Volume 20, pp. 164-179, 2005.

A BDDC algorithm for a mixed formulation of flow in porous media

Xuemin Tu

Abstract

The BDDC (balancing domain decomposition by constraints) algorithms are similar to the balancing Neumann-Neumann methods, with a small number of continuity constraints enforced across the interface throughout the iterations. These constraints form a coarse, global component of the preconditioner. The BDDC methods are powerful for solving large sparse linear algebraic systems arising from discretizations of elliptic boundary value problems. In this paper, the BDDC algorithm is extended to saddle point problems generated from the mixed finite element methods used to approximate the scalar elliptic problems for flow in porous media. Edge/face average constraints are enforced and the same rate of convergence is obtained as for simple elliptic cases. The condition number bound is estimated and numerical experiments are discussed. In addition, a comparison of the BDDC method with an edge/face-based iterative substructuring method is provided.

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Key words

BDDC, domain decomposition, saddle point problem, condition number, benign space, edge/face-based iterative substructuring method

AMS subject classifications

65N30, 65N55, 65F10

ETNA articles which cite this article

Vol. 26 (2007), pp. 146-160 Xuemin Tu: A BDDC algorithm for flow in porous media with a hybrid finite element discretization

Vol. 45 (2016), pp. 354-370 Xuemin Tu and Bin Wang: A BDDC algorithm for second-order elliptic problems with hybridizable discontinuous Galerkin discretizations

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

Vol. 58 (2023), pp. 66-83 Yanru Su, Xuemin Tu, and Yingxiang Xu: Robust BDDC algorithms for finite volume element methods

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