Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems

Camille Negrello, Pierre Gosselet and Christian Rey
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Camille Negrello: ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France
Pierre Gosselet: ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France
Christian Rey: Safran Corporate Reseach Center, 92230 Gennevilliers, France

Mathematics, 2021, vol. 9, issue 24, 1-25

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.

Keywords: domain decomposition; nonlinear problems; Newton solver; FETI solver; parallel processing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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