Some applications of the adjoint variable method in electromagnetic optimization and inverse problems

In this paper we present two applications of the adjoint variable method (AVM). First we consider a design optimization problem in magnetic shielding. The objective is to reduce the magnetic stray field of an axisymmetric induction heating device for the heat treatment of aluminum discs. We involve two types of shielding, the passive and the active shielding. In the former, one needs to optimize the geometry of the passive shield. In the latter, the position of all coils and the real and imaginary components of the currents (when working in the frequency domain) must be determined. Second application involves determination of the dissipation parameter in micromagnetic model of ferromagnetism. The micromagnetic model governed by the Landau-Lifshitz equation includes the dissipation parameter α that in some cases can be a space dependent function. The actual distribution of α however can be unknown and must be determined by measurements of the magnetization in the workpiece. Using AVM method, one obtains the derivative of cost functional in terms of an adjoint variable. The main advantage is that the number of direct problem simulations needed to evaluate the derivative is independent of the number of parameters

Adjoint variable method for the study of combined active and passive magnetic shielding

For shielding applications that cannot sufficiently be shielded by only a passive shield, it is useful to combine a passive and an active shield. Indeed, the latter does the "finetuning" of the field reduction that is mainly caused by the passive shield. The design requires the optimization of the geometry of the passive shield, the position of all coils of the active shield, and the real and imaginary components of the currents (when working in the frequency domain). As there are many variables, the computational effort for the optimization becomes huge. An optimization using genetic algorithms is compared with a classical gradient optimization and with a design sensitivity approach that uses an adjoint system. Several types of active and/or passive shields with constraints are designed. For each type, the optimization was carried out by all three techniques in order to compare them concerning CPU time and accuracy. Copyright (C) 2008 Peter Sergeant et al

A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism

The Landau-Lifshitz (LL) equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex side-constraints, strongly nonlinear terms. These effects influence also numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed