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.