Optimal Convergence of the Fixed-Point Method for Nonlinear Eddy Current Problems

Koczka, Gergely; Bíró, Oszkár; Preis, Kurt

doi:10.1109/tmag.2009.2012477

Cited by 30 publications

(31 citation statements)

References 5 publications

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“…Convergence is guaranteed by choosing the fixed-point reluctivity as described in Koczka et al 15 The B − H curve can be given as a piecewise linear monotonous function.…”

Section: Figure 1 Fixed-point Iteration Sequencementioning

confidence: 99%

Comparison of 2 methods for the finite element steady‐state analysis of nonlinear 3D periodic eddy‐current problems using the A,V− formulation

Plasser

Takahashi

Koczka

et al. 2017

Int J Numerical Modelling

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Two different techniques for the analysis of nonlinear, periodic eddy-current problems are compared using a three-dimensional benchmark problem. The methods are the parallel time periodic finite element method and the time periodic fixed-point technique. KEYWORDS computational electromagnetics, eddy currents, finite element analysis, nonlinear magnetics Int J Numer Model. 2018;31:e2279.wileyonlinelibrary.com/journal/jnm

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“…Convergence is guaranteed by choosing the fixed-point reluctivity as described in Koczka et al 15 The B − H curve can be given as a piecewise linear monotonous function.…”

Section: Figure 1 Fixed-point Iteration Sequencementioning

confidence: 99%

Comparison of 2 methods for the finite element steady‐state analysis of nonlinear 3D periodic eddy‐current problems using the A,V− formulation

Plasser

Takahashi

Koczka

et al. 2017

Int J Numerical Modelling

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“…end for 15: end for 16: return y s,0 − y s,N 17: end function 18: function SNMVP(z s,0 ) MVP used with GMRES 19: return z s,0 − z s,N 30: end function…”

Section: B Shooting-newtonmentioning

confidence: 99%

Steady-State Algorithms for Nonlinear Time-Periodic Magnetic Diffusion Problems Using Diagonally Implicit Runge–Kutta Methods

Pries

Hofmann

2015

IEEE Trans. Magn.

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A general framework is presented for the formulation of steady-state simulation algorithms for magnetically nonlinear eddy-current problems using implicit Runge-Kutta (RK) methods. A close analogy is drawn between equations discretized using the backwardEuler method and fully implicit RK methods. Detailed formulations of the time-periodic finite-element method (TPFEM) and the shooting-Newton method (SNM) are derived using the popular family of diagonally implicit RK (DIRK) methods. Both algorithms employ the generalized minimum residual method to solve the linear equations arising at each Newton iteration. The benefits of higher-order DIRK methods are demonstrated by simulating a surface mount permanent magnet synchronous machine. The effects of using a solid versus a laminated rotor back iron on the simulation time are examined. Simulation results indicate that the performance of TPFEM and SNM is quite similar and much faster than transient analysis.Index Terms-Diagonally implicit Runge-Kutta (DIRK) methods, eddy currents, generalized minimum residual (GMRES) method, nonlinear equations, rotating machinery, shooting-Newton method (SNM), steady-state analysis, time-periodic finite-element method (TPFEM).

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“…When electromagnetic devices are excited by voltage, the electromagnetic coupling should be taken into account in computation [13], (9) where is the harmonic voltage in the k-th winding and is the corresponding impedance matrix.…”

Section: Globally Convergent Fixed-point Technique In Harmonic-bamentioning

confidence: 99%

Fixed-Point Harmonic-Balanced Method for DC-Biasing Hysteresis Analysis Using the Neural Network and Consuming Function

Zhao

et al. 2012

IEEE Trans. Magn.

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The magnetic flux includes dc component and ac component in the square laminated core (SLC) under dc-biased magnetization. Hysteresis loops are distorted by dc component of magnetic field intensity in ferromagnetic core and exhibit asymmetrical and special nonlinearities. A neural network (NN) is trained on the basis of the experimental data to model hysteresis effects in the limb-yoke of the SLC. Hysteresis effects in the mitered-joint region are modeled by the consuming function combined with the dc-biasing magnetization curve. The global fixed-point magnetic reluctivity is properly determined in harmonic-balanced finite-element method (HBFEM) to ensure globally convergent computation. The magnetic field in the SLC under dc-biased magnetization is computed by the proposed method taking account of the dc-biasing hysteresis effects.Index Terms-Consuming function, dc-biasing hysteresis loops, fixed-point magnetic reluctivity, neural network.

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Optimal Convergence of the Fixed-Point Method for Nonlinear Eddy Current Problems

Cited by 30 publications

References 5 publications

Comparison of 2 methods for the finite element steady‐state analysis of nonlinear 3D periodic eddy‐current problems using the A,V− formulation

Comparison of 2 methods for the finite element steady‐state analysis of nonlinear 3D periodic eddy‐current problems using the A,V− formulation

Steady-State Algorithms for Nonlinear Time-Periodic Magnetic Diffusion Problems Using Diagonally Implicit Runge–Kutta Methods

Fixed-Point Harmonic-Balanced Method for DC-Biasing Hysteresis Analysis Using the Neural Network and Consuming Function

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