Utilization of wavelet concepts in finite elements for efficient solution of Maxwell's equation

Tapan Kumar Sarkar, Luis Emilio Garcia-Castillo, Magdalena Salazar-Palma

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Scopus citations

Abstract

The wavelet concept has been introduced in the applied mathematics literature as a new mathematical subject for performing localized `Time-frequency' characterization. It is a versatile tool with `very rich mathematical content and great potential for applications'. Because of this localized property both in the original and in the transform domain it is expected that its application particularly to solution of partial differential equations would be quite interesting. Utilization of a wavelet type basis has the advantage that the condition number of the system matrix does not increase rapidly with an increase in the number of unknowns unlike the original version of the finite element methods. In this paper the wavelet concepts have been developed and explained with application to 1D-differential equations. It will be shown how this can be incorporated in a Galerkin's method (or equivalently, e.g. Finite Element Method) for efficient solution of 2D problems. Numerical examples will be been presented for efficient solution of waveguide problems utilizing this approach.

Original languageEnglish (US)
Title of host publicationIEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
PublisherIEEE Computer Society
Pages7
Number of pages1
Volume1
StatePublished - 1994
EventProceedings of the IEEE Antennas and Propagation International Symposium. Part 3 (of 3) - Seattle, WA, USA
Duration: Jun 19 1994Jun 24 1994

Other

OtherProceedings of the IEEE Antennas and Propagation International Symposium. Part 3 (of 3)
CitySeattle, WA, USA
Period6/19/946/24/94

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Utilization of wavelet concepts in finite elements for efficient solution of Maxwell's equation'. Together they form a unique fingerprint.

  • Cite this

    Sarkar, T. K., Garcia-Castillo, L. E., & Salazar-Palma, M. (1994). Utilization of wavelet concepts in finite elements for efficient solution of Maxwell's equation. In IEEE Antennas and Propagation Society, AP-S International Symposium (Digest) (Vol. 1, pp. 7). IEEE Computer Society.