Iterative Methods for Model Reduction by Domain Decomposition

Marcelo Buffoni (1) , Haysam Telib (2) , Angelo Iollo (1)

1 MC2 - Modélisation, contrôle et calcul
2 DIASP - Dipartimento di Ingegneria Aeronautica e Spaziale [Torino]

We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the two subdomains. In particular, in one subdomain we discretize the governing equations by a canonical scheme, whereas in the other one we solve a reduced order model of the original problem. Different approaches to couple the low-order model to the usual discretization are presented. The effectiveness of these approaches is tested on numerical examples pertinent to non-linear model problems including the Laplace equation with non-linear boundary conditions and the compressible Euler equations.

Mots clés: low-order models; domain decomposition; compressible flows

Domaines: Modélisation et simulation; Mécanique des fluides [physics.class-ph]

Marcelo Buffoni, Haysam Telib, Angelo Iollo. Iterative Methods for Model Reduction by Domain Decomposition. [Research Report] 2007. ⟨inria-00193962v1⟩