volume | PIER Journals

2024-03-31

A Stable and Efficient Interpolation Method for Two-Dimensional Periodic Green's Functions

Lian Feng Ma,

Dr. Lian Feng Ma

The University of Electronic Science and Technology of China

China

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Qing Guang Zhao,

Dr. Qing Guang Zhao

Shanghai Institute of Satellite Egineering

China

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Chong Guo,

Mr. Chong Guo

School of Electronic Engineering

Xidian University

China

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Yi Ren

Professor Yi Ren

School of Electronics Engineering

Xidian University

China

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Progress In Electromagnetics Research M, Vol. 126, 29-36, 2024

doi:10.2528/PIERM24020207

Abstract

This paper presents an efficient and stable interpolation method for calculating two-dimensional periodic Green's function and its gradient. The method consists of two steps: constructing an interpolation table in the first step and using linear interpolation to extract the desired Green's function from the interpolation table in the second step. In the construction of the interpolation table, several properties of the two-dimensional periodic Green's function are fully utilized, which minimize the size of the interpolation table. When the elements in the interpolation table are computed, all possible singular terms are removed, ensuring that the interpolation function maintains high linearity even under extreme skew periodic grids. This means that linear interpolation can guarantee sufficient accuracy. Numerical results demonstrate effectiveness of the proposed method, making it suitable for combining with numerical methods for electromagnetic field calculation and analysis of periodic structures.

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Lian Feng Ma, Qing Guang Zhao, Chong Guo, and Yi Ren, "A Stable and Efficient Interpolation Method for Two-Dimensional Periodic Green's Functions," Progress In Electromagnetics Research M, Vol. 126, 29-36, 2024.
doi:10.2528/PIERM24020207

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