We can solve electromagnetic problems using two main mathematical tools: vector calculus and differential equations. These tools command the computational electromagnetic domain. However, these tools are not always needed for the realistic modeling of electromagnetic problems. In reality, we are interested in the measurement of scalar quantities in electromagnetics, not vector quantities. Conventional electromagnetic simulation approaches are proving to be more mathematical than physical. Furthermore, the use of differential equations leads us along a different route for modeling fundamental physics. Since computers need discrete formulations, we can’t directly transform continuous differential equations into numerical algorithms. The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities. This paper simulates a parallel plate capacitor using global variables and calculating and comparing the potentials with the analytical method. The measured results show a good agreement between the analytical and the algebraic topological methods.
| Published in | American Journal of Electromagnetics and Applications (Volume 9, Issue 2) |
| DOI | 10.11648/j.ajea.20210902.11 |
| Page(s) | 13-18 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Topological, Scalar, Vector, Variables, Simplex, Primal, Dual, Capacitor
| [1] | Sommerfeld, A., Electrodynamics - Lectures on Theoretical Physics, Vol. 3, Academic Press, Inc, 1952. |
| [2] | W. L. Burke, Applied Differential Geometry. Cambridge: Cambridge University Press, 1985. |
| [3] | Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, 1941. |
| [4] | G. A. Deschamps, “Electromagnetics and differential forms,” in IEEE Proceedings, vol. 69, pp. 676–696, 1981. |
| [5] | Tonti, E., “Why starting with differential equations for computational physics,” Journal of Computational Physics, Vol. 257, 1260–1290, 2014. |
| [6] | Algebraic Topological Method: An Alternative Modelling Tool for Electromagnetics. |
| [7] | Burke, W. L., Div, grad, curl are dead, version 2.0, Oct 1995. |
| [8] | K. Sankaran and B. Sairam, “Modelling of nanoscale quantum tunnelling structures using algebraic topology method,” in AIP Conference Proceedings. |
| [9] | K. Sankaran, “Old tools are not enough: Recent trends in computational electromagnetics for defense applications,” DRDO Defence Science Journal, 2018. In review. |
| [10] | K. Sankaran, “Perspective: Are you using the right tools in computational electromagnetics?” Journal of Applied Physics, 2018. |
| [11] | Aakash, A. Bhatt, and K. Sankaran, “How to model electromagnetic problems without using vector calculus and differential equations?” IETE Journal of Education, vol. 59, no. 2, 2018. |
| [12] | E. Tonti, “Why starting with differential equations for computational physics,” J. Comput. Phys., Vol. 257, no. Part B, pp. 1260–1290, 2014. |
| [13] | R. Feynman, Lectures in Physics vol. 2. New York: Addison-Wesley. |
| [14] | T. Karunakaran, “Algebraic structure of network topology,” in Proceedings of the Indian National Science Academy, vol. 41, pp. 213–215, 1975. |
| [15] | ALGEBRAIC TOPOLOGY AND COMPUTATIONAL ELECTROMAGNETISM E. Tonti University di Trieste, 34127 Trieste, Italia. |
| [16] | T. Tarhasaari and L. Kettunen, “Topological approach to computational electromagnetism,” Progress Electromagn. Res., Vol. 32, pp. 189–206, 2001. |
| [17] | H. M. Schey, Div, Grad, Curl and All That - An Informal Text on Vector Calculus. 1 ed., W. W. Norton & Company, 1973. |
| [18] | A brief history of maxwells equation document-8685744. |
| [19] | Deschamps, Georges. A.,“Electromagnetics and Differential Forms,” Proceedings of the IEEE, Vol. 69, No. 6, 676–696, Jun 1981. |
| [20] | Fan, Ting-Jun, Describing and Recognizing 3D Objects Using Surface Properties, Berlin-New York, 1990. |
| [21] | Hatcher, Allen, Algebraic topology, Cambridge University Press, Cambridge, 2002. |
| [22] | Langefors, B., Algebraic Topology and Networks, Technical Report TN 43, Svenska Aeroplan Aktiebolaget, 1959. |
| [23] | An algebraic topological method and future identification Erik Carlsson, Gunnar Carlsson, and Vin de Silva. |
| [24] | Recent Trends in Computational Electromagnetics for Defence Applications._Computational_Electromagnetics_for_Defence Application. |
| [25] | J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Philos. Trans. R. Soc. London, Vol. 155, pp. 459–512, 1865. |
