Related papers: Linearized frequency domain Landau-Lifshitz-Gilber…
We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau-Lifshitz-Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover…
For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order $5$ combined with higher-order non-conforming finite element space…
We consider the numerical approximation of a nonlinear system of partial differential equations modeling magnetostriction in the small-strain regime consisting of the Landau--Lifshitz--Gilbert equation for the magnetization and the…
We present efficient numerical methods for the simulation of small magnetization oscillations in three-dimensional micromagnetic systems. Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation, linearized in the…
To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows to include magnetostrictive effects…
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume…
Magnetization dynamics in ferromagnetic materials is modeled by the Landau-Lifshitz (LL) equation, a nonlinear system of partial differential equations. Among the numerical approaches, semi-implicit schemes are widely used in the…
We study the effect of an elliptically polarized magnetic field on a system of non-interacting, single-domain ferromagnetic nanoparticles characterized by a uniform distribution of easy axis directions. Our main goal is to determine the…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for…
A linearized backward Euler Galerkin-mixed finite element method is investigated for the time-dependent Ginzburg--Landau (TDGL) equations under the Lorentz gauge. By introducing the induced magnetic field ${\sigma} = \mathrm{curl} \,…
In this work, we consider the construction of efficient surrogates for the stochastic version of the Landau-Lifshitz-Gilbert (LLG) equation using model order reduction techniques, in particular, the Reduced Basis (RB) method. The Stochastic…
Spin currents act on ferromagnets by exerting a torque on the magnetisation. This torque is modelled by appending additional terms to the Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous Landau-Lifshitz-Gilbert…
Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
In this article, we study the controllability issues of the Landau-Lifshitz-Gilbert Equations (LLGEs), accompanied with non-zero exchange energy only, in an interval in one spatial dimension with Neumann boundary conditions. The paper is of…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
A third-order accurate implicit-explicit Runge-Kutta time marching numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with arbitrary damping…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…