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A multilevel adaptive solver based on second‐generation wavelet thresholding techniques
Author(s) -
Limon Alfonso,
Morris Hedley
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.479
Subject(s) - wavelet , solver , multigrid method , thresholding , mathematics , algorithm , gaussian , quantum , poisson's equation , representation (politics) , wavelet transform , computer science , mathematical optimization , mathematical analysis , partial differential equation , artificial intelligence , quantum mechanics , image (mathematics) , physics , politics , political science , law
In this manuscript, we introduce a second‐generation wavelet thresholding technique used to construct a numerically stable non‐dyadic sparse grid representation. The resulting second‐generation wavelet projectors, when coupled to a multigrid solver, provide an elegant method for integrating the numerical solution. The combined method is then utilized in the solution of a singular perturbation problem that arises when modelling an n‐MOS gate exhibiting quantum tunnelling. The resulting solution is compared with the full Schrödinger–Poisson system, and the two solutions are shown to be in good agreement. Copyright © 2006 John Wiley & Sons, Ltd.