260 Ë 7 Numerical simulations of HTS Maglev
[47]Miya K, Hashizume H. Application of T-method to AC problem based on boundary element
method. IEEE Trans on Magnetics. 1988;24(1):134–137.
Further readings
Detailed introduction of the finite-element method for electromagnetics:
[1] Jin JM. The finite element method in electromagnetics. Wiley; 2002.
Three-dimensional model the HTS bulk using magnetic vector potential:
[2] Ueda H, Azumaya S, Tsuchiya S, Ishiyama A. 3D electromagnetic analysis of levitating
transporter using bulk superconductor. IEEE Trans on Appl Supercond. 2006;16(2):1092–1095.
[3] Alloui L, Bouillault F, Mimoune SM. Numerical study of the influence of flux creep and of thermal
effect on dynamic behaviour of magnetic levitation systems with a high-Tcsuperconductor using
control volume method. Eur Phys J Appl Phys. 2009;45:020801.
Numerical techniques to solve the nonlinear problems and the large algebraic equations:
[4] Alloui L, Ben Alia K, Bouillault F, Mimoune SM, Bernard L, Lévêque J. Numerical study of the
relation between the thermal effect and the stability of the levitation system excited by an
external source. Physica C. 2013;487(4):1–10.
[5] Knoll DA, Keyes DE. Jacobian-free Newton-Krylov methods: a survey of approaches and
applications. J Comput Phys. 2004;193(2):357–397.
[6] Saad Y, Schultz MH. GMRES: A generalised minimal residual algorithm for solving nonsymmetric
linear systems. SIAM J Sci Stat Comput. 1986;7(3):856–869.
[7] Saad Y. Iterative methods for sparse linear systems. Philadelphia: Society for industrial and
applied mathematics; 2003.
[8] Kelley CT. Iterative methods for linear and nonlinear equations. Philadelphia: Society for
industrial and applied mathematics; 1995.