Fat Boundary Method
) is a fictitious domain like method for solving partial differential equations in a domain with holes
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
, that can be performed fully in parallel. In this work, we give some results on a semi-discrete
in the framework of a finite element discretization, and we present some numerical experiments.