The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments

Silvia Bertoluzza (1) , Mourad Ismail (2) , Bertrand Maury (3)

1 Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R.
2 LIPhy - Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères]
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential equations in a domain with holes Ω\B - where B is a collection of smooth open subsets - that consists in splitting the initial problem into two parts to be coupled via Schwartz type iterations: the solution, with a fictitious domain approach, of a problem set in the whole domain Ω, for which fast solvers can be used, and the solution of a collection of independent problems defined on narrow strips around the connected components of B, that can be performed fully in parallel. In this work, we give some results on a semi-discrete FBM in the frame- work of a finite element discretization, and we present some numerical experiments.

Mots clés: Finite Element Method; Domain Decomposition Method; Navier-Stokes Equations

Domaines: Modélisation et simulation; Analyse numérique [math.NA]

Silvia Bertoluzza, Mourad Ismail, Bertrand Maury. The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments. DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING, springer, pp.513, 2005, Lecture Notes in Computational Science and Engineering. ⟨hal-00666064⟩