SHIFTED BOUNDARY METHOD FOR POISSON PROBLEMS IN LIBMESH

Resumo

The embedded finite element method is one approach to diminish the mesh generation burden in
finite element analysis. It consists of dealing with a description of a boundary that does not necessarily
match the problem’s physical boundary. It can potentially shrink the workflow giving the opportunity
of immediately inputting a CAD geometry or tomographic image into a simulation, without necessarily

using isogeometric elements or performing substantial preprocessing. This work presents an imple-
mentation of the recently proposed embedded formulation for Poisson problems in the general purpose

library libMesh. In the formulation, the boundary condition is shifted and enforced weakly by a Nitsche

approach, and then referred as surrogated boundary. This is accomplished provided the surrogate bound-
ary is close enough to the physical boundary so a Taylor expansion can be used to describe the chopped

off region. This approach provides a significant computational relief compared to the alternative selected

point integration, especially when dealing with complex domains where the total point-locating opera-
tions’ cost can be significantly high. Moreover, computational experiments indicates that second order

convergence can achieved.