Related papers: Second-order semi-implicit projection methods for …
Micromagnetics simulation based on the classical Landau-Lifshitz-Gilbert (LLG) equation has long been a powerful method for modeling magnetization dynamics and reversal of three-dimensional (3D) magnets. For two-dimensional (2D) magnets,…
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…
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For…
We analyze a second-order projection method for the incompressible Navier-Stokes equations on bounded Lipschitz domains. The scheme employs a Backward Differentiation Formula of order two (BDF2) for the time discretization, combined with…
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the…
3D numerical simulations of ferromagnetic materials can be compared with experimental results via microwave susceptibility. In this paper, an optimised computation of this microwave susceptibility for large meshes is proposed. The microwave…
Compared with ferromagnetic counterparts, antiferromagnetic materials are considered as the future of spintronic applications since these materials are robust against the magnetic perturbation, produce no stray field, and display ultrafast…
Deep neural networks are used to model the magnetization dynamics in magnetic thin film elements. The magnetic states of a thin film element can be represented in a low dimensional space. With convolutional autoencoders a compression ratio…
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…
Magnetic materials host a wealth of nonlinear dynamics, textures, and topological defects. This is possible due to the competition between strong nonlinearity and dispersion that act at the atomic scale as well as long-range interactions.…
We propose a finite-difference algorithm for solving the time-dependent Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for…
Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by…
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…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
In this paper, we propose Galerkin-Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrodinger equation with nonhomogeneous Dirichlet boundary conditions and initial condition. We apply a…
Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving…
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe the evolution of the magnetization of a magnetic material, particularly in response to an external applied magnetic field. It allows one to take into account…