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The dynamic matrix method addresses the Landau-Lifshitz-Gilbert (LLG) equation in the frequency domain by transforming it into an eigenproblem. Subsequent numerical solutions are derived from the eigenvalues and eigenvectors of the dynamic…

Computational Physics · Physics 2024-04-02 D. E. Gonzalez-Chavez , G. P. Zamudio , R. L. Sommer

We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated ferromagnet with competing first and second order exchange interactions exposed to deterministic and random spin transfer torques in form of transport noise. We prove…

Probability · Mathematics 2023-06-29 Beniamin Goldys , Chunxi Jiao , Christof Melcher

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

Numerical Analysis · Mathematics 2022-11-10 Zhichao Peng , Yanlai Chen , Yingda Cheng , Fengyan Li

This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines…

Numerical Analysis · Mathematics 2022-11-29 Francesca Bonizzoni , Moritz Hauck , Daniel Peterseim

An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for…

Materials Science · Physics 2009-11-13 D. M. Edwards , O. Wessely

We propose and implement a third-order accurate numerical scheme for the Landau-Lifshitz-Gilbert equation, which describes magnetization dynamics in ferromagnetic materials under large damping parameters. This method offers two key…

Mathematical Physics · Physics 2025-10-29 Changjian Xie , Cheng Wang

The ultra-fast magnetisation relaxation rates during the laser-induced magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. The LLB equation is equivalent in the limit $S…

Materials Science · Physics 2015-05-20 U. Atxitia , O. Chubykalo-Fesenko

We present a methodology to investigate phase-diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian…

Quantum Physics · Physics 2022-04-13 Michael F. Herbst , Stefan Wessel , Matteo Rizzi , Benjamin Stamm

This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…

Computational Engineering, Finance, and Science · Computer Science 2015-04-16 Kevin Carlberg , Ray Tuminaro , Paul Boggs

Sparsity-inducing regularization problems are ubiquitous in machine learning applications, ranging from feature selection to model compression. In this paper, we present a novel stochastic method -- Orthant Based Proximal Stochastic…

Optimization and Control · Mathematics 2020-07-24 Tianyi Chen , Tianyu Ding , Bo Ji , Guanyi Wang , Jing Tian , Yixin Shi , Sheng Yi , Xiao Tu , Zhihui Zhu

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…

Numerical Analysis · Mathematics 2022-01-19 Bangti Jin , Zehui Zhou , Jun Zou

To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows to include magnetostrictive effects…

Numerical Analysis · Mathematics 2014-12-10 L'ubomir Banas , Marcus Page , Dirk Praetorius , Jonathan Rochat

We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…

Numerical Analysis · Mathematics 2020-05-12 Sebastian Ullmann , Christopher Müller , Jens Lang

The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…

Numerical Analysis · Mathematics 2025-11-14 Changjian Xie , Cheng Wang

We investigate the stochastic Landau-Lifshitz-Gilbert (LLG) equation on a periodic 2D domain, driven by infinite-dimensional Gaussian noise in a Sobolev class. We establish strong local well-posedness in the energy space and characterize…

Analysis of PDEs · Mathematics 2025-04-28 Ben Goldys , Chunxi Jiao , Christof Melcher

We consider the coupled system of the Landau--Lifshitz--Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For…

Numerical Analysis · Mathematics 2025-01-15 Hywel Normington , Michele Ruggeri

The theory predicts that the spin-wave lifetime $\tau_L$ and the linewidth of ferromagnetic resonance $\Delta B$ can be governed by random fields and spatial memory. To that aim the effective field around which the magnetic moments perform…

Mesoscale and Nanoscale Physics · Physics 2015-05-28 Thomas Bose , Steffen Trimper

In this work, we propose viable and efficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of wRB (weighted reduced basis) method for stochastic…

Numerical Analysis · Mathematics 2018-11-05 Davide Torlo , Francesco Ballarin , Gianluigi Rozza

We report here on the recent application of a now classical general reduction technique, the Reduced-Basis approach initiated in [C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A. T. Patera, and G. Turinici. Reliable real-time solution of…

Numerical Analysis · Mathematics 2010-04-05 Sébastien Boyaval , Claude Le Bris , Tony Lelièvre , Yvon Maday , Ngoc Cuong Nguyen , Anthony T. Patera

In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale…

Numerical Analysis · Mathematics 2026-05-11 Zetao Ma , Jingrun Chen , Rui Du , Lei Zhang