Speaker
Description
We present a local hp space-time multigrid method for tensor-product finite element discretizations of the Stokes equations, using Qₚ/Pₚ₋₁ᵈⁱˢᶜ elements in space and a discontinuous Galerkin (DG) discretization in time. A key novelty of this work is the application of \textit{hp} multigrid techniques in both space and time. The method is facilitated by the matrix-free capabilities of the \texttt{deal.II} library. While multigrid methods are well-established for stationary problems, their application in space-time formulations presents unique challenges, particularly in constructing suitable smoothers. To address these challenges, we employ a space-time cell-wise Vanka smoother. Extensive tests on high-performance computing platforms demonstrate its efficiency, handling large-scale problems with over a trillion degrees of freedom, confirming its potential for complex, high-fidelity simulations.
