Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators

A. Feher, Sz Nagy, J. Pipek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation.

Original languageEnglish
Title of host publication2nd Middle East Conference on Antennas and Propagation, MECAP 2013
DOIs
Publication statusPublished - 2013
Event2nd Middle East Conference on Antennas and Propagation, MECAP 2013 - Cairo, Egypt
Duration: Dec 29 2012Dec 31 2012

Other

Other2nd Middle East Conference on Antennas and Propagation, MECAP 2013
CountryEgypt
CityCairo
Period12/29/1212/31/12

Fingerprint

Electromagnetic waves
Error analysis
Resonators
Waveguides
Differential equations
Economics

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Feher, A., Nagy, S., & Pipek, J. (2013). Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators. In 2nd Middle East Conference on Antennas and Propagation, MECAP 2013 [6618193] https://doi.org/10.1109/MECAP.2012.6618193

Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators. / Feher, A.; Nagy, Sz; Pipek, J.

2nd Middle East Conference on Antennas and Propagation, MECAP 2013. 2013. 6618193.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Feher, A, Nagy, S & Pipek, J 2013, Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators. in 2nd Middle East Conference on Antennas and Propagation, MECAP 2013., 6618193, 2nd Middle East Conference on Antennas and Propagation, MECAP 2013, Cairo, Egypt, 12/29/12. https://doi.org/10.1109/MECAP.2012.6618193
Feher A, Nagy S, Pipek J. Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators. In 2nd Middle East Conference on Antennas and Propagation, MECAP 2013. 2013. 6618193 https://doi.org/10.1109/MECAP.2012.6618193
Feher, A. ; Nagy, Sz ; Pipek, J. / Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators. 2nd Middle East Conference on Antennas and Propagation, MECAP 2013. 2013.
@inproceedings{ed2200935a6145479aa416da2370cd86,
title = "Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators",
abstract = "Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation.",
author = "A. Feher and Sz Nagy and J. Pipek",
year = "2013",
doi = "10.1109/MECAP.2012.6618193",
language = "English",
isbn = "9781479912780",
booktitle = "2nd Middle East Conference on Antennas and Propagation, MECAP 2013",

}

TY - GEN

T1 - Error estimation of wavelet based modeling of electromagnetic waves in waveguides and resonators

AU - Feher, A.

AU - Nagy, Sz

AU - Pipek, J.

PY - 2013

Y1 - 2013

N2 - Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation.

AB - Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation.

UR - http://www.scopus.com/inward/record.url?scp=84887714462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887714462&partnerID=8YFLogxK

U2 - 10.1109/MECAP.2012.6618193

DO - 10.1109/MECAP.2012.6618193

M3 - Conference contribution

SN - 9781479912780

BT - 2nd Middle East Conference on Antennas and Propagation, MECAP 2013

ER -