Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity

Mathematics of Computation

Volumn 67, Issue 223, 1998, Pages 965-986

  Du, Qiang ^a,b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

Convergence; Error estimates; Gauge invariance; Ginzburg Landau model of superconductivity; Nonstandard difference approximations; Time dependent equations

Indexed keywords

EID: 0032367087     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-98-00954-5     Document Type: Article

References (25)

1. S. L. Adler, and T. Piran, Relaxation methods for gauge field equilibrium equations, Rev. Mod. Phys. 56 (1984), pp. 1-40. MR 85c:81022
2. Z. Chen, and K.-H. Hoffmann, Numerical studies of a nonstationary Ginzburg-Landau model for superconductivity, Adv. Math. Sci. Appl. 5(1995), 363-389. MR 97e:82051
3. G. Crabtree, G. Leaf, H. Kaper, V. Vinokur, A. Koshelev, D. Braun, D. Levine, W. Kkwok, and J. Fendrich, Time-dependent Ginzburg-Landau simulations of vortex guidance by twin boundaries, Physica C., 263(1996), pp. 401-408.
4. M. Doria, J. Gubernatis, and D. Rainer, Solving the Ginzburg-Landau equations by simulated annealing, Phys. Rev. B, 41 (1990), pp. 6335-6340.
5. Q. Du, Global existence and uniqueness of solutions for the time dependent Ginzburg-Landau model of superconductivity, Applicable Analysis, 53 (1994), 1-2, pp. 1-17. MR 97a:82085
6. Q. Du, Finite element methods for the time dependent Ginzburg-Landau model of superconductivity, Comp. Math. Appl., 27 (1994), pp. 119-133. MR 95g:65131
7. Q. Du, M. Gunzburger, and J. Peterson, Analysis and approximation of Ginzburg-Landau models for superconductivity, SIAM Review, 34(1992), pp. 54-81. MR 93g:82109
8. Q. Du, M. Gunzburger, and J. Peterson, Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors, Numer. Math., 64(1993), pp. 85-114. MR 93j:65178
9. Q. Du, M. Gunzburger, and J. Peterson, Solving the Ginzburg-Landau equations by finite element methods, Phy. Rev. B., 46(1992), pp. 9027-9034.
10. Q. Du, M. Gunzburger, and J. Peterson, Computational simulation of type-II superconductivity including pinning phenomena, Phy. Rev. B., 51(1995), pp. 15194-16203.
11. F. Lin and Q. Du, Ginzburg-Landau vortices, dynamics, pinning and hysteresis, SIAM Math. Anal. 28 (1997), pp. 1265-1293. CMP 98:02
12. Q. Du, R. Nicolaides, and X. Wu, Analysis and convergence of a covolume approximation of the Ginzburg-Landau model of superconductivity, to appear in SIAM Numer. Anal., (1997).
13. J. Fleckinger-Pelle, H. Kaper, and P. Takac, Dynamics of the Ginzburg-Landau equations of superconductivity, preprint, MCS P565-0296, Argonne National Lab..
14. H. Frahm, S. Ullah and A. Dorsey, Flux dynamics and the growth of the superconducting phase, Phys. Rev. Letters, 66 (1991), pp. 3067-3072.
15. L. Freitag, M. Jones and P. Plassmann, New techniques for parallel simulation of high tem-perature superconductors, MCS preprint, Argonne National Lab., (1994).
16. J. Garner, M. Spanbauer, R. Benedek, K. Strandburg, S. Wright and P. Plassman, Critical fields of Josephson-coupled superconducting multilayers, preprint.
17. W. Gropp, H. Kaper, G. Leaf, D. Levine, M. Plumbo, and V. Vinokur, Numerical simulation of vortex dynamics in type-II superconductors, J. Comp. Phys. 123(1996), pp. 254-266. CMP 96:07
18. H. Kaper, and M. Kwong, Vortex configurations in type-II superconducting films, J. Com. Phys. 119(1995), pp. 120-131.
19. M. K. Wong, Sweeping algorithms for inverting the discrete Ginzburg-Landau operators, Applied Math. Comp., 53(1993), pp.12d90-150.
20. S. Lin and Y. Yang, Computation of superconductivity in thin films, J. Comp. Phys., 89(1990), pp. 257-275. MR 91g:82059
21. F. Liu, M. Mondello and N. Goldenfeld, Kinetics of the superconducting transition, Phys. Rev. Lett., 66 (1991), pp. 3071-3074.
22. R. Nicolaides, Direct discretization of planar div-curl problems, SIAM Numer. Anal., 29 (1992), pp. 32-56. MR 93b:65176
23. R. Nicolaides, and X. Wu, Analysis and convergence of the MAC scheme 2. Navier-Stokes equations, Math. Comp., 65(1996), pp. 29-44. MR 96d:65148
24. Q. Tang and S. Wang, Time-dependent Ginzburg-Landau equations of superconductivity, Physica D., 88(1995), pp. 139-166. MR 96i:82156
25. M. Tinkham, Introduction to Superconductivity, 2nd edition, McGraw-Hill, New York, 1994.