Cost-effective way to speed up micromagnetic simulations in granular media. (English) Zbl 0987.78020
Summary: An investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations of granular media has been done. The stiffness of the problem has been investigated using two different solvers, a nonstiff (Adams) and a stiff one (Backward Differentiation Formulae, BDF) for the solution of the large system of ODEs. Them micromagnetic simulations have been run for a variety of values of the maximum dimension of the Krylov subspace for different sizes of finite elements in order to establish an optimum value. Adams method requires 3 times more CPU time than BDF for the same simulation time. The latter result shows that granular media micromagnetic simulations are stiff. Furthermore, it has been found that increasing the maximum dimension of the Krylov subspace to 15 (default value \(=5\)) a considerable increase with respect to the speed of the simulations occurs in the order of 20-52%.
MSC:
| 78M05 | Method of moments applied to problems in optics and electromagnetic theory |
| 82D40 | Statistical mechanics of magnetic materials |
| 74E20 | Granularity |
References:
| [1] | Brown, P. N.; Hindmarsh, A. C., Matrix-free methods for stiff systems of ODEs, SIAM J. Numer. Anal., 23, 610-638 (1986) · Zbl 0615.65078 |
| [2] | Brown, P. N.; Hindmarsh, A. C., Reduced storage matrix methods in stiff ODE systems, J. Appl. Math. Comput., 31, 40-91 (1989) · Zbl 0677.65074 |
| [3] | Brown, W. F., Micromagnetics (1963), Wiley: Wiley New York |
| [4] | S.D. Cohen, A.C. Hindmarsh, CVODE: User guide, LLNL, Technical Report UCRL-MA-118618, September 1994; S.D. Cohen, A.C. Hindmarsh, CVODE: User guide, LLNL, Technical Report UCRL-MA-118618, September 1994 |
| [5] | Fredkin, D. R.; Koehler, T. R., Hybrid method for computing demagnetizing fields, IEEE Trans. Magnetic, 26, 415-417 (1990) |
| [6] | Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0217.21701 |
| [7] | Giles, R.; Alexopoulos, P. S.; Mansuripur, M., Micromagnetics of thin film cobalt-based media for magnetic recording, Comput. Phys., 6, 53-70 (1992) |
| [8] | Lodder, J. C., Magnetic structures in Co-Cr media for perpendicular magnetic recording, J. Magn. Magn. Mater., 159, 238-248 (1996) |
| [9] | Saad, Y.; Schultz, M. H., GMRES: A generalised minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7, 856-869 (1986) · Zbl 0599.65018 |
| [10] | Tsiantos, V. D.; Miles, J. J., Stiffness in micromagnetic simulations, (Proceedings of the 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation (August 21-25, 2000), Lausanne: Lausanne Switzerland) · Zbl 0995.78043 |
| [11] | Tsiantos, V. D.; Miles, J. J.; Middleton, B. K., (Neittaanmaki, P.; etal., Proceedings of the 3rd European Conference on Numerical Mathematics and Advanced Applications (ENUMATH ’99), Jyväskylä, Finland (2000), World Scientific: World Scientific Singapore), 743-752 · Zbl 0995.78043 |
| [12] | Tsiantos, V. D.; Miles, J. J.; Middleton, B. K., BDF-NEWTON-GMRES method in stiff micromagnetic simulations, Int. J. Nonlinear Syst. Num. Sim. (2000), submitted · Zbl 0995.78043 |
| [13] | Victora, R. H.; Brucker, C. F.; Spada, F. E., Structure and micromagnetic predictions for hysteretic phenomena in a novel Co-Pt permanent magnet thin film, J. Magn. Magn. Mater., 97, 343-352 (1991) |
| [14] | Yang, B.; Fredkin, D., Dynamical micromagnetics by the finite element method, IEEE Trans. Magnetics, 34, 3842-3852 (1998) |
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