Papers › Monolithic Algebraic Multigrid Preconditioners for the Stokes Equations
Monolithic Algebraic Multigrid Preconditioners for the Stokes Equations
Alexey Voronin, Scott MacLachlan, Luke N. Olson, Raymond Tuminaro
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We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood (ℙ₂/ℙ₁) and Scott-Vogelius (ℙ₂/ℙ₁ᵈⁱˢᶜ) discretizations of the Stokes equations. The algorithm is based on the use of the lower-order ℙ₁iso1ptℙ₂/ℙ₁ operator within a defect-correction setting, in combination with AMG construction of interpolation operators for velocities and pressures. The preconditioning framework is primarily algebraic, though the ℙ₁iso1ptℙ₂/ℙ₁ operator must be provided. We investigate two relaxation strategies in this setting. Specifically, a novel block factorization approach is devised for Vanka patch systems, which significantly reduces storage requirements and computational overhead, and a Chebyshev adaptation of the LSC-DGS relaxation is developed to improve parallelism. The preconditioner demonstrates robust performance across a variety of 2D and 3D Stokes problems, often matching or exceeding the effectiveness of an inexact block-triangular (or Uzawa) preconditioner, especially in challenging scenarios such as elongated-domain problems.
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