Textbook Efficiency: Massively Parallel Matrix-Free Multigrid for the Stokes System

We employ textbook multigrid efficiency (TME), as introduced by Achi Brandt, to construct an asymptotically optimal monolithic solver for the Stokes system. The geometric builds upon concept of hierarchical hybrid grids, which is extended higher-order finite element discretizations, and a corresponding matrix-free implementation. computational cost full iteration quantified, applied multiple benchmark problems. Through parameter study, we suggest configurations that achieve theoretical TME both stabilized equal order Taylor--Hood discretizations. then identify quantify gaps parallel implementations in practice. excellent node-level performance relevant compute kernels presented via roofline analysis. Finally, demonstrate weak strong scalability up 147,456 processes solve systems with more than $3.6\times 10^{12}$ (trillion) unknowns.