Effective simulation of a macroscopic model for stationary micromagnetics

The effective behaviour of stationary micromagnetic phenomena is modelled by a convexified Landau–Lifshitz minimization problem for the limit of large and soft magnets X without the exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-restriction jmj 6 1 and the stray field energy on the unbounded domain R d . A penalty method models the side-restriction and the exterior Maxwell equation is recast via a nonlocal integral operator P. As shown in [Numer. Anal. Macrosc. Model Micromagnet, submitted for publication; Analysis, Numerik und Simulation eines Relaxierten Modellproblems zum Mikromagnetismus, doctoral thesis, Vienna University of Technology, 2003], the discretization leads to a nonlocal problem with piecewise constant ansatz and test functions and (dense) stiffness matrices with closed form formula for their entries. This paper addresses the numerical solution with Newton–Raphson schemes and the scientific computation of effective micromagnetic simulations. � 2004 Published by Elsevier B.V.

[1]  Carsten Carstensen,et al.  Numerical Analysis of microstructure , 2001 .

[2]  CARSTEN CARSTENSEN,et al.  A Posteriori Error Control in Adaptive Qualocation Boundary Element Analysis for a Logarithmic-Kernel Integral Equation of the First Kind , 2003, SIAM J. Sci. Comput..

[3]  P. Pedregal.  Parametrized measures and variational principles , 1997 .

[4]  Andreas Prohl,et al.  Convergence for stabilisation of degenerately convex minimisation problems , 2004 .

[5]  Luc Tartar,et al.  Beyond young measures , 1995 .

[6]  Stefan A. Sauter,et al.  Variable Order Panel Clustering , 2000, Computing.

[7]  W. Hackbusch,et al.  Introduction to Hierarchical Matrices with Applications , 2003 .

[8]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[9]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[10]  David Kinderlehrer,et al.  Frustration in ferromagnetic materials , 1990 .

[11]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[12]  Dirk Praetorius,et al.  Analysis of the Operator Δ^-1div Arising in Magnetic Models , 2004 .

[13]  Andreas Prohl,et al.  Numerical analysis of relaxed micromagnetics by penalised finite elements , 2001, Numerische Mathematik.

[14]  Antonio DeSimone,et al.  Energy minimizers for large ferromagnetic bodies , 1993 .

[15]  Mitchell Luskin,et al.  Analysis of the finite element approximation of microstructure in micromagnetics , 1992 .

[16]  Antonio De Simone,et al.  Energy minimizers for large ferromagnetic bodies , 1993 .

[17]  D. Praetorius.  Analysis of the Operator ∆ − 1 div Arising in Magnetic Models 1 , 2022 .

[18]  Carsten Carstensen,et al.  Adaptive Finite Element Methods for Microstructures? Numerical Experiments for a 2-Well Benchmark , 2003, Computing.

[19]  Carsten Carstensen,et al.  Numerical Analysis for a Macroscopic Model in Micromagnetics , 2004, SIAM J. Numer. Anal..

[20]  Jens Markus Melenk,et al.  Approximation of Integral Operators by Variable-Order Interpolation , 2005, Numerische Mathematik.

[21]  Dirk Praetorius,et al.  Applications of -Matrix Techniques in Micromagnetics , 2005, Computing.

[22]  Wolfgang Hackbusch.  Direct Integration of the Newton Potential over Cubes , 2002, Computing.