Boundary Integral Equation Method for Compensating Magnetostatic Fields of Thin Shells

In traditional design of degaussing systems, the layout of degaussing coils is usually predefined. In order to calculate the electric currents in coils, the inverse problem of minimizing the magnetic field in a set of points outside the demagnetized object is solved. The article proposes a direct approach which allows estimating the coil currents together with the coil geometry based on computing surface distributions of compensating currents. For a thin ferromagnetic shell, these currents can be represented by a single boundary layer placed on the inner or outer side of the shell. The surface density of the current layer is expressed via a stream function and computed using a boundary-integral equation derived from zero tangential trace of the vector magnetic potential on the exterior side of the shell. Unlike other integral equations with respect to boundary layer densities, new equation contains rotation operator, which maps the div-conforming edge element space to the curl-conforming one. This involves alternative representations of the surface magnetization of the shell. As a result, the field compensation error depends on the layer position (inside or outside the shell), mesh size, and approximation of the surface magnetization. The accuracy of compensation and spatial characteristics of compensation currents are investigated using test models of spherical and cubic shells, and a ship computer model.