An \(hp\) Multigrid Approach for Tensor-Product Space-Time Finite Element Discretizations of the Stokes Equations.
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| Title: | An \(hp\) Multigrid Approach for Tensor-Product Space-Time Finite Element Discretizations of the Stokes Equations. |
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| Authors: | Margenberg, Nils1 (AUTHOR) nils.margenberg@ovgu.de, Bause, Markus2 (AUTHOR) bause@hsu-hh.de, Munch, Peter3 (AUTHOR) p.muench@tu-berlin.de |
| Source: | SIAM Journal on Scientific Computing. 2025, Vol. 47 Issue 6, pB1503-B1529. 27p. |
| Subjects: | Multigrid methods (Numerical analysis), Stokes equations, Galerkin methods, Finite element method, High performance computing |
| Abstract: | We present a monolithic \(hp\) space-time multigrid method for tensor-product space-time 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 \(\mathbb Q_{r+1}/\mathbb P_{r}^{\text{disc}}\) 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. Reproducibility of computational results. This paper has been awarded the "SIAM Reproducibility Badge: Code and data available" as recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at and in the supplementary materials ( [ 126KB]). [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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