On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach
Computer Methods in Applied Mechanics and Engineering
On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization
Computer Methods in Applied Mechanics and Engineering
A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
SIAM Journal on Numerical Analysis
A Gauss-Seidel projection method for micromagnetics simulations
Journal of Computational Physics
Numerical study of nonlinear ferromagnetic materials
Applied Numerical Mathematics
Geometric space-time integration of ferromagnetic materials
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule
Journal of Computational Physics
Spin-polarized currents in ferromagnetic multilayers
Journal of Computational Physics
Numerical methods for the landau-lifshitz-gilbert equation
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility of these algorithms, we present representative calculations for reduced free rigid body motion (a conservative ODE) and a discretization of micromagnetics (a dissipative PDE). We emphasize the role of isotropy in geometric integration and link numerical integration schemes to modern differential geometry through the use of partial connection forms; this theoretical framework generalizes moving frames and connections on principal bundles to manifolds with nonfree actions.