Related papers: A novel third-order accurate and stable scheme for…
In this paper, we present a class of nonuniform time-stepping, high-order linear stabilized schemes that can preserve both the discrete energy stability and maximum-bound principle (MBP) for the time-fractional Allen-Cahn equation. To this…
We developed a method to calculate the magnetoresistance of magnetic nanostructures. We discretize a magnetic disk in small cells and numerically solve the Landau-Lifshitz-Gilbert (LLG) equation in order to obtain its magnetization profile.…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We design a conservative finite difference scheme for ideal magnetohydrodynamic simulations that attains high-order accuracy, shock-capturing, and divergence-free condition of the magnetic field. The scheme interpolates pointwise physical…
We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic…
We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…
The Z2 gauge-Higgs model in three dimensions has two different types of phase transition, confinement-deconfinement and Higgs magnetization. Here they are explored through two order parameters, the Coulomb magnetization which is a local…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
Magnetization dynamics in magnetic materials are well described by the modified semiclassical Landau-Lifshitz-Gilbert (LLG) equation, which includes the magnetic damping $\alpha$ and the magnetic moment of inertia $\mathrm{I}$ tensors as…
Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena.…
We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization…
We extend a renormalization group-based course-graining method for micromagnetic simulations to include properly scaled magnetostatic interactions. We apply the method in simulations of dynamic hysteresis loops at clinically relevant sweep…
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…
We present a new code that performs a relaxation of a magnetic field towards a force-free state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical…
In the framework of the Landau-Lifshitz equations without any dissipation (an approximation which may also be helpful for finite but weak Gilbert damping), with all interactions included, for general ground states, geometries and domain…
We propose a novel model which efficiently describes the magnetization dynamics in a magnetic bilayer system. By applying a particular gauge transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully convert the model…
The shape of ferromagnetic resonance spectra of highly dispersed, chemically disordered Fe_{0.2}Pt_{0.8} nanospheres is perfectly described by the solution of the Landau-Lifshitz-Gilbert (LLG) equation excluding effects by crystalline…
We review recent advances in machine-learning (ML) force-field methods for large-scale Landau-Lifshitz-Gilbert (LLG) simulations of metallic spin systems. We generalize the Behler-Parrinello (BP) ML architecture -- originally developed for…
We introduce Gradient Particle Magnetohydrodynamics (GPM), a new Lagrangian method for magnetohydrodynamics based on gradients corrected for the locally disordered particle distribution. The development of a numerical code for MHD…
The usefulness of modeling magnetocaloric materials expands from the understanding of their behavior to the prediction of new materials, playing a fundamental role in the optimization of their performance. In contrast with other areas of…