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- W2022274231 abstract "The macroscopic behavior of stationary micromagnetic phenomena can be modeled by a relaxed version of the Landau--Lifshitz minimization problem. In the limit of large and soft magnets $Omega$, it is reasonable to exclude the exchange energy and convexify the remaining energy densities. The numerical analysis of the resulting minimization problem, begin{align*} min E_0^{**}({bf m})text{ amongst }{bf m}:Omegatomathbb{R}^dtext{ with } |{bf m}(x)|le1text{ for almost every }xinOmega, end{align*} for $d=2,3$, faces difficulties caused by the pointwise side-constraint $|{bf m}|le1$ and an integral over the whole space $mathbb{R}^d$ for the stray field energy. This paper involves a penalty method to model the side-constraint and reformulates the exterior Maxwell equation via a nonlocal integral operator $mathcal{P}$ acting on functions exclusively defined on $Omega$. The discretization with piecewise constant discrete magnetizations leads to edge-oriented boundary integrals, the implementation of which and related numerical quadrature are discussed, as are adaptive algorithms for automatic mesh-refinement. A priori and a posteriori error estimates provide a thorough rigorous error control of certain quantities. Three classes of numerical experiments study the penalization, empirical convergence rates, and performance of the uniform and adaptive mesh-refining algorithms." @default.
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- W2022274231 date "2005-01-01" @default.
- W2022274231 modified "2023-09-24" @default.
- W2022274231 title "Numerical Analysis for a Macroscopic Model in Micromagnetics" @default.
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- W2022274231 doi "https://doi.org/10.1137/s003614290343565x" @default.
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