Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity
<|reference_start|>Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity: The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and robust preconditioning techniques are necessary for an iterative solution. Here, a balancing domain decomposition by constraints (BDDC) preconditioner is considered. Techniques to enrich the coarse space of BDDC applied to a Stokes problem with heterogeneous viscosity are proposed. In this framework a comparison between two adaptive techniques and a computationally cheaper heuristic approach is carried out. Numerical results computed on a physically realistic model show that the latter approach in combination with the deluxe scaling is a promising alternative.<|reference_end|>
@article{bevilacqua2024adaptive,
    title={Adaptive and frugal BDDC coarse spaces for virtual element
  discretizations of a Stokes problem with heterogeneous viscosity},
    author={Tommaso Bevilacqua, Axel Klawonn and Martin Lanser},
    journal={arXiv preprint arXiv:2409.02860},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02860},
    primaryClass={math.NA cs.NA}
}