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A key use of the PEEC method is the solution of combined electromagnetic and circuit problems as they occur in many situations in todays very large scale integrated circuits (VLSI) and systems. An important aspect of this approach is the fast and accurate computation of PEEC circuit matrix elements, the partial inductances and normalized coefficients of potential. Recently, fast multipole methods (FMM) have been applied to the PEEC method in the frequency domain as a way to speed up the solution. In this paper, we consider the fast evaluation of the PEEC circuit matrix elements by two different methods, a matrix version of the (FMM) PEEC method and a method, which we call the fast multi-function (FMF) PEEC approach. In this technique, the matrix coefficients are evaluated using analytical functions approximation of the coefficients in combination with a proper choice of numerical quadrature formulas.