  This paper presents a new concept of geometric multipole expansion for the
conductivity or anti-plane elasticity problem in two dimensions by using the
Faber polynomials. As an application, we construct semi-neutral inclusions of
general shape that show relatively negligible field perturbations for low-order
polynomial loadings. These inclusions are of the multilayer structure whose
material parameters are determined such that some coefficients of geometric
multipole expansion vanish.
