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- Title
Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems.
- Authors
Negrello, Camille; Gosselet, Pierre; Rey, Christian
- Abstract
We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior.
- Subjects
NONLINEAR equations; ELLIPTIC differential equations; TELECOMMUNICATION equipment; PARALLEL algorithms; PARALLEL processing
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 24, p3165
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9243165