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Article
Publication date: 1 June 2001

Irina Munteanu, Silvia Drobny, Thomas Weiland and Daniel Ioan

This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in…

Abstract

This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in nonlinear media. The hybrid technique is based on new theoretical results regarding the similarities between the Picard‐Banach fixed‐point (polarization) method and the Newton method. At each iteration, the solution is obtained as a linear combination of the old solution, and the new Picard‐Banach and Newton solutions. The numerical solutions are calculated through a “triangle” (bidimensional) minimization of the residual or of the energy functional. The goal of this combination is to increase the robustness of the iterative method, without losing the quadratic speed of convergence in the vicinity of the solution. The proposed method generalizes and unifies in a single algorithm the overrelaxed Picard‐Banach and the underrelaxed Newton methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 11 May 2010

Xi Chen, Zhengwei Du and Ke Gong

The purpose of this paper is to study the impact of high‐power microwave interferences on electronic devices needs the simulation of semiconductor components. Although the…

Abstract

Purpose

The purpose of this paper is to study the impact of high‐power microwave interferences on electronic devices needs the simulation of semiconductor components. Although the semiconductor equations can be solved numerically by Newton method, the conventional Newton method exhibits significant speed degradation when the power of interference is high enough to cause device burnout. Therefore, this paper aims at speeding up the simulation of the semiconductor components under high‐power microwave interferences.

Design/methodology/approach

Some approximations in conventional Newton method works efficiently only when the electric field in the simulated semiconductor is relatively low. This is the reason of the formerly mentioned speed degradation problem. The proposed method speeds up the simulation by modifying these approximations to acquire enough precision in these high‐power situations.

Findings

The modified Newton method proposed in this paper shows an acceleration of 100‐150 percent compared to conventional method for typical applications. Moreover, the simulation speed becomes