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Title Interpolating Wavelets and Adaptive Finite Difference Schemes for Solving Maxwell's Equations: The Effects of Gridding
Author Pedro Pinho, Margarete Domingues, Paulo J S G Ferreira, Sônia M. Gomes, Anamaria Gomide, José Rocha Pereira
Journal IEEE Transactions on Magnetics
Volume 43
Number 3
Pages 1013-1022
Month March
Year 2007
DOI [1]
Group (before 2015) Signal Processing Laboratory
Indexed by ISI Yes


This paper discusses the use of sparse point representations (SPR) in computational eletromagnetics. The idea is to represent the solution using only those samples that correspond to significant wavelet coefficients. The paper studies staggered and non-staggered grids for the discretization of the magnetic and electrical fields. Both lead to sparse grids that adapt in space to the local smoothness of the fields, and, at the same time, track the evolution of the fields over time. The conclusion is that schemes based on staggered grids lead to better numerical dispersion, specially for low order schemes and coarse grids; however, for a given accuracy, the adaptive, non-staggered grid scheme requires less computational effort, and its dispersion characteristics can be controlled by varying the order and the grid density. The SPR method combined with non-staggered grids therefore seems to have a good potential in computational electromagnetics.