Computational methods in micromagnetics

With the continued growth of computational power, computational modelling has become an increasingly important part of modern science. The field of micromagnetism has benefited from the increase of computational power, leading in recent decades to the development of many important micromagnetic methods. This thesis aims to address some computational challenges relevant to the field of micromagnetism today.The computation of the demagnetising field is often the most time-consuming part of a micromagnetic simulation. In the finite difference method, this computation is usually done using the Fourier transform method, in which the demagnetising field is computed as the convolution of the magnetisation field with the demagnetising tensor. An analytical formula for the demagnetising tensor is available, however due to numerical cancellation errors it can only be applied for close distances between the interacting cells. For far distances between the interacting cells other approaches, such as asymptotic expansion, have to be used. In this thesis, we present a new method to compute the demagnetising tensor by means of numerical integration. The method offers improved accuracy over existing methods for the intermediate range of distances.In the finite element method, the computation of the demagnetising field is commonly done using the hybrid FEM/BEM method. The fast multipole method offers potential theoretical advantages over the hybrid FEM/BEM method particularly for the current and future generations of computing hardware. In micromagnetics, it has been applied to compute the demagnetising field in the finite difference setting and to compute the magnetostatic interaction between nanoparticles, however no implementation of the fast multipole method in finite elements is yet available. As one of the steps towards it, in this thesis we develop a new formula for the energy of the magnetostatic interaction between linearly magnetized polyhedrons. This formula can be used to compute the direct interaction between finite element cells in the fast multipole method.Ferromagnetic resonance is a popular experimental technique for probing the dynamical properties of magnetic systems. We extend the eigenvalue method for the computation of resonance modes to the computation of the FMR spectrum, and apply it to compute ferromagnetic resonance for a proposed FMR standard reference problem