Haar wavelet based algorithm for solution of second order electromagnetic problems in time and space domains

Abstract

In this paper, a novel wavelet algorithm has been proposed for solving second order electromagnetic problems both in time and space domains. The algorithm has been used to solve four different problems, i.e. the transmission line problem, the problems associated with electromagnetic waves travelling in different media, the problem related to uniform plane wave in lossy dielectric and problem associated with the telegrapher's equation. The comparison between the results obtained using the proposed approach and the conventional numerical techniques demonstrate that the proposed technique exhibits better time complexity. In essence, the proposed algorithm possesses complexity of order $O\left(n\right)$ whereas the conventional technique possesses complexity order of $O\left(n^2\right)$. Furthermore, the memory requirement of the proposed algorithm is significantly lower when compared to the conventional technique.

Keywords:

• 2nd order EM problem
• Haar wavelet
• space domain
• time domain

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Arun Kumar  http://orcid.org/0000-0002-9085-2682

Additional information

Notes on contributors

Arun Kumar

Arun Kumar is pursuing Ph.D. in Electrical Engineering Department from Jamia Millia Islamia University, New Delhi, India, with the specialization of computational Electromagnetics. He earned his M.Tech degree from Electronics Engineering Department of Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India, with specialization of Digital System in 2012.