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

The DOI matches its Crossref record.

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
Open this paper in CoChat — free account

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.

Overview

Integrity signals

Registry

Crossref · 10.1109/map.2014.6931698

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Still being checked.

Research works printed but not linked: 19

  1. 10.1109/APS.2011.5997050 · DOI
  2. 10.1109/JSEN.2012.2227996 · DOI
  3. paul, 2008, Analysis of Multiconductor Transmission Lines
  4. press, 2007, Numerical Recipes The Art of Scientific Computing
  5. 10.1109/20.497508 · DOI
  6. ulaby, 2010, Fundamentals of Applied Electromagnetics Sixth Edition
  7. 10.1006/jcph.2000.6545 · DOI
  8. 10.1109/TMTT.1969.1126998 · DOI
  9. 10.1002/jcc.540120405 · DOI
  10. 10.1002/(SICI)1096-987X(199608)17:11<1344::AID-JCC7>3.3.CO;2-K · DOI
  11. southwell, 1940, Relaxation Methods in Engineering Science— A Treatise in Approximate Computation
  12. 10.1049/piee.1967.0159 · DOI
  13. sakidu, 2001, Numerical Techniques in Electromagnetics
  14. 10.1109/TMTT.1965.1126063 · DOI
  15. 10.1007/978-0-387-68624-0 · DOI
  16. 10.1007/978-3-642-50319-1 · DOI
  17. 10.1109/TMTT.1967.1126537 · DOI
  18. 10.1088/0508-3443/1/4/303 · DOI
  19. jin, 2002, The Finite Element Method in Electromagnetics

Cited by

Sorted by citations

See all 52

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Numerical Solutions to Poisson Equations Using the Finite-Difference Method [Education Column]. https://app.cochat.ai/papers/10.1109/map.2014.6931698
The paper
Nagel, J. R. (2014). Numerical Solutions to Poisson Equations Using the Finite-Difference Method [Education Column]. IEEE Antennas and Propagation Magazine. https://doi.org/10.1109/map.2014.6931698