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3.3.3 Micromagnetic simulations of
Contents
4. Geometric integration of Landau-Lifshitz-Gilbert equation
Subsections
4.1 Introduction
4.2 The mathematical model
4.2.1 General properties of the effective field
4.2.2 Constraints for magnetization dynamics
and hamiltonian structure of conservative dynamics
4.3 Spatially semi-discretized LLG equation
4.3.1 Discretized free energy and effective field
4.3.2 Semi-discretized LLG equation properties
4.4 Mid-point LLG discrete dynamics
4.4.1 Properties of mid-point rule induced dynamics
4.4.1.1 Point-wise magnitude conservation
4.4.1.2 Energy balance and discrete Lyapunov structure
4.4.1.3 Preservation of Hamiltonian structure
4.5 Solution of the time-stepping equation
4.6 Accuracy tests for LLG discrete dynamics
4.7 Finite differences spatial discretization of LLG equation
4.8 Numerical Simulations of
-mag standard problem n. 4
4.8.1 Definition of the problem
4.8.2 Numerical results
4.8.3 Discussion about computational cost
Massimiliano d'Aquino 2005-11-26
-mag standard problem n. 4