Monolithic two-level Schwarz preconditioner for Biot's consolidation model in two space dimensions
| Autor: | Meggendorfer, Stefan, Kanschat, Guido, Kraus, Johannes |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time discretization by the implicit Euler method and space discretization by a family of strongly mass-conserving methods exploiting $H^{div}$-conforming approximations of the solid displacement and fluid flux fields. For the resulting saddle-point problem, we construct monolithic overlapping domain decomposition (DD) methods whose analysis relies on a transformation into an equivalent symmetric positive definite system and on stable decompositions of the involved finite element spaces under proper problem-dependent norms. Numerical results on two-dimensional test problems are in accordance with the provided theoretical uniform convergence estimates for the two-level multiplicative Schwarz method. Comment: 33 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|