A nonlinear singular integral equation model for hysteresis in magneto-statics

A 3D nonlinear singular integral equation model is considered, which describes the magneto-static field in a ferromagnetic medium with hysteresis. The integral equation is derived from the magneto-static field equations and the hysteresis is represented by vector Preisach models. The solvability of the integral equation model is posed and numerical algorithms are discussed. Finally a totally discrete model is supposed, which is based on the integral equation model and allows a physical interpretation as a dipole model.