An hp multigrid approach for tensor-product space-time finite element discretizations of the stokes equations
Publication date
2025-12-02
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Series or journal
SIAM Journal on Scientific Computing
ISSN
Periodical volume
47
Periodical issue
6
First page
B1503
Last page
B1529
Has another version
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
High-performance computing
Higher-order finite elements
Matrix-free
Monolithic multigrid
Space-time finite elements
Space-time multigrid
Abstract
We present a monolithic hp space-time multigrid method for tensor-product spacetime finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm is expressed through rigorous mathematical mappings. For the discretization, we use inf-sup stable pairs of elements in space and a discontinuous Galerkin (DG(k)) discretization in time with piecewise polynomials of order k. The key novelty of this work is the application of hp multigrid techniques in space and time, facilitated and accelerated by the matrix-free capabilities of the deal.II library. While multigrid methods are well-established for stationary problems, their application in space-time formulations encounter unique challenges, particularly in constructing suitable smoothers. To overcome these challenges, we employ space-time cell and vertex star patch based Vanka smoothers. Extensive tests on high-performance computing platforms demonstrate the efficiency of our hp multigrid approach on problem sizes exceeding a trillion degrees of freedom (dofs), sustaining throughputs of hundreds of millions of dofs per second.
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Published version
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