Toplogical derivative for nonlinear magnetostatic problem

The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical engineering, we derive the topological derivative for an optimization problem which is constrained by the quasilinear equation of two-dimensional magnetostatics. Here, the main ingredient is to establish a sufficiently fast decay of the variation of the direct state at scale 1 as $|x|\rightarrow \infty$. In order to apply the method in a bi-directional topology optimization algorithm, we derive both the sensitivity for introducing air inside ferromagnetic material and the sensitivity for introducing material inside an air region. We explicitly compute the arising polarization matrices and introduce a way to efficiently evaluate the obtained formulas. Finally, we employ the derived formulas in a level-set based topology optimization algorithm and apply it to the design optimization of an electric motor.Comment: 54 pages, 9 figure

General Classical Electrodynamics

Maxwell’s Classical Electrodynamics (MCED) suffers several inconsistencies: (1) the Lorentz force law of MCED violates Newton’s Third Law of Motion (N3LM) in case of stationary and divergent or convergent current distributions; (2) the general Jefimenko electric field solution of MCED shows two longitudinal far fields that are not waves; (3) the ratio of the electrodynamic energy-momentum of a charged sphere in uniform motion has an incorrect factor of 4/3. A consistent General Classical Electrodynamics (GCED) is presented that is based on Whittaker’s reciprocal force law that satisfies N3LM. The Whittaker force is expressed as a scalar magnetic field force, added to the Lorentz force. GCED is consistent only if it is assumed that the electric potential velocity in vacuum, ’a’, is much greater than ’c’ (a ≫ c); GCED reduces to MCED, in case we assume a = c. Longitudinal electromagnetic waves and superluminal longitudinal electric potential waves are predicted. This theory has been verified by seemingly unrelated experiments, such as the detection of superluminal Coulomb fields and longitudinal Ampère forces, and has a wide range of electrical engineering applications