Numerical methods for the stray-field calculation: A comparison of recently developed algorithms

Abert, Claas; Exl, Lukas; Selke, Gunnar; Drews, André; Schrefl, T.

doi:10.1016/j.jmmm.2012.08.041

Cited by 67 publications

(83 citation statements)

References 25 publications

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“…only rely on the geometry of the problem, see for instance [7]. Thus, in our asymptotic operation counts, we neglect the effort for computing these steps and refer to as precomputation or setup phase.…”

Section: Introductionmentioning

confidence: 99%

“…Several methods address the approximation of the solution to (1). Integral methods with a regular discretization of the domain Ω aim to directly compute the integral representation of the solution inside the magnetic body Ω [7,8], i.e. …”

Section: Introductionmentioning

confidence: 99%

“…the costs are O(N log N) for N grid points [4,7,8]. Also the fast multipole method and combination with FFT was applied to compute the magnetostatic field and energy [9][10][11], as well as a nonuniform grid (NG) algorithm [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…The discrete formulation of (1) translates to only one sparse linear system, which, however, tends to be very ill-conditioned due to the transformation. Algebraic multigrid preconditioners were successfully applied to address this issue [7]. On the other hand, the well-known hybrid FEM-BEM coupling by the ansatz of Fredkin and Koehler [23] aims to solve (1) by the splitting φ = φ 1 + φ 2 , where φ 1 is determined by a Poisson equation with Neumann boundary conditions and φ 2 by a Laplace equation where the Dirichlet data are computed by the values of φ 1 through a boundary integral representation of the potential φ 2 .…”

Section: Introductionmentioning

confidence: 99%

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Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

Exl

Schrefl

2014

Journal of Computational Physics

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We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet problem and evaluation of the single layer potential by a fast approximation technique based on Fourier approximation of the kernel function. The latter approximation leads to a generalization of the well-known convolution theorem used in finite difference methods. We address it by a non-uniform FFT approach. Overall, our method scales O(M + N + N log N) for N nodes and M surface triangles. We confirm our approach by several numerical tests.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

Exl

Schrefl

2014

Journal of Computational Physics

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“…The magnetostatic interaction field is computed from the magnetic scalar potential. 23 We use a three step procedure to compute the magnetization as function of field and temperature:…”

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confidence: 99%

High energy product in Battenberg structured magnets

Bance

Oezelt

Schrefl

et al. 2014

Applied Physics Letters

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Multiphase nano-structured permanent magnets show a high thermal stability of remanence and a high energy product while the amount of rare-earth elements is reduced. Non-zero temperature micromagnetic simulations show that a temperature coefficient of remanence of −0.073%/K and that an energy product greater than 400 kJ/m3 can be achieved at a temperature of 450 K in a magnet containing around 40 volume percent Fe65Co35 embedded in a hard magnetic matrix.

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New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

et al. 2021

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condensed matter physics, including cell membranes, [1] nematic crystals, [2,3] superfluids, [4] semiconductors, [5][6][7][8] ferromagnets, [9] and superconductors. [10,11] Currently, much attention is paid to strongly correlated electronic systems, for example, ferromagnets and superconductors, as they provide a unique tool to manipulate the topology of coexisting vector and scalar fields, associated with geometries of conventional systems.Until recently, in the case of magnetism, the influence of the geometry on the spin vector fields was addressed primarily by the design of the sample boundaries. This approach naturally brings the shape anisotropy to the system and leads to the formation of specific spin textures, for example, magnetic vortices [12] and antivortices [13] as well as provides control over the dynamics of the topologically nontrivial magnetic solitons. [14][15][16][17][18] This discussion also tackles the state of the art in modern experimental antiferromagnetism, where the design of the sample topography and boundaries allows to control the domain wall states. [19][20][21][22] With the development of novel fabrication techniques allowing to realize complex 3D architectures, not only the boundary effects but also the extrinsic geometrical properties (e.g., local curvatures) can be addressed rigorously for the case of ferromagnets [23][24][25][26][27] as well as superconductors. [28][29][30] The explored effects are directly related to the interplay between the Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro-and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-...

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Numerical methods for the stray-field calculation: A comparison of recently developed algorithms

Cited by 67 publications

References 25 publications

Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

High energy product in Battenberg structured magnets

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

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