Computationally Effective Modeling of Self-Demagnetization and Magnetic Field for Bodies of Arbitrary Shape Using Polyhedron Discretization

Abstract

A performance-effective numerical method for magnetic field calculations is proposed. The method can accept either regular or irregular polyhedron discretization that enables us to construct magnetic object models of an arbitrary shape. A concise, closed-form expression for the magnetic field of a polyhedron is presented, which allows for the high accuracy of the method. As a case study, models of a solid sphere, an ellipsoid, a cuboid, and a well are considered. The models are approximated with a dense irregular grid, elements of which are polyhedrons. The approximation leads to the system of linear algebraic equations that we solve with a gradient method, which allows for finding the self-demagnetization of the body and then calculating the total magnetic field. For the presented example of a well in the medium of relatively strong magnetic susceptibility (0.2), the contribution of the self-demagnetization to the secondary magnetic field reaches an RMS of 24%.