Premium
Constraint Preserving, Inexact Solution of Implicit Discretizations of Landau–Lifshitz–Gilbert Equations and Consequences for Convergence
Author(s) -
Bartels Sören
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610006
Subject(s) - discretization , constraint (computer aided design) , convergence (economics) , mathematics , nonlinear system , regular polygon , mathematical analysis , physics , geometry , quantum mechanics , economics , economic growth
The Landau‐Lifshitz‐Gilbert equation describes dynamics of ferromagnetism. Nonlinearity of the equation and a non‐convex side constraint make it difficult to design reliable approximation schemes. In this paper, we discuss the numerical solution of nonlinear systems of equations resulting from implicit, unconditionally convergent discretizations of the problem. Numerical experiments indicate that finite‐time blow‐up of weak solutions can occur and thereby underline the necessity of the design of reliable discretization schemes that approximate weak solutions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)