A FINITE ELEMENT APPROACH FOR THE DUAL RUDIN-OSHER-FATEMI MODEL AND ITS NONOVERLAPPING DOMAIN DECOMPOSITION METHODS

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We consider a finite element discretization for the dual Rudin-Osher-Fatemi model using a Raviart-Thomas basis for H-0 (div; Omega). Since the proposed discretization has a splitting property for the energy functional, which is not satisfied for existing finite difference-based discretizations, it is more adequate for designing domain decomposition methods. In this paper, a primal domain decomposition method is proposed which resembles the classical Schur complement method for the second order elliptic problems, and it achieves O(1/n(2)) convergence. A primal-dual domain decomposition method based on the method of Lagrange multipliers on the subdomain interfaces is also considered. Local problems of the proposed primal-dual domain decomposition method can be solved at a linear convergence rate. Numerical results for the proposed methods are provided.
Publisher
SIAM PUBLICATIONS
Issue Date
2019-03
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON SCIENTIFIC COMPUTING, v.41, no.2, pp.B205 - B228

ISSN
1064-8275
DOI
10.1137/18M1165499
URI
http://hdl.handle.net/10203/262763
Appears in Collection
MA-Journal Papers(저널논문)
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