Fast tensor product Schwarz smoothers for high-order discontinuous Galerkin methods

• Verfasst von: Witte, Julius [VerfasserIn]
• Verfasst von: Arndt, Daniel [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Titel: Fast tensor product Schwarz smoothers for high-order discontinuous Galerkin methods
• Verf.angabe: Julius Witte, Daniel Arndt, and Guido Kanschat
• Jahr: 2021
• Umfang: 20 S.
• Fussnoten: Veröffentlicht von De Gruyter 11. November 2020 ; Gesehen am 29.09.2021
• Titel Quelle: Enthalten in: Computational methods in applied mathematics
• Ort Quelle: Berlin : De Gruyter, 2001
• Jahr Quelle: 2021
• Band/Heft Quelle: 21(2021), 3, Seite 709-728
• ISSN Quelle: 1609-9389
• DOI: doi:10.1515/cmam-2020-0078
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Discontinuous Galerkin Finite Element
• Sach-SW: Domain Decomposition
• Sach-SW: Fast Diagonalization
• Sach-SW: Geometric Multigrid
• K10plus-PPN: 1772047392

Abstract

We discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in order to obtain fast local solvers for additive and multiplicative subspace correction methods. The effort of inverting local matrices for tensor product polynomials of degree k is reduced from ???? ⁢ ( k 3 ⁢ d ) {\mathcal{O}(k^{3d})} to ???? ⁢ ( d ⁢ k d + 1 ) {\mathcal{O}(dk^{d+1})} by exploiting the separability of the differential operator and resulting low rank representation of its inverse as a prototype for more general low rank representations in space dimension d .