Related papers: Conjugate gradient methods in micromagnetics
In this paper, based on the limited memory techniques and subspace minimization conjugate gradient (SMCG) methods, a regularized limited memory subspace minimization conjugate gradient method is proposed, which contains two types of…
We present the open source micromagnetic framework, MagTense, which utilizes a novel discretization approach of rectangular cuboid or tetrahedron geometry "tiles" to analytically calculate the demagnetization field. Each tile is assumed to…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
The magnetic properties of dilute magnetic semiconductors (DMS) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. It is found that the range of the exchange interaction in (Ga, Mn)N is…
We formulated a technique which combines the first-principles, micromagnetic and microstructural calculations and allows us to study the nature of hysteretic phenomena in hard magnets. Two distinct sources of coercivity in polytwinned CoPt…
The magnetocaloric effect or "magnetic Gr\"uneisen ratio" $\Gamma_H=T^{-1}(dT/dH)_S$ quantifies the cooling or heating of a material when an applied magnetic field is changed under adiabatic conditions. Recently this property has attracted…
The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…
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…
(Mini-batch) Stochastic Gradient Descent is a popular optimization method which has been applied to many machine learning applications. But a rather high variance introduced by the stochastic gradient in each step may slow down the…
Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often…
We systematically investigate the magnetophoresis of weakly paramagnetic manganese oxide nanoparticles under nonuniform magnetic fields using a combination of experiments and multiphysics numerical simulations. Experiments were conducted in…
In a recent paper (J. Chem. Theory. Comput., 2017, 13, 180-190) we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very…
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…
Decoherence processes in crystals of molecular magnets are prototypical for interacting electronic spin systems. We analyze the Landau-Zener dynamics of the archetypical TbPc$_2$ complex diluted in a diamagnetic monocrystal. The dependence…
We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of…
The numerical solution of algebraic tensor equations is a largely open and challenging task. Assuming that the operator is symmetric and positive definite, we propose two new gradient-descent type methods for tensor equations that…
Connections of the conjugate gradient (CG) method with other methods in computational mathematics are surveyed, including the connections with the conjugate direction method, the subspace optimization method and the quasi-Newton method BFGS…