TY  - JOUR
T1  - BDDC for Mixed-Hybrid Formulation of Flow in Porous Media with Combined Mesh Dimensions
A1  - Šístek, Jakub
A1  - Březina, Jan
A1  - Sousedík, Bedřich
JA  - Numerical Linear Algebra with Applications
Y1  - 2015
VL  - 22
IS  - 6
SP  - 903
EP  - 929
M2  - doi: 10.1002/nla.1991
N2  - We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are modelled by 1D or 2D elements inside three-dimensional domains. In thisset-up,theglobalproblemaswellasthesubstructureproblemshaveasymmetricsaddle-pointstructure, containing a ‘penalty’ block due to the combination of meshes. We show that the problem can be reduced by means of iterative substructuring to an interface problem, which is symmetric and positive definite. The interface problem can thus be solved by conjugate gradients with the BDDC method as a preconditioner. Aparallelimplementationofthisalgorithmisincorporatedintoanexistingsoftwarepackageforsubsurface flow simulations. We study the performance of the iterative solver on several academic and real-world problems. Numerical experiments illustrate its efficiency and scalability. Preprint version.
M1  - Preprint project = NCMM
M1  - Preprint year = 2015
M1  - Preprint number = 03
M1  - Preprint ID = NCMM/2015/03
ER  -