1,720,958 research outputs found
Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics
Full text linkRecently, Kim & Wilkening (Convergence of a mass-lumped finite element method for the Landau–Lifshitz equation, Quart. Appl. Math., 76, 383–405, 2018) proposed two novel predictor-corrector methods for the Landau–Lifshitz–Gilbert equation (LLG) in micromagnetics, which models the dynamics of the magnetization in ferromagnetic materials. Both integrators are based on the so-called Landau–Lifshitz form of LLG, use mass-lumped variational formulations discretized by first-order finite elements, and only require the solution of linear systems, despite the nonlinearity of LLG. The first(-order in time) method combines a linear update with an explicit projection of an intermediate approximation onto the unit sphere in order to fulfill the LLG-inherent unit-length constraint at the discrete level. In the second(-order in time) integrator, the projection step is replaced by a linear constraint-preserving variational formulation. In this paper, we extend the analysis of the integrators by proving unconditional well-posedness and by establishing a close connection of the methods with other approaches available in the literature. Moreover, the new analysis also provides a well-posed integrator for the Schrödinger map equation (which is the limit case of LLG for vanishing damping). Finally, we design an implicit-explicit strategy for the treatment of the lower-order field contributions, which significantly reduces the computational cost of the schemes, while preserving their theoretical properties
The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics
Full text linkWe discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field contributions, our setting covers the non-standard Dzyaloshinskii-Moriya interaction, which is the essential ingredient for the enucleation and stabilization of magnetic skyrmions. Our analysis also includes the inexact solution of the arising nonlinear systems, for which we discuss both a constraint-preserving fixed-point solver from the literature and a novel approach based on the Newton method. We numerically compare the two linearization techniques and show that the Newton solver leads to a considerably lower number of nonlinear iterations. Moreover, in a numerical study on magnetic skyrmions, we demonstrate that, for magnetization dynamics that are very sensitive to energy perturbations, the midpoint scheme, due to its conservation properties, is superior to the dissipative tangent plane schemes from the literature
Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation
Full text linkCombining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step
Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics
No full textWe consider the numerical approximation of the Landau–Lifshitz–Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic contributions, the energy comprises the Dzyaloshinskii–Moriya interaction, which is the most important ingredient for the enucleation and the stabilization of chiral magnetic skyrmions. We propose and analyze three tangent plane integrators, for which we prove (unconditional) convergence of the finite element solutions towards a weak solution of the problem. The analysis is constructive and also establishes existence of weak solutions. Numerical experiments demonstrate the applicability of the methods for the simulation of practically relevant problem sizes
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
No full textThe tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau–Lifshitz–Gilbert equation, which describes the time evolution of ferromagnetic configurations. Exploiting the geometric structure of the equation, the tangent plane scheme requires only the solution of one linear variational form per time-step, which is posed in the discrete tangent space determined by the nodal values of the current magnetization. We develop an effective solution strategy for the arising constrained linear systems, which is based on appropriate Householder reflections. We derive possible preconditioners, which are (essentially) independent of the time-step, and prove linear convergence of the preconditioned GMRES algorithm. Numerical experiments underpin the theoretical findings
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Computational micromagnetics with Commics
Full text linkWe present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau–Lifshitz–Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab. Program summary: Program title: Commics Program Files doi: http://dx.doi.org/10.17632/29wv9h78h7.1 Licensing provisions: GPLv3 Programming language: Python3 Nature of problem: Numerical integration of the Landau–Lifshitz–Gilbert equation in three space dimensions Solution method: Tangent plane scheme [1]: original first-order version, projection-free version, second-order version, efficient second-order IMEX version; Midpoint scheme [2]: original version, IMEX version; Magnetostatic Maxwell equations are treated by the hybrid FEM–BEM method [3] Additional comments including restrictions and unusual features: An installation of the finite element software Netgen/NGSolve and an installation of the boundary element library BEM++ are required. References [1] F. Alouges. A new finite element scheme for Landau–Lifchitz equations. Discrete Contin. Dyn. Syst. Ser. S, 1(2):187–196, 2008. [2] S. Bartels and A. Prohl. Convergence of an implicit finite element method for the Landau–Lifshitz–Gilbert equation. SIAM J. Numer. Anal., 44(4):1405–1419, 2006. [3] D. R. Fredkin and T. R. Koehler. Hybrid method for computing demagnetization fields. IEEE Trans. Magn., 26(2):415–417, 1990
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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