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Recently, a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, has been proposed to analyze the electromagnetic scattering from a zero-thickness perfectly electrically conducting disk. The convergence of the discretization scheme is guaranteed and of exponential type, i.e., few expansion functions are needed to achieve highly accurate solutions. However, it leads to the numerical evaluation of improper integrals of asymptotically oscillating and slowly decaying functions. Asymptotic acceleration techniques allow to obtain faster decaying integrands without overcoming the problem of the oscillating nature of the integrands themselves, i.e., the convergence of the integrals becomes slower and slower as the accuracy required for the solution is higher. In this paper, by means of algebraic manipulations and a suitable integration procedure in the complex plane, an alternative expression for the scattering matrix coefficients involving only fast converging proper integrals is devised. As shown in the numerical results section, the proposed technique is very effective and drastically outperforms the classical analytical asymptotic acceleration technique.

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The partial element equivalent circuit (PEEC) method provides an electromagnetic model of interconnections and packaging structures in terms of standard circuit elements. The surface-based PEEC (S-PEEC) formulation can reduce the number of unknowns compared to the standard volume-based PEEC (V-PEEC) method. This reduction is of particular use in the case of high-speed circuits and high-switching power electronics, where the bandwidth extends from low frequencies to the GHz range. In this article, the S-PEEC formulation is revised and cast in a matrix form. The main novelty is that the interaction integrals involving the curl of the magnetic and electric vector potentials are computed through the Taylor series expansion of the full-wave Green's function, leading to analytical forms that are rigorously derived. Therefore, the numerical integration is avoided, with a consequent reduction of the computation time. The proposed formulas are studied in terms of the frequency, size of the mesh, and distance between the basis function domains. Three examples are presented, confirming the accuracy of the proposed method compared to the V-PEEC method and surface-based numerical methods from literature.

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