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

Geometric multipole expansion and its application to semi-neutral inclusions of general shape