102,176 research outputs found
Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation
No full textCombining 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
Unterthänigste glückwündschende Aufwartung Bey der Erb-Huldigung/ Welche Der Durchlauchtigste/ und Großmächtige Fürst und Herr/ Hr. Friderich Wilhelm/ Marggraf zu Brandenburg ... Als erster Hertzog zu Magdeburg/ In Dero Stadt Halle/ von dem gantzen Hertzogthum Magdeburg/ und besagter Stadt einnahm/ Abgeleget In einer Nacht-Music von den Salanischen Musen selbiges Orts : [Hall den 5. Iunii, Ao. Christi M.DC.LXXXI.]
No full text[Johannes Praetorius, Quedlinburgensi G. H R.]Autor als Unterzeichner des Widmungstexte
Unterthänigste und Glückwünschende Aufwartung Bey der Erb-Huldigung/ Welche Der Durchlauchtigste/ und Großmächtigste Fürst und Herr/ Hr. Friderich der Dritte/ Marggraf zu Brandenburg/ des Heil. Röm. Reichs Ertz-Cämmerer und Chur-Fürst ... Als anderer regierender Hertzog zu Magdeburg/ In dero Stadt Halle den 21. Maii des 1689. Jahrs einnahm/ In einer Nacht-Music Von den Salanischen Musen Selbiges Orts abgeleget
No full text[Johannes Praetorius, Quedlinburgensi G. H. R.]Autor als Unterzeichner des Widmungstexte
Weak–strong uniqueness for the Landau–Lifshitz–Gilbert equation in micromagnetics
No full textWe consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts for the emergence of magnetic Skyrmions). Moreover, our proof gives a template on how to approach weak–strong uniqueness for even more complicated problems, where LLG is (nonlinearly) coupled to other (nonlinear) PDE systems
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
No full textWe revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [P. Heid and T. P. Wihler, Adaptive iterative linearization Galerkin methods for nonlinear problems, Math. Comp. 89 2020, 326, 2707–2734; P. Heid and T. P. Wihler, On the convergence of adaptive iterative linearized Galerkin methods, Calcolo 57 2020, Paper No. 24] satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [G. Gantner, A. Haberl, D. Praetorius and S. Schimanko, Rate optimality of adaptive finite element methods with respect to the overall computational costs, preprint 2020]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
No full textIn this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary Γ-convergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove that, in the limiting model, part of the DMI term behaves like the projection of the magnetic moment onto the normal to the film, contributing this way to an increase in the shape anisotropy arising from the magnetostatic self-energy. Finally, we discuss a convergent finite element approach for the approximation of the time-dependent case and use it to numerically compare the original three-dimensional (3D) model with the 2D thin-film limit
Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators
No full textWe discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general
Axioms of adaptivity revisited: Optimal adaptive IGAFEM
No full textThe axioms of adaptivity from [C. Carstensen, M. Feischl, M. Page, D. Praetorius. Axioms of adaptivity. Computers & Mathematics with Applications, 67, 1195-1253, 2014] analyze under which assumptions on the a posteriori error estimator and the mesh-refinement strategy, a mesh re fining adaptive algorithm yields convergence with optimal algebraic rates. In our talk, which is based on our recent work [G. Gantner, D. Haberlik, D. Praetorius. Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines. Mathematical Models and Methods in Applied Sciences, 27, 2631-2674, 2017], we now address the question which properties of the FEM are sufficient to ensure that the usual weighted-residual error estimator is well-defined and satisfies the axioms of adaptivity. In particular, our analysis covers conforming FEM in the framework of isogeometric analysis with hierarchical splines
17 beta-Estradiol induces nongenomic effects in renal intercalated cells through G protein-coupled estrogen receptor 1
No full textHofmeister MV, Damkier HH, Christensen BM, Olde B, Leeb-Lundberg LM, Fenton RA, Praetorius HA, Praetorius J. 17 beta-Estradiol induces nongenomic effects in renal intercalated cells through G protein-coupled estrogen receptor 1. Am J Physiol Renal Physiol 302: F358-F368, 2012. First published October 12, 2011; doi: 10.1152/ajprenal.00343.2011.-Steroid hormones such as 17 beta-estradiol (E2) are known to modulate ion transporter expression in the kidney through classic intracellular receptors. Steroid hormones are also known to cause rapid nongenomic responses in a variety of nonrenal tissues. However, little is known about renal short-term effects of steroid hormones. Here, we studied the acute actions of E2 on intracellular Ca2+ signaling in isolated distal convoluted tubules (DCT2), connecting tubules (CNT), and initial cortical collecting ducts (iCCD) by fluo 4 fluorometry. Physiological concentrations of E2 induced transient increases in intracellular Ca2+ concentration ([Ca2+](i)) in a subpopulation of cells. The [Ca2+](i) increases required extracellular Ca2+ and were inhibited by Gd3+. Strikingly, the classic E2 receptor antagonist ICI 182,780 also increased [Ca2+](i), which is inconsistent with the activation of classic E2 receptors. G proteincoupled estrogen receptor 1 (G.PER1 or GPR30) was detected in microdissected DCT2/CNT/iCCD by RT-PCR. Stimulation with the specific GPER1 agonist G-1 induced similar [Ca2+](i) increases as E2, and in tubules from GPER1 knockout mice, E2, G-1, and ICI 182,780 failed to induce [Ca2+](i) elevations. The intercalated cells showed both E2-induced concanamycin-sensitive H+-ATPase activity by BCECF fluorometry and the E2-mediated [Ca2+](i) increment. We propose that E2 via GPER1 evokes [Ca2+](i) transients and increases H+-ATPase activity in intercalated cells in mouse DCT2/CNT/iCCD
Coupling of dynamical micromagnetism and a stationary spin drift-diffusion equation: A step towards a fully self-consistent spintronics framework
No full textWe consider the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation to describe the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures. For this problem, we propose and analyze a convergent finite element integrator, where, in contrast to prior work, we consider the stationary limit for the spin diffusion. Numerical experiments underline that the new approach is more effective, since it leads to the same experimental results as for the model with time-dependent spin diffusion, but allows for larger time-steps of the numerical integrator
- …
