The computational modelling of micromagnetic fine structures in uniaxial ferromagnets using the nonconforming domain decomposition method

  • P. Klouček
  • L. A. Melara
Conference paper


We propose a reformulation of singularly perturbated non-convex functionals using the global scaling laws and the nonconforming domain decomposition. We implement the method using an equi-distribution principle to guarantee a convergence of minimizing sequences. We present a computational example demonstrating the capability of this method.


Domain Decomposition Differential Inclusion Domain Decomposition Method Eikonal Equation Sharp Interface Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Choksi, R., Kohn, R., (1998): Bounds on the micromagnetic energy of a uniaxial ferromagnet. Comm. Pure Appl. Math. 51, 259–289MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Collins, C., Luskin, M. (1989): The computation of the austenitic-martensitic phase transition. In: Rascle, M. et al. (eds.): PDEs and continuum models of phase transitions (Lecture Notes in Physics, vol. 344). Springer, Berlin, pp. 34–50CrossRefGoogle Scholar
  3. [3]
    Dacorogna, B., Marcellini, P. (1999): Implicit partial differential equations. Birkhäuser Boston, Boston, MAMATHCrossRefGoogle Scholar
  4. [4]
    Klouček, P., Melara, L.A. (2002): The computational modeling of internal surfaces in crystals. J. Comput. Phys. 183, 623–651MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Kohn, R., Müller, S. (1992): Branching of twins near an austenite-twinned-martensite interface. Philos. Mag. A 66, 697–715CrossRefGoogle Scholar
  6. [6]
    Kohn, R., Müller, S. (1992): Relaxation and regularization of nonconvex variational problems. Rend. Sem. Mat. Fis. Milano 62, 89–113MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Kohn, R., Müller, S. (1994): Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 47, 405–435MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Lifshitz, E. (1944): On the magnetic structure of iron. J. Phys. 8, 337–346MathSciNetGoogle Scholar
  9. [9]
    Luskin, M. (1996): On the computation of crystalhne microstructure. In: Iserles, A. (ed.): Acta Numerica. 1996. Cambridge University Press, Cambridge, pp. 191–257Google Scholar
  10. [10]
    Privorotskii, I.A. (1976): Thermodynamic theory of domain structures. Wiley, New YorkGoogle Scholar
  11. [11] Quarteroni, A., Valli, A. (1999): Domain decomposition methods for partial differential equations. Oxford University Press, OxfordMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • P. Klouček
    • 1
  • L. A. Melara
    • 1
  1. 1.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

Personalised recommendations