Convergence properties of the Newton-Raphson method for nonlinear problems

Jänicke, L.; Kost, A.

doi:10.1109/20.717577

Cited by 26 publications

(18 citation statements)

References 7 publications

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“…Next to the numerical method itself, there are however several user-dependent factors influencing the convergence of the Newton-Raphson method, like the geometric description of the model and the mathematical representation of the data [7].…”

Section: Practical Newton Line Search Methodsmentioning

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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Section: Practical Newton Line Search Methodsmentioning

confidence: 99%

Solving nonlinear magnetic problems using newton trust region methods

et al. 2003

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“…Several techniques for convergence improvement have been proposed. It is a common practice to use a single scalar relaxation factor because of its computational advantage [6][7][8]. This kind of scalar relaxation factor can be calculated as the optimum, or it can be computed based on the L 2 residual or functional minimization norms.…”

Section: Determination Of Relaxation Factormentioning

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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“…When the scalar potential is used, it might lead to a very unstable iteration process [1]. In order to ensure the convergence, a damped iterative algorithm with a proper relaxation factor has to be used [2]- [4]. At each iterative step of the N-R method, a set of linear algebraic equations is required to be solved.…”

Section: Introductionmentioning

confidence: 99%

An effective method to reduce the computing time of nonlinear time-stepping finite-element magnetic field computation

et al. 2002

IEEE Trans. Magn.

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Abstract-Time-stepping finite-element methods have been widely used to compute the magnetic field of electrical machines. Because the reluctivities of magnetic materials are nonlinear, the finite-element equations have to be solved iteratively. In this paper, an effective method for reducing the computing time of the Newton-Raphson method coupled with the incomplete Cholesky-conjugate gradient algorithm for solving time-stepping finite-element problems is presented. The proposed method is based on a proper prediction of some predefined error tolerances in the iteration processes at each time-stepping finite-element computation. The computational analysis on an induction motor shows that the proposed strategy can reduce the nominal computing time by as much as 50%.

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Convergence properties of the Newton-Raphson method for nonlinear problems

Cited by 26 publications

References 7 publications

Solving nonlinear magnetic problems using newton trust region methods

Solving nonlinear magnetic problems using newton trust region methods

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

An effective method to reduce the computing time of nonlinear time-stepping finite-element magnetic field computation

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