The Fat Boundary Method: semidiscrete scheme and some numerical experiments

The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential equations in a domain with holes ? \ 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 ?, 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 framework of a finite element discretization, and we present some numerical experiments.