A reduced-order Robin-Robin domain decomposition method for parametric elliptic Partial Differential Equations

par Tomas Chacon Rebollo (Universidad de Sevilla)

mardi 30 sept. 2025, 14:00 → 15:00 Europe/Paris

UTC - GI

This talk deals with the general purpose of building fast solvers for parametric PDEs. We combine reduced order with domain decomposition techniques. The first one allows to approximate the solution using reduced number of degrees of freedom, while the second one allows the use of parallel techniques. We afford the solution of linear elliptic PDEs. We split the computational domain into two subdomains, and reformulate the problem in terms of a broken formulation with Robin-Robin transmission conditions across the interface between subdomains. We build a reduced order space to approximate the solution in each of the sub-domains, plus an additional reduced order space to approximate the transmission conditions. We prove the convergence of the iterative domain decomposition procedure for the reduced formulation, as well as error estimates between the full order and the reduced order iterates. We present some numerical tests for symmetric elliptic PDEs and for convection-diffusion problems, that exhibit the reduction in computational time provided by this technique.