Computational Micromagnetism (Advances in Numerical Mathematics) - Softcover

Prohl, Andreas

Softcover

ISBN 10: 3519003589 ISBN 13: 9783519003588

Publisher: Vieweg+Teubner Verlag, 2001

Synopsis

In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non­ stationary context. Electromagnetic effects are accounted for in an extended model to study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe­ nomena share common features like (i) strong nonlinearities, and (ii) non­ convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: • Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets).

About this title

About the Author

Dr. Andreas Prohl, Universität Kiel

From the Back Cover

Ferromagnetic materials are widely used as recording media.
Their magnetic patterns are described by the well-accepted model of Landau and Lifshitz. Over the last years, different strategies habe been developed to tackle the related non-convex minimization problem: direct minimization, convexification, and relaxation by using Young measures. Nonstationary effects are considered in the extended models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets.
The objective of this monograph is a numerical analysis of these models. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications.

Edition details

• Publisher: Vieweg+Teubner Verlag
• Publication date: 2001
• Language: English
• ISBN 10: 3519003589
• ISBN 13: 9783519003588
• Binding: Paperback
• Number of pages: 322