Related papers: Conjugate gradient methods in micromagnetics
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
We present two magnetometry-based methods suitable for assessing gradients in the critical temperature and hence the composition of multifilamentary superconductors: AC magnetometry and Scanning Hall Probe Microscopy. The novelty of the…
This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying…
We show that to describe properly the low energy excitations of $CuGeO_{3}$ one must include the effects of a transverse antiferromagnetic coupling, which is estimated to be $J_{\perp}=0.15 J$. Owing to this coupling the frustration in the…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…
The conjugate gradient method (CG) has long been the workhorse for inner-iterations of second-order algorithms for large-scale nonconvex optimization. Prominent examples include line-search based algorithms, e.g., Newton-CG, and those based…
An overview of the effect of a magnetic field gradient on fluids with linear magnetic susceptibilities is given. It is shown that two commonly encountered expressions, the magnetic field gradient force and the concentration gradient force…
We implement an efficient energy-minimization algorithm for finite-difference micromagnetics that proofs especially useful for the computation of hysteresis loops. Compared to results obtained by time integration of the…
Magnetic properties of 2D systems of magnetic nanoobjects (2D regular lattices of the magnetic nanoparticles or magnetic nanostripes) are considered. The analytical calculation of the hysteresis curve of the system with interaction between…
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our previous computational work. This paper presents a numerical…
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars…
Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…
The shape gradient is a local sensitivity function that provides the change in a figure of merit associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity…
This paper develops a weak Galerkin (WG) finite element method of arbitrary order for the steady incompressible Magnetohydrodynamics equations. The WG scheme uses piecewise polynomials of degrees $k(k\geq 1),k,k-1$, and $k-1$ respectively…
Dynamic quantities related to hysteresis have been measured in micromagnetic simulations of single-domain nanoscale magnets at nonzero temperature. The hysteresis-loop area and magnetization-field correlation display the characteristics of…
We study hysteresis in a micron-sized bead: a non-magnetic matrix embedded with super- paramagnetic nanoparticles. These hold tremendous promise in therapeutic applications as heat generating machines. The theoretical formulation uses a…
The efficient coupling between lattice degrees of freedom and spin degrees of freedom in magnetic materials can be used for refrigeration and energy conversion. This coupling is enhanced in materials exhibiting the giant magnetocaloric…
In this paper, we propose a modified nonlinear conjugate gradient (NCG) method for functions with a non-Lipschitz continuous gradient. First, we present a new formula for the conjugate coefficient \beta_k in NCG, conducting a search…