A Thin-Layer Volume Integral Equation Formulation for Linear and Non-Linear Magnetostatic Problems

A thin-layer approximation of the magnetostatic volume integral equation (VIE) method is presented. This method, referred to as the thin-VIE (TVIE), utilizes a thin approximation of Green's function. The TVIE approximates both the transverse and the normal magnetization in the material represented by a surface mesh, dramatically improving the accuracy of the method. The TVIE is solved via a locally corrected Nyström formulation, supporting high-order meshing and solution accuracy. A high-order singularity extraction method is used to compute the hypersingular terms required by near-field local corrections, leading to a very efficient algorithm. The method is applied to linear media, as well as non-linear, anisotropic, and hysteretic medium. The method is also hybridized with the VIE method, allowing for mixed meshes for solving general problems.