<title>Computational micromagnetics for magnetostrictive actuators</title>

Computational micromagnetics plays an important role in design and control of magnetostrictive actuators. A sys- tematic approach to calculate magnetic dynamics and magnetostriction is presented. A finite difference method is developed to solve the coupled Landau-Lifshitz-Gilbert(LLG) equation for dynamics of magnetization and a one dimensional elastic motion equation. The effective field in the LLG equation consists of the external field, the i demagnetizing field, the exchange field, and the anisotropy field. A hierarchical algorithm using multipole approxi- mation speeds up the evaluation of the demagnetizing field, reducing computational cost from O(N2) to O(N1ogN). A hybrid 3D/1D rod model is adopted to compute the magnetostriction: a 3D model is used in solving the LLG equation for the dynamics of magnetization; then assuming that the rod is along z-direction, we take all cells with same i-cordinate as a new cell. The values of the magnetization and the effective field of the new cell are obtained I from averaging those of the original cells that the new cell contains. Each new cell is represented as a mass-spring in 5 solving the motion equation. Numerical results include: 1. domain wa!! dynamics, including domain wall formation and motion; 2. effects of physical parameters, grid geometry, grid refinement and field step on H - M hysteresis curves; 3. magnecostriction curve.