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arXiv · 2409.02860

Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity

Tommaso Bevilacqua·Axel Klawonn·Martin Lanser
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Abstract

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.

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Tommaso Bevilacqua, Axel Klawonn, Martin Lanser. 2024-09-04. Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity. https://arxiv.org/abs/2409.02860

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