| [26] | E. Tonti, The Mathematical Structure of Classical and Relativistic Physics - A General Classification Diagram. Basel: Birkhäuser Basel. |
| [27] | A. Shaji and K. Sankaran, “Thermal integrity modelling using finite-element, finite-volume, and algebraic topological methods”, inAIP Conference Proceedings. |
APA Style
Vikram Reddy Anapana, Venkata Kowshik Sivva, Pranav Sai, Venkatesh Gongolu, Lanka Mithin Chakravarthy. (2021). Electromagnetic Problems Modeling Using Algebraic Topological Method. American Journal of Electromagnetics and Applications, 9(2), 13-18. https://doi.org/10.11648/j.ajea.20210902.11
ACS Style
Vikram Reddy Anapana; Venkata Kowshik Sivva; Pranav Sai; Venkatesh Gongolu; Lanka Mithin Chakravarthy. Electromagnetic Problems Modeling Using Algebraic Topological Method. Am. J. Electromagn. Appl. 2021, 9(2), 13-18. doi: 10.11648/j.ajea.20210902.11
AMA Style
Vikram Reddy Anapana, Venkata Kowshik Sivva, Pranav Sai, Venkatesh Gongolu, Lanka Mithin Chakravarthy. Electromagnetic Problems Modeling Using Algebraic Topological Method. Am J Electromagn Appl. 2021;9(2):13-18. doi: 10.11648/j.ajea.20210902.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajea.20210902.11,
author = {Vikram Reddy Anapana and Venkata Kowshik Sivva and Pranav Sai and Venkatesh Gongolu and Lanka Mithin Chakravarthy},
title = {Electromagnetic Problems Modeling Using Algebraic Topological Method},
journal = {American Journal of Electromagnetics and Applications},
volume = {9},
number = {2},
pages = {13-18},
doi = {10.11648/j.ajea.20210902.11},
url = {https://doi.org/10.11648/j.ajea.20210902.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20210902.11},
abstract = {We can solve electromagnetic problems using two main mathematical tools: vector calculus and differential equations. These tools command the computational electromagnetic domain. However, these tools are not always needed for the realistic modeling of electromagnetic problems. In reality, we are interested in the measurement of scalar quantities in electromagnetics, not vector quantities. Conventional electromagnetic simulation approaches are proving to be more mathematical than physical. Furthermore, the use of differential equations leads us along a different route for modeling fundamental physics. Since computers need discrete formulations, we can’t directly transform continuous differential equations into numerical algorithms. The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities. This paper simulates a parallel plate capacitor using global variables and calculating and comparing the potentials with the analytical method. The measured results show a good agreement between the analytical and the algebraic topological methods.},
year = {2021}
}
TY - JOUR T1 - Electromagnetic Problems Modeling Using Algebraic Topological Method AU - Vikram Reddy Anapana AU - Venkata Kowshik Sivva AU - Pranav Sai AU - Venkatesh Gongolu AU - Lanka Mithin Chakravarthy Y1 - 2021/09/26 PY - 2021 N1 - https://doi.org/10.11648/j.ajea.20210902.11 DO - 10.11648/j.ajea.20210902.11 T2 - American Journal of Electromagnetics and Applications JF - American Journal of Electromagnetics and Applications JO - American Journal of Electromagnetics and Applications SP - 13 EP - 18 PB - Science Publishing Group SN - 2376-5984 UR - https://doi.org/10.11648/j.ajea.20210902.11 AB - We can solve electromagnetic problems using two main mathematical tools: vector calculus and differential equations. These tools command the computational electromagnetic domain. However, these tools are not always needed for the realistic modeling of electromagnetic problems. In reality, we are interested in the measurement of scalar quantities in electromagnetics, not vector quantities. Conventional electromagnetic simulation approaches are proving to be more mathematical than physical. Furthermore, the use of differential equations leads us along a different route for modeling fundamental physics. Since computers need discrete formulations, we can’t directly transform continuous differential equations into numerical algorithms. The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities. This paper simulates a parallel plate capacitor using global variables and calculating and comparing the potentials with the analytical method. The measured results show a good agreement between the analytical and the algebraic topological methods. VL - 9 IS - 2 ER -
Information
Email: