Computation and Storage of the Bianisotropic Scalar Green's Function and Its Derivatives

A set of algorithms is proposed for the accurate and efficient computation and storage of the bianisotropic scalar Green's function. The computation is based on an expansion of the Green's function into Chebyshev polynomials. The analytical properties of these polynomials are exploited to allow the accurate computation of the derivatives of the Green's function as well as the Green's function itself. For lossy materials, the proposed computation strategy is provably robust. In addition, a multilevel storage scheme with a favorable complexity, based on the Chebyshev polynomial expansion, is proposed for the storage of the expansion coefficients. Numerical results showcase the accuracy and computational complexity of the proposed algorithms.