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Efficient Triangular Interpolation Methods: Error Analysis and Applications
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PRE
AI
DOI：10.1109/LAWP.2020.2988289.png)
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Abstract
En 中文
The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (rms) errors on the right triangular, equilateral triangular, and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and rms errors are directly proportional to the (p + 1)th power of kh for both 1-D and (2-D, bivariate) interpolations, where k is the wavenumber and h is the mesh size. The interpolation regions for the right triangular, equilateral triangular, and rectangular interpolations are selected based on the regions with smallest errors. The triangular and rectangular interpolations are applied to evaluate the 2-D singly periodic Green's function. The numerical results show that the equilateral triangular interpolation is the most accurate interpolation method, whereas the right triangular interpolation is the most efficient interpolation method.
Keywords:
Interpolation
Two dimensional displays
Finite element analysis
Nonhomogeneous media
Error analysis
Method of moments
Propagation
Bivariate interpolation
equilateral triangular interpolation
Lagrange polynomial interpolation
periodic Green's function (PGF)
right-triangular interpolation
Journal
IF:
4.8
Papers:
1.0W
Citations:
2.9W
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Cited Papers
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