Related papers: Midpoint geometric integrators for inertial magnet…
This article is concerned with the integration of the time-dependent Ginzburg--Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability,…
The Landau-Lifshitz-Gilbert (LLG) equations are widely used to study spin dynamics in Mott insulators. However, because energy dissipation is typically introduced phenomenologically, its validity for describing nonequilibrium processes and…
This article is concerned with the integration of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability, accuracy,…
The magnetization control problem for the Landau-Lifshitz-Gilbert (LLG) equation $m_t= m \times (\Delta m +u)- m \times (m \times (\Delta m +u)),\ (x,t) \in \Omega\times (0,T] $ with zero Neumann boundary data on a two-dimensional bounded…
In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating,…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…
Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast…
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential…
We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange energy functional containing second-order derivatives of the unknown field. Such regularizations are featured in advanced micromagnetic models recently introduced…
In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into Landau-Lifshitz (LL) equation, which describes the…
The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects.…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfv\'en…
This paper deals with the numerical simulation of the 2D magnetic time-dependent Ginzburg-Landau (TDGL) equations in the regime of small but finite (inverse) Ginzburg-Landau parameter $\epsilon$ and constant (order $1$ in $\epsilon$)…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
The Landau-Lifshitz (L-L) equation describing the time dependence of the magnetisation vector is numerically integrated fully without any simplifying assumptions in the time domain and the magnetisation time series obtained is Fourier…
We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale…
Heat assisted magnetic recording (HAMR) technology represents the most promising candidate to replace the current perpendicular recording paradigm to achieve higher storage densities. To better understand HAMR dynamics in granular media we…