American Journal of Applied Mathematics and Statistics, 2014, Vol. 2, No. 3, 96-105 Available online at http://pubs.sciepub.com/ajams/2/3/3 © Science and Education Publishing DOI:10.12691/ajams-2-3-3 Application of Haar Wavelets and Method of Moments for Computing Performance Characteristics of Electromagnetic Materials Vishwa Nath Maurya 1,* , Avadhesh Kumar Maurya 2 1 Department of Mathematics, School of Science & Technology, University of Fiji, Fiji Ex-Professor & Director, Vision Institute of Technology, U.P. Technical University, India 2 Department of Electronics & Communication Engineering Lucknow Institute of Technology, U.P. Technical University, India *Corresponding author: prof.drvnmaurya@gmail.com, prof_vnmaurya@yahoo.in Received April 02, 2014; Revised April 18, 2014; Accepted April 20, 2014 Abstract Present paper demonstrates on application aspect of Haar wavelets and method of moments for computing performance characteristics in electromagnetic field. In this paper, some significant results including performance characteristics relevant to application of the Haar wavelets as the expansion function in the method of moments have been successfully explored. The present analysis for performance evaluation has been focused for three different electromagnetic materials- finite straight, thin plane plate and eddy current problem. The main results explored are described in the main text and also concluded at the end with discussions. Keywords: matrix, method of moments, Haar wavelets, performance characteristics, electromagnetic, square plane plate, eddy current problem Cite This Article: Vishwa Nath Maurya, and Avadhesh Kumar Maurya, “Application of Haar Wavelets and Method of Moments for Computing Performance Characteristics of Electromagnetic Materials.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 3 (2014): 96-105. doi: 10.12691/ajams-2-3-3. 1. Introduction Literature reveals that wavelets and different mathematical techniques have been applied in different frameworks rigorously by tremendous previous researchers. In the early of seventh decade, Harrington [13] studied time-harmonic electromagnetic fields and Phillips [38] presented numerical solution of certain integral equations occurring in electromagnetic. Later in 1965, Richmond [40] confined to explore digital computer solutions of the rigorous equations for scattering problems in electromagnetic. Subsequently keeping in view of increased interest of researchers in this direction Mittra [31] authored a noteworthy textbook on computer techniques for electromagnetic and Stoll [43] also succeeded to present a marvelous textbook on analysis of eddy currents. On the subject some other textbooks are available, for more details we refer Chui [7] and Constantine [10]. It is noticeable that demand of applications of wavelets in electromagnetic engineering problems by previous researchers has been significantly increased since eighth decade and therefore a number of previous noteworthy researchers e.g. [3,4,5,6,8,9,12,14,19,21,28,29,34,36,37,39,42] confined their attention in this direction in order to analyze rigorously using different mathematical and computer techniques. Among them, Belardi et al. [3,4] focused their keen attention on applications of Harrs wavelets for solving electrostatic problems and their computational aspects. Furthermore, it is universally accepted that different mathematical techniques have their wide applications in solving engineering problems including electromagnetic materials. Perhaps this may the reason why some earlier researchers e.g. Bossavit [5], Datta [11], Petre P. et al. [36,37], Maurya [22-27] applied different mathematical techniques in different frameworks. To be more specific, Bossavit [5] used a numerical approach to transient nonlinear eddy current problems in applied electromagnetic field. Petre P. et al. [36] applied integral equation approach to analyze scattering from one- dimensional periodic coated strips. In this connection it is remarkable here that Harrington [13] succeeded to compute electromagnetic field using moment method. Here, we are keenly interested to focus the main theoretical aspects of the method of moments and of the Haar wavelets for computing some significant performance characteristics in electromagnetic field. 2. The Method of Moments As stated earlier that the method of moments is a mathematical technique having its numerical nature which has already been applied by some previous researchers e.g. Harrington [13], and hence the complete description and details of this method have already been presented in many papers, in order to guide the reader through the overall method explanation, a brief summary is here shown. In a simplified way, it can be mentioned that the