Summary
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.
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References
Choksi, R., Kohn, R., (1998): Bounds on the micromagnetic energy of a uniaxial ferromagnet. Comm. Pure Appl. Math. 51, 259–289
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. 34–50
Dacorogna, B., Marcellini, P. (1999): Implicit partial differential equations. Birkhäuser Boston, Boston, MA
Klouček, P., Melara, L.A. (2002): The computational modeling of internal surfaces in crystals. J. Comput. Phys. 183, 623–651
Kohn, R., Müller, S. (1992): Branching of twins near an austenite-twinned-martensite interface. Philos. Mag. A 66, 697–715
Kohn, R., Müller, S. (1992): Relaxation and regularization of nonconvex variational problems. Rend. Sem. Mat. Fis. Milano 62, 89–113
Kohn, R., Müller, S. (1994): Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 47, 405–435
Lifshitz, E. (1944): On the magnetic structure of iron. J. Phys. 8, 337–346
Luskin, M. (1996): On the computation of crystalhne microstructure. In: Iserles, A. (ed.): Acta Numerica. 1996. Cambridge University Press, Cambridge, pp. 191–257
Privorotskii, I.A. (1976): Thermodynamic theory of domain structures. Wiley, New York
[11] Quarteroni, A., Valli, A. (1999): Domain decomposition methods for partial differential equations. Oxford University Press, Oxford
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Klouček, P., Melara, L.A. (2003). The computational modelling of micromagnetic fine structures in uniaxial ferromagnets using the nonconforming domain decomposition method. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_27
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DOI: https://doi.org/10.1007/978-88-470-2089-4_27
Publisher Name: Springer, Milano
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