Geodesic
Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 186-201
In this paper we analyze in detail the spectral properties of the block-triangular preconditioner introduced by Gerardo-Giorda et al. [J. Comput. Phys., 228 (2009), pp. 3625 -- 3639] for the Bidomain system in non-symmetric form. We show that the conditioning of the preconditioned problem is bounded in the Fourier space independently of the frequency variable, ensuring quasi-optimality with respect to the mesh size. We derive an explicit formula to optimize the preconditioner performance by identifying a parameter that depends only on the coefficients of the problem and is easy to compute. We provide numerical tests in three dimensions that confirm the optimality of the parameter and the substantial independence of the mesh size.
Classification : 65M60, 65M12, 65F08
Keywords: electrocardiology, bidomain system, preconditioning, finite elements 
@article{ETNA_2012__39__a15,
     author = {Gerardo-Giorda,  Luca and Mirabella,  Lucia},
     title = {Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology},
     journal = {Electronic transactions on numerical analysis},
     pages = {186--201},
     year = {2012},
     volume = {39},
     zbl = {1287.65078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a15/}
}
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%J Electronic transactions on numerical analysis
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Gerardo-Giorda,  Luca; Mirabella,  Lucia. Spectral analysis of a block-triangular preconditioner for the bidomain system in electrocardiology. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 186-201. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a15/