# Semi-analytical formulas

## Introduction

This section presents the semi-analytical formulation used for modeling with the PEEC method parallelepipedic conductors positioned at an angle.

The formulation is named semi-analytical or semi-numerical, as for the six successive integrations presented in Real case: volume conductors, some solutions can be expressed by analytical formulas, while the others must be approached by means of numerical techniques of the ‘Gauss points' type.

The use of numerical integration on the one hand makes the calculation of partial inductances more difficult, but on the other hand it improves the quality of results, as the formulation appears to be more stable.

These formulas are only used for the calculation of mutual inductances, as only one conductor at a time is concerned for the calculation of self-inductances, and therefore the analytical formulas are always valid.