Preconditioning and stabilization of poromechanics problem with CutFem approximation

Daniele Cerroni

MOX- Politecnico di Milano

Friday 11th May 2018

11:30:00

Aula Seminari 'Saleri' VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano - Edificio 14

We investigate the conditioning of a computational model for poroelasticity in the case of a moving domain boundary. We approximate the problem by means of a numerical scheme which does not require that the computational mesh conforms with the moving boundary (CutFem approximation) and, we use a Nitsche’s method to apply boundary condition onto this region. The ill conditioning driven by the approximation with CutFem is combined with the naturally ill conditioning due to the saddle point nature of the poroelastic problem. The latter problem can be addressed with a splitting iterative scheme that decouple the solution of the mechanics problem from the solution of the pressure equation. In this work we investigate the conditioning of the two sub-problems in the case of tiny intersection produced by the CutFem approximation. In particular we explore the possibility of adding a stabilization term into the pressure equation and use a propoer preconditioner for the displacement equation. Contact: paolo.zunino@polimi.it