Volume 58, pp. 66-83, 2023.

Robust BDDC algorithms for finite volume element methods

Yanru Su, Xuemin Tu, and Yingxiang Xu


The balancing domain decomposition by constraints (BDDC) method is applied to the linear system arising from the finite volume element method (FVEM) discretization of a scalar elliptic equation. The FVEMs share nice features of both finite element and finite volume methods and are flexible for complicated geometries with good conservation properties. However, the resulting linear system usually is asymmetric. The generalized minimal residual (GMRES) method is used to accelerate convergence. The proposed BDDC methods allow for jumps of the coefficient across subdomain interfaces. When jumps of the coefficient appear inside subdomains, the BDDC algorithms adaptively choose the primal variables deriving from the eigenvectors of some local generalized eigenvalue problems. The adaptive BDDC algorithms with advanced deluxe scaling can ensure good performance with highly discontinuous coefficients. A convergence analysis of the BDDC method with a preconditioned GMRES iteration is provided, and several numerical experiments confirm the theoretical estimate.

Full Text (PDF) [1.2 MB], BibTeX

Key words

finite volume element methods, domain decomposition, BDDC, deluxe scaling

AMS subject classifications

65F10, 65N30, 65N55

Links to the cited ETNA articles

[24]Vol. 45 (2016), pp. 75-106 Axel Klawonn, Patrick Radtke, and Oliver Rheinbach: A comparison of adaptive coarse spaces for iterative substructuring in two dimensions
[36]Vol. 46 (2017), pp. 273-336 Clemens Pechstein and Clark R. Dohrmann: A unified framework for adaptive BDDC
[40]Vol. 20 (2005), pp. 164-179 Xuemin Tu: A BDDC algorithm for a mixed formulation of flow in porous media
[42]Vol. 26 (2007), pp. 146-160 Xuemin Tu: A BDDC algorithm for flow in porous media with a hybrid finite element discretization
[44]Vol. 45 (2016), pp. 354-370 Xuemin Tu and Bin Wang: A BDDC algorithm for second-order elliptic problems with hybridizable discontinuous Galerkin discretizations
[46]Vol. 52 (2020), pp. 553-570 Xuemin Tu, Bin Wang, and Jinjin Zhang: Analysis of BDDC algorithms for Stokes problems with hybridizable discontinuous Galerkin discretizations

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