A one-shot overlapping Schwartz method for component-based model order reduction of nonlinear PDEs.

  • Taddei, Tommaso (Inria)

Please login to view abstract download link

We discuss the development of an optimization-based (one-shot) procedure for component-based (CB) model order reduction (MOR) of parametric nonlinear PDEs. We first devise a constrained optimization procedure that minimizes jumps at components' interfaces subject to the (approximate) satisfaction of the PDE in each component. Then, we introduce suitable low-dimensional control variables to recast the optimization statement into an unconstrained nonlinear least-square problem that can be effectively solved using the Gauss-Newton method (GNM). In this talk, we focus on overlapping domain partitions; we consider the application to a nonlinear neo-Hookean problem to illustrate the main features of the method; finally, we tackle an unsteady thermo-hydro-mechanical problem with internal variables.