Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques

Appendix E

Auxiliary Techniques for Partial Element Computations

E.1 Multi-function Partial Element Integration

An important part of the overall solution is a mixture of techniques for the efficient partial element evaluation. We call the overall approach multifunction method (MFM) [1, 2] since it involves different algorithms or functions with the main goal of keeping the compute time for the partial elements low.

The partial and coefficients formulations given in Appendices C and D represent an important collection of integrals for analytic solutions. The analytic solutions usually lead to the efficient evaluation of the coefficients. However, it is obvious from Appendices C and D that the efficient analytic evaluation of nonorthogonal coefficients is much more challenging.

The overall approach also needs to include numerical integration methods especially for cases where the analytic integration may not exist or is too complicated. Fortunately, more work has been conducted that contributes to the multifunction approach [2] and to the solution of total or partially numerically evaluated coefficients, for example, Ref. [3].

The efficient numerical computation of nonorthogonal partial inductances is very challenging especially if the length-to-width ratio between the sides ...