Improvements of convergence characteristics of Newton-Raphson method for nonlinear magnetic field analysis

Nakata, T.; Takahashi, Norio; Fujiwara, Koji; Okamoto, Naohisa; Muramatsu, Kazuhiro

doi:10.1109/20.123861

Cited by 57 publications

(30 citation statements)

References 4 publications

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“…Nakata et al [5] studied the divergence of the Newton-Raphson method in magnetic field analysis. They developed a method that determines the optimum relaxation factor, which uses the residual of Galerkin method.…”

Section: Methods 1: Optimum Relaxation Factormentioning

confidence: 99%

“…Bastos et al [10] proposed a local relaxation factor which was applied to individual nodes, however the high computation time is the main disadvantage of this method. Nakata et al [5] developed a method that finds an optimum relaxation factor by using interpolation functions. Functional and L 2 norms are also alternative techniques that have been used in developing relaxation factors, where good results were reported by Fujiwara et al [9].…”

Section: Introductionmentioning

confidence: 99%

“…The Newton-Raphson method, which is sometimes unstable, is generally applied to this kind of numerical problems due to its fast convergence characteristics. In order to improve the convergence of the Newton-Raphson method or achieve a solution in some problems, a modification to the method is commonly required through a relaxation factor, which is applied during the iterative process [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Convergence improvement in two-dimensional finite element nonlinear magnetic problems—a fuzzy logic approach

Arjona

Escarela‐Perez

Melgoza-Vázquez

et al. 2005

Finite Elements in Analysis and Design

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Section: Methods 1: Optimum Relaxation Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence improvement in two-dimensional finite element nonlinear magnetic problems—a fuzzy logic approach

Arjona

Escarela‐Perez

Melgoza-Vázquez

et al. 2005

Finite Elements in Analysis and Design

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“…The second term represents the work done by the exciting currents imposed to the system. By Manuscript discretizing the problem and interpolating the solution over all elements, (3) transforms into (4) with being the vector of unknown nodal or edge values of the vector potential, is the magnetic energy density J/m , and is the source vector (A) [1]. For magnetic systems with nonhysteretic ferromagnetic materials, is a nonlinear function of .…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear magnetic problems using newton trust region methods

et al. 2003

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In this paper, a Newton trust region method is presented as an alternative to the Newton-Raphson method for solving nonlinear magnetic problems. Instead of underrelaxing the Newton step in a line search algorithm, the step is determined by minimizing a local quadratic model of the functional within a trust region. If the Newton step lies outside the trust region, a step with a smaller norm and different direction is computed. The size of the trust region plays a similar role as the relaxation factor in the line search approach. To ensure that the method converges, the trust region size is automatically adjusted from one iteration to the next one, depending on the local accuracy of the quadratic model. The trust region approach is applied for the simulation of an 8/6 switched reluctance motor.

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“…Therefore, 2-D calculations may be applied [3] to these heads. We have examined the field distribution of these heads using 2-D and 3-D [4] calculations. Taking advantage of their symmetrical structures, the problems were halved and then divided into 3-D meshes by an automatic mesh-generating pre-processor [5]: for the MIG head, 335,566 tetrahedra and 57,523 nodes; for the thin-film head, 241,603 tetrahedra and 42,303 nodes.…”

Section: Iintroduc~onmentioning

confidence: 99%

Modeling of magnetic recording heads for 2-D and 3-D finite element analysis

Kanai

Ogawa

1994

IEEE Trans. Magn.

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Modeling of magnetic recording heads using 2-D and 3-D finite element analysis was investigated for Metal-In-Gap and thin-film heads. It is confirmed that flux concentration as well as core thickness has to be carefully modeled when trying to solve in two dimensions. It is noted that nonlinear 2-D calculations of Metal-In-Gap heads are acceptable, however, 3-D analysis is strongly recommended for thin-film heads. I.INTRODUC~ONIn designing magnetic recording heads, finite-element magnetic field analysis is one of the best tools for a better understanding of the various phenomena [l]. However, because of their complex structures and the presence of a gap, meshing is quite difficult and the number of elements becomes huge when trying to solve in three dimensions. Therefore, a 2-D calculation is often used, especially for ferrite Metal-In-Gap (MIG) heads. Instead of the finite element method, integral methods are sometimes used [2] since their meshings are considerably easier. However, the limitation or possibility of 2-D calculations and the necessity of 3-D calculation have only been examined analytically using very simplified structures [3].This paper describes the modeling of magnetic recording heads using 2-D and 3-D finite element method for various heads. Linear and nonlinear calculations of Metal-In-Gap and thin-film heads were carried out using 3-D T -0 141 and 2-D A-$ magnetostatic solvers. For 3-D meshing, an automatic mesh-generating pre-processor [5] was used. It was found that flux concentration as well as core thickness have to be carefully considered when trying to solve in two dimensions. It is confirmed that nonlinear 2-D calculations of MIG heads are acceptable. On the other hand, three-dimensional analysis is strongly recommended for thin-film heads. 11. ANALYSIS of MIG and THIN-FILM HEADS Figs. 1 (a) and (b) show the gap regions of a single-sided MIG, which has a metal film only on the trailing side, and a thin-film head, respectively. For the MIG head: gap length G,=0.5, throat height Gd=5 and half of the track width T,,/2=7.5 p. For the thin-film h a & G$.3, Gd=l.O and T,,/2=3.25pm.Note here that their track width is more than twenty times Manuscript received November 1. 1993. their gap length. Therefore, 2-D calculations may be applied [3] to these heads. We have examined the field distribution of these heads using 2-D and 3-D [4] calculations. Taking advantage of their symmetrical structures, the problems were halved and then divided into 3-D meshes by an automatic mesh-generating pre-processor [5]: for the MIG head, 335,566 tetrahedra and 57,523 nodes; for the thin-film head, 241,603 tetrahedra and 42,303 nodes. Figs. 2(a) and (b), respectively, show the gap region of the finite-element meshes of MIG and thin-film heads used for the calculations. For accuracy, several 3-D meshes were used for each model and no major differences were found. A. Linear CalculationsFor simplicity, linear calculations are sometimes used, especially for read-back processes. Fig.3 shows the calculated maximum recor...

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Improvements of convergence characteristics of Newton-Raphson method for nonlinear magnetic field analysis

Cited by 57 publications

References 4 publications

Convergence improvement in two-dimensional finite element nonlinear magnetic problems—a fuzzy logic approach

Convergence improvement in two-dimensional finite element nonlinear magnetic problems—a fuzzy logic approach

Solving nonlinear magnetic problems using newton trust region methods

Modeling of magnetic recording heads for 2-D and 3-D finite element analysis

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