Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

Exl, Lukas; Fischbacher, Johann; Kovacs, Alexander; Oezelt, Harald; Gusenbauer, Markus; Schrefl, T.

doi:10.1016/j.cpc.2018.09.004

Cited by 35 publications

(19 citation statements)

References 44 publications

(75 reference statements)

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“…However, if the function to be minimized, F(x), is not quadratic, the nonlinear conjugate gradient method is applied to update iteratively the solution vector x, until the convergence is reached as shown in Algorithm 2. [7] Algorithm 2: Nonlinear conjugate gradient method Task: Minimize F(x). Initialize:…”

Section: Conjugate Gradient Methodsmentioning

confidence: 99%

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A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

Dalla¹,

Silva²,

Dutra³

et al. 2021

Blucher Physics Proceedings

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Optimization methods are frequently applied to solve real-world problems such, engineering design, computer science, and computational chemistry. This paper aims to compare gradient-based algorithms and the meta-heuristic particle swarm optimization to minimize the multidimensional benchmark Griewank function, a multimodal function with widespread local minima. Several approaches of gradient-based methods such as steepest descent, conjugate gradient with Fletcher-Reeves and Polak-Ribiere formulations, and quasi-Newton Davidon-Fletcher-Powell approach were compared. The results presented showed that the meta-heuristic method is recommended for function with this behavior because is no needed prior information of the search space. The performance comparison includes computation time and convergence of global and local optimum.

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Section: Conjugate Gradient Methodsmentioning

confidence: 99%

“…According to Exl et al [7] the nonlinear conjugate gradient method that use (3) instead of ( 2) are believed to have more efficient convergence characteristics due the self-correcting behavior of term (g j+1 − g j ).…”

Section: Set the Initial Search Directionmentioning

confidence: 99%

A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

Dalla¹,

Silva²,

Dutra³

et al. 2021

Blucher Physics Proceedings

View full text Add to dashboard Cite

show abstract

“…A Python script controlling the open-source CAD software Salome [12] introduces the grain boundary phase with a specific thickness and produces the finite element mesh. For these synthetic microstructures the demagnetization curve is computed through minimization of the micromagnetic energy with a preconditioned nonlinear conjugate gradient method [13]. The search for higher coercive fields, µ0Hc, and energy density products, (BH)max, is managed via the open-source optimization framework Dakota [14].…”

Section: Methodsmentioning

confidence: 99%

Computational Design of Rare-Earth Reduced Permanent Magnets

et al. 2020

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Multiscale simulation is a key research tool for the quest for new permanent magnets. Starting with first principles methods, a sequence of simulation methods can be applied to calculate the maximum possible coercive field and expected energy density product of a magnet made from a novel magnetic material composition. Fe-rich magnetic phases suitable for permanent magnets can be found by adaptive genetic algorithms. The intrinsic properties computed by ab initio simulations are used as input for micromagnetic simulations of the hysteresis properties of permanent magnets with realistic structure. Using machine learning techniques, the magnet's structure can be optimized so that the upper limits for coercivity and energy density product for a given phase can be estimated. Structure property relations of synthetic permanent magnets were computed for several candidate hard magnetic phases. The following pairs (coercive field (T), energy density product (kJ/m³)) were obtained for Fe3Sn0.75Sb0.25: (0.49, 290), L10 FeNi: (1, 400), CoFe6Ta: (0.87, 425), and MnAl: (0.53, 80).

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“…(1) With state-of-the-art micromagnetic energy minimization codes it is possible to calculate the demagnetization curve of a permanent magnet with a size of 250 × 250 × 250 nm 3 within 1-2 days 15 . Using a finite differences code, optimized for massively parallel computing on a supercomputer, a cube with the size of about 1 × 1 × 1 μm can be solved within a reasonable time.…”

Section: Introductionmentioning

confidence: 99%

Extracting local nucleation fields in permanent magnets using machine learning

et al. 2020

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Microstructural features play an important role in the quality of permanent magnets. The coercivity is greatly influenced by crystallographic defects, like twin boundaries, as is well known for MnAl-C. It would be very useful to be able to predict the macroscopic coercivity from microstructure imaging. Although this is not possible now, in the present work we examine a related question, namely the prediction of simulated nucleation fields of a quasi-three-dimensional (rescaled and extruded) system constructed from a two-dimensional image. We extract features of the image and analyze them via machine learning. A large number of extruded systems are constructed from 10 × 10 pixel sub-images of an Electron Backscatter Diffraction (EBSD) image using an automated meshing procedure. A local nucleation field is calculated by micromagnetic simulation of each quasi-three-dimensional system. Decision trees, trained with the simulation results, can predict nucleation fields of these quasi-three-dimensional systems from new images within seconds. As for now we cannot quantitatively predict the macroscopic coercivity, nevertheless we can identify weak spots in the magnet and see trends in the nucleation field distribution.

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Preconditioned nonlinear conjugate gradient method for micromagnetic energy minimization

Cited by 35 publications

References 44 publications

A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function

Computational Design of Rare-Earth Reduced Permanent Magnets

Extracting local nucleation fields in permanent magnets using machine learning

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