A fat boundary method for the Poisson problem in a domain with holes (Q1597537)

The author proposes a new method to solve elliptic problems in domains with holes. The significant features in this paper are that the computation on the domain is based a cartesian mesh and the discretised operator does not depend on the geometry. This makes it possible to use parallel solvers. The local computations are performed on a mesh which only depends on the geometry of the body. Finally, a convergence analysis is made with numerical experiments.