Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena

Lombardini R, Acevedo R, Kuczala A, Keys KP, Goodrich CP, Johnson BR. 2016. Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena. Journal of Computational Physics. 305, 244–262.

Download
No fulltext has been uploaded. References only!

Journal Article | Published | English
Author
Lombardini, Richard; Acevedo, Ramiro; Kuczala, Alexander; Keys, Kerry P.; Goodrich, Carl PeterIST Austria ; Johnson, Bruce R.
Abstract
An orthogonal wavelet basis is characterized by its approximation order, which relates to the ability of the basis to represent general smooth functions on a given scale. It is known, though perhaps not widely known, that there are ways of exceeding the approximation order, i.e., achieving higher-order error in the discretized wavelet transform and its inverse. The focus here is on the development of a practical formulation to accomplish this first for 1D smooth functions, then for 1D functions with discontinuities and then for multidimensional (here 2D) functions with discontinuities. It is shown how to transcend both the wavelet approximation order and the 2D Gibbs phenomenon in representing electromagnetic fields at discontinuous dielectric interfaces that do not simply follow the wavelet-basis grid.
Publishing Year
Date Published
2016-01-15
Journal Title
Journal of Computational Physics
Volume
305
Page
244-262
ISSN
IST-REx-ID

Cite this

Lombardini R, Acevedo R, Kuczala A, Keys KP, Goodrich CP, Johnson BR. Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena. Journal of Computational Physics. 2016;305:244-262. doi:10.1016/j.jcp.2015.10.035
Lombardini, R., Acevedo, R., Kuczala, A., Keys, K. P., Goodrich, C. P., & Johnson, B. R. (2016). Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena. Journal of Computational Physics. Elsevier. https://doi.org/10.1016/j.jcp.2015.10.035
Lombardini, Richard, Ramiro Acevedo, Alexander Kuczala, Kerry P. Keys, Carl Peter Goodrich, and Bruce R. Johnson. “Higher-Order Wavelet Reconstruction/Differentiation Filters and Gibbs Phenomena.” Journal of Computational Physics. Elsevier, 2016. https://doi.org/10.1016/j.jcp.2015.10.035.
R. Lombardini, R. Acevedo, A. Kuczala, K. P. Keys, C. P. Goodrich, and B. R. Johnson, “Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena,” Journal of Computational Physics, vol. 305. Elsevier, pp. 244–262, 2016.
Lombardini R, Acevedo R, Kuczala A, Keys KP, Goodrich CP, Johnson BR. 2016. Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena. Journal of Computational Physics. 305, 244–262.
Lombardini, Richard, et al. “Higher-Order Wavelet Reconstruction/Differentiation Filters and Gibbs Phenomena.” Journal of Computational Physics, vol. 305, Elsevier, 2016, pp. 244–62, doi:10.1016/j.jcp.2015.10.035.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar