This paper focuses on two special aspects regarding fast partial inductance computations in the nonorthogonal partial element equivalent circuit (PEEC) method. First, a multifunction PEEC algorithm is proposed, which is able to calculate partial inductances as efficient as possible for mixed environments with nonorthogonal as well as orthogonal cells. Second, a new numerical integration routine for the self-inductance terms of nonorthogonal cells is focused on by using averaged orthogonal subelements. It is presented that the slow convergence caused by the singularities is avoided and a fast evaluation of the self-terms is enabled consequently. The approach is verified by two examples where a good agreement is obtained when comparing the proposed results with analytical solutions as well as finite-element method reference results.