On adaptive BDDC for the flow in heterogeneous porous media

Bedřich Sousedík

Applications of Mathematics (2019)

  • Volume: 64, Issue: 3, page 309-334
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Sousedík, Bedřich. "On adaptive BDDC for the flow in heterogeneous porous media." Applications of Mathematics 64.3 (2019): 309-334. <http://eudml.org/doc/294444>.

@article{Sousedík2019,
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.},
author = {Sousedík, Bedřich},
journal = {Applications of Mathematics},
keywords = {iterative substructuring; balancing domain decomposition; BDDC; multiscale methods; adaptive methods; flow in porous media; reservoir simulation; SPE 10 benchmark},
language = {eng},
number = {3},
pages = {309-334},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On adaptive BDDC for the flow in heterogeneous porous media},
url = {http://eudml.org/doc/294444},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Sousedík, Bedřich
TI - On adaptive BDDC for the flow in heterogeneous porous media
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 309
EP - 334
AB - 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.
LA - eng
KW - iterative substructuring; balancing domain decomposition; BDDC; multiscale methods; adaptive methods; flow in porous media; reservoir simulation; SPE 10 benchmark
UR - http://eudml.org/doc/294444
ER -

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