Schur Preconditioning of the Stokes Equations in Channel-Dominated Domain

Schur Preconditioning of the Stokes Equations in Channel-Dominated Domain

Andreas Meier, Eberhard Bänsch, Florian Frank

We propose to use an unconventional precondition operator for the Schur complement of the stationary Stokes equations on porous domains. Discrete diffusion is added to the established precondition operator, which is heuristically motivated by Darcy’s law—a homogenization result of Stokes’ equations. The resulting operator is embedded into a block-diagonal precondition matrix for MINRES. For low-porosity domains or domains that contain thin channels, the number of iterations required to meet a certain tolerance is significantly reduced.

Computer Methods in Applied Mechanics and Engineering, Volume 398, 115264, 2022
Corresponding Author: Florian Frank

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