Formulation of the DC Inductance Solution

The DC inductance solver uses the volume current density solutions computed by the DC conduction solver as its starting point. Suppose that the n^th source has been excited. Given the DC current density , the resulting magnetic vector potential can be calculated from the volume integral equation:

Here V denotes the volume of the conducting objects. The calculation of the vector potential can be time-consuming if direct integration from every source to every observation point is used. To make the calculation efficient, Q3D uses the fast multipole method.

If magnetic materials are present, Q3D uses Adaptive Cross Approximation (ACA) with the help of the fast multipole method.