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On adaptive BDDC for the flow in heterogeneous porous media. (English) Zbl 07088743
Summary: We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection of flux constraints. Performance of the method is illustrated on the benchmark problem from the 10th SPE Comparative Solution Project (SPE 10). Numerical experiments in both 2D and 3D demonstrate that the first two steps of the method exhibit some numerical upscaling properties, and the adaptive preconditioner in the last step allows a significant decrease in the number of iterations of conjugate gradients at a small additional cost.
##### MSC:
 65F08 Preconditioners for iterative methods 65F10 Iterative numerical methods for linear systems 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
##### Software:
BDDC; SINTEF; METIS; lobpcg.m; BDDCML
Full Text:
##### References:
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