values are not restricted if the unknown function is expanded in terms of intervallic wavelets. Very sparse impedance matrices have been obtained with this method. Zero elements of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. The majority of matrix elements are evaluated directly, without performing numerical integration procedures such as Gaussian quadrature. The construction of intervallic wavelets is presented. Numerical examples of 2-D and 3-D scattering problems are discussed, and the relative error of this method is studied analytically.

Original languageEnglish (US)
Title of host publicationIEE Proceedings: Microwaves, Antennas and Propagation
Pages471-479
Number of pages9
Volume145
Edition6
StatePublished - 1998

Fingerprint

Scattering
Method of moments
Multiresolution analysis
Antennas
Data storage equipment

Keywords

  • Coifman wavelets
  • Intervallic wavelets
  • Scattering

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

Pan, G., Toupikov, M., Du, J., & Gilbert, B. K. (1998). Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems. In IEE Proceedings: Microwaves, Antennas and Propagation (6 ed., Vol. 145, pp. 471-479)

Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems. / Pan, George; Toupikov, M.; Du, J.; Gilbert, B. K.

IEE Proceedings: Microwaves, Antennas and Propagation. Vol. 145 6. ed. 1998. p. 471-479.

Research output: Chapter in Book/Report/Conference proceedingChapter

Pan, G, Toupikov, M, Du, J & Gilbert, BK 1998, Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems. in IEE Proceedings: Microwaves, Antennas and Propagation. 6 edn, vol. 145, pp. 471-479.
Pan G, Toupikov M, Du J, Gilbert BK. Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems. In IEE Proceedings: Microwaves, Antennas and Propagation. 6 ed. Vol. 145. 1998. p. 471-479
Pan, George ; Toupikov, M. ; Du, J. ; Gilbert, B. K. / Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems. IEE Proceedings: Microwaves, Antennas and Propagation. Vol. 145 6. ed. 1998. pp. 471-479
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