Generalized Magnetostatic Analysis by Boundary Integral Equation Derived From Scalar Potential

The volume integral equation approach replaces the loop currents over the volume elements in magnetic material with the loop currents on the material surface to derive a boundary integral equation (BIE). The surface loop current is equivalent to the double layer charge, which offers an integral form of scalar potential to give the BIE. Once BIE has been solved, the loop current gives the magnetic flux density B by Biot-Savart law. The BIE has many advantages such as giving accurate solutions and evaluating B at edges and corners. But it has some severe drawbacks due to a multi-valued function of the excitation potential caused by the source currents and that is why its application has been restricted mostly to simply connected problem. This paper presents a novel generalized approach, which is applicable for solving generic problems such as multi-material, multiply connected and thin shielding problems.