Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems

Camille Negrello, Pierre Gosselet, Christian Rey
2021 Mathematics  
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
more » ... 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.
doi:10.3390/math9243165 fatcat:2v7kga2o3rd4vgsohmshsavk3a