Thermodynamically consistent mesoscopic model of the ferro/paramagnetic transition

Abstract

A continuum evolutionary model for micromagnetics is presented that, beside the standard magnetic balance laws, includes thermo-magnetic coupling. To allow conceptually efficient computer implementation, inspired by relaxation method of static minimization problems, our model is mesoscopic in the sense that possible fine spatial oscillations of the magnetization are modeled by means of Young measures. Existence of weak solutions is proved by backward Euler time discretization. AMS Subj. Classification: 35K85, 35Q60, 49S05, 78A30, 78M30, 80A17.

Computational modeling of magnetic hysteresis with thermal effects

“…In [3], the authors built and analyzed a mesoscopic model in anisothermal situations. A closely related thermodynamically consistent model on the microscopic level was previously introduced in [25] to model a ferro/para magnetic transition.…”

“…Another related microscopic model with a prescribed temperature field was investigated in [2]. The goal of this contribution is to discretize the model from [3] and test it on computational examples. In order to make our exposition reasonably self-content, we closely follow the derivation of the model presented in [3].…”

“…The goal of this contribution is to discretize the model from [3] and test it on computational examples. In order to make our exposition reasonably self-content, we closely follow the derivation of the model presented in [3]. We also point out that computationally efficient numerical implementation of isothermal models can be found in [6,14,16,17], where such a model was used in the isothermal variant.…”

“…As done already in [3], we relax the constraint (4) by augmenting the total Gibbs free energy (i.e., ψ integrated over Ω) by the term κ 2 λ − L • ν 2 H −1 (Ω;R d+1 ) with (presumably large) κ ∈ R + and with…”

“…The following the data qualification are needed in [3] to prove the existence of weak solutions; cf. [3]:…”