NDLI: Adaptive cell-centered finite volume method for diffusion equations on a consistent quadtree grid

Content Provider	Springer Nature Link
Author	Krivá, Zuzana Mikula, Karol Handlovičová, Angela
Copyright Year	2015
Abstract	Models applied in image processing are often described by nonlinear PDEs in which a good approximation of gradient plays an important role especially in such cases where irregular finite volume grids are used. In image processing, such a situation can occur during a coarsening based on quadtree grids. We present a construction of a deformed quadtree grid in which the connection of representative points of two adjacent finite volumes is perpendicular to their common boundary enabling us to apply the classical finite volume methods. On the other hand, for such an adjusted grid, the intersection of representative points connection with a finite volume boundary is not a middle point of their common edge and standard methods cannot achieve a good accuracy. In this paper we present a new cell-centered finite volume method to evaluate solution gradients, which results into a solution of a simple linear algebraic system and we prove its unique solvability. Finally we present numerical experiments for the regularized Perona-Malik model in which we applied this new method.
Ending Page	277
Page Count	29
Starting Page	249
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	2
Volume Number	42
Language	English
Publisher	Springer US
Publisher Date	2015-08-12
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Adaptivity Visualization Computational Mathematics and Numerical Analysis The linear heat equation Image processing Mathematical and Computational Biology Mesh generation and refinement Finite volume method Mathematical Modeling and Industrial Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Computational Science and Engineering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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