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Cited by 52Electromagnetic Simulation and Numerical MethodsElectromagnetic Scattering and AnalysisAdvanced Numerical Methods in Computational Mathematics

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Numerical Solutions to Poisson Equations Using the Finite-Difference Method [Education Column]

Nagel, James R.·2014·IEEE Antennas and Propagation Magazine
DOI 10.1109/map.2014.6931698
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Abstract

The Poisson equation is an elliptic partial differential equation that frequently emerges when modeling electromagnetic systems. However, like many other partial differential equations, exact solutions are difficult to obtain for complex geometries. This motivates the use of numerical methods in order to provide accurate results for real-world systems. One very simple algorithm is the Finite-Difference Method (FDM), which works by replacing the continuous derivative operators with approximate finite differences. Although the Finite-Difference Method is one of the oldest methods ever devised, comprehensive information is difficult to find compiled in a single reference. This paper therefore provides a tutorial-level derivation of the Finite-Difference Method from the Poisson equation, with special attention given to practical applications such as multiple dielectrics, conductive materials, and magnetostatics.

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Research works printed but not linked: 19

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  14. 10.1109/TMTT.1965.1126063 · DOI
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  18. 10.1088/0508-3443/1/4/303 · DOI
  19. jin, 2002, The Finite Element Method in Electromagnetics

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Metadata

Authors
Nagel, J. R.
Corresponding author
Nagel, James R.
ORCID
Nagel, James R.
Venue
IEEE Antennas and Propagation Magazine
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2014-08
Volume
56
Issue
4
Pages
209-224
ISSN
1045-9243 (ISSN-L)
DOI
10.1109/map.2014.6931698
OpenAlex
W2316277765
Cited by
52
References
0
Citations by year
2026: 3 · 2025: 10 · 2024: 8 · 2023: 6 · 2022: 6 · 2021: 5 · 2020: 4 · 2019: 4 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 3
FWCI
0.89
Type
journal article
Language
en
Open access
closed
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations
IEEE Antennas and Propagation Magazine (publishedVersion)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Electromagnetic Simulation and Numerical Methods
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Electromagnetic Scattering and Analysis
  • Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Methods in Computational Mathematics
Keywords
Poisson equation, finite difference method, elliptic equations, electromagnetic simulation, numerical solution of partial differential equations, conductive materials, magnetostatics

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