On adaptive BDDC for the flow in heterogeneous porous media

Abstract

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.

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Correspondence to Bedřich Sousedík.

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Supported by the U.S. National Science Foundation under grant DMS1521563.

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Sousedík, B. On adaptive BDDC for the flow in heterogeneous porous media. Appl Math 64, 309–334 (2019). https://doi.org/10.21136/AM.2019.0222-18

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Keywords

  • iterative substructuring
  • balancing domain decomposition
  • BDDC
  • multiscale methods
  • adaptive methods, flow in porous media
  • reservoir simulation
  • SPE 10 benchmark

MSC 2010

  • 65F08
  • 65F10
  • 65M55
  • 65N55