Discretization-Induced Stiffness in Micromagnetic Simulations

Shepherd, David; Miles, J.J.; Heil, Matthias; Mihajlović, Milan

doi:10.1109/tmag.2014.2325494

Cited by 6 publications

(7 citation statements)

References 8 publications

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“…The vectors x, h d (x), and h ext hold the unit vectors of the magnetization, the demagnetizing field, and the external field at the nodes of the finite element mesh or the cells of a finite difference grid, respectively. For computing the demagnetizating field, equations ( 12) to ( 15) can be solved using an algebraic multigrid method on the finite element mesh [14,44,45].…”

Section: Finite Element and Finite Difference Discretizationmentioning

confidence: 99%

Micromagnetics of rare-earth efficient permanent magnets

Fischbacher

Kovacs

Gusenbauer

et al. 2018

J. Phys. D: Appl. Phys.

100

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The development of permanent magnets containing less or no rareearth elements is linked to profound knowledge of the coercivity mechanism. Prerequisites for a promising permanent magnet material are a high spontaneous magnetization and a sufficiently high magnetic anisotropy. In addition to the intrinsic magnetic properties the microstructure of the magnet plays a significant role in establishing coercivity. The influence of the microstructure on coercivity, remanence, and energy density product can be understood by using micromagnetic simulations. With advances in computer hardware and numerical methods, hysteresis curves of magnets can be computed quickly so that the simulations can readily provide guidance for the development of permanent magnets. The potential of rare-earth reduced and free permanent magnets is investigated using micromagnetic simulations. The results show excellent hard magnetic properties can be achieved in grain boundary engineered NdFeB, rare-earth magnets with a ThMn 12 structure, Co-based nano-wires, and L1 0 -FeNi provided that the magnet's microstructure is optimized.

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Section: Finite Element and Finite Difference Discretizationmentioning

confidence: 99%

Micromagnetics of rare-earth efficient permanent magnets

Fischbacher

Kovacs

Gusenbauer

et al. 2018

J. Phys. D: Appl. Phys.

100

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show abstract

“…The derivative and function evaluations in dynamical and static micromagnetic computations are very expensive, mostly due to the nonlocal stray field component. However, the use of a stray field algorithm that scales optimally or quasi-optimially with problem size such as the algebraic multigrid method [46,42,13], the fast multipole method [50,4,33] and hierarchical matrices [36], fast Fourier transform based methods (FFT) [50,16,49] or non-uniform FFT algorithms [29,15,20] is not sufficient to obtain a micromagnetic solver that scales linearly with problem size. Owing to the exchange interactions the micromagnetic equations can be considered as stiff [9] and the number of time steps in a dynamical solver or the number of iterations in a static solver increase with increasing problem size.…”

Section: Introductionmentioning

confidence: 99%

“…However, practical tests show that rough approximations of the solution of such preconditioning systems suffice. Suess et al [45] and Sheperd et al [42] investigated the correlation between the microstructure of the magnet and the discretization on the stiffness of the Landau-Lifshitz Gilbert equation. They show, that implicit or semi-implicit integrators of the Landau-Lifshitz equation with a preconditioned linear system for the Newton step, successfully tackles stiffness in micromagnetic systems.…”

Section: Introductionmentioning

confidence: 99%

Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

Exl

Fischbacher

Kovacs

et al. 2019

Computer Physics Communications

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Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead to a speed up by a factor of 3 and 7 for computing hysteresis in soft magnetic and hard magnetic materials, respectively. As a preconditioner an approximation of the Hessian of the Lagrangian is used, which only takes local field terms into account. Preconditioning requires a few additional sparse matrix vector multiplications per iteration of the nonlinear conjugate gradient method, which is used for minimizing the energy for a given external field. The time to solution for computing the demagnetization curve scales almost linearly with problem size.

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“…This is chosen to be a 3-element stencil, which is correct to second order, but when the exchange coupling is strong a higher order operator may be needed. It has also previously been shown that the spatial discretization with an analytical demagnetization calculations can result in the Landau-Lifshitz equation becoming stiff Shepherd et al [2014].…”

Section: µMag Standard Problemmentioning

confidence: 99%

MagTense: A micromagnetic framework using the analytical demagnetization tensor

Bjørk

Poulsen

Nielsen

et al. 2021

Journal of Magnetism and Magnetic Materials

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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 be uniformly magnetized, and from this assumption only, the demagnetization field can be analytically calculated. Using this novel approach we calculate the solution to the µmag standard micromagnetic problems 2, 3 and 4 and find that the MagTense framework accurately predicts the solution to each of these. Finally, we show that simulation time can be significantly improved by performing the dense demagnetization tensor matrix multiplications using NVIDIA CUDA.

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Discretization-Induced Stiffness in Micromagnetic Simulations

Cited by 6 publications

References 8 publications

Micromagnetics of rare-earth efficient permanent magnets

Micromagnetics of rare-earth efficient permanent magnets

Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

MagTense: A micromagnetic framework using the analytical demagnetization tensor

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