Title
Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics
Campus Units
Electrical and Computer Engineering
Document Type
Article
Publication Version
Published Version
Publication Date
10-12-2020
Journal or Book Title
IEEE Open Journal of Antennas and Propagation
Volume
1
First Page
590
Last Page
597
DOI
10.1109/OJAP.2020.3030091
Abstract
The interpolation errors of the higher order bivariate Lagrange polynomial interpolation based on the rectangular, right and equilateral triangular interpolations are measured by using the maximum and root-mean-square (RMS) errors. The error distributions of above three kinds of interpolations are analyzed to find the regions having the smallest interpolation error. Both analytical and numerical results show that the right triangular interpolation is the most efficient interpolation method. Although both the maximum and RMS errors of the right triangular interpolation are larger than that of the rectangular interpolation, the number of data points used in the triangular interpolation is up to 50% less than that used in the rectangular one. On the other hand, the equilateral triangular interpolation using the regions inside a big triangle as interpolation area is proved to be the most accurate interpolation method. The interpolation errors of the equilateral triangular are almost half of that of the rectangular interpolation. In addition, the right triangular, equilateral triangular and rectangular interpolations for the third and fourth orders are applied to accelerate the calculation of doubly periodic Green’s function (PGF).
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Owner
The Author(s)
Copyright Date
2020
Language
en
File Format
application/pdf
Recommended Citation
Luo, Wen; Liu, Jinbo; Li, Zengrui; and Song, Jiming, "Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics" (2020). Electrical and Computer Engineering Publications. 268.
https://lib.dr.iastate.edu/ece_pubs/268
Comments
This article is published as Luo, Wen, Jinbo Liu, Zengrui Li, and Jiming Song. "Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics." IEEE Open Journal of Antennas and Propagation 1 (2020): 590-597. DOI: 10.1109/OJAP.2020.3030091. Posted with permission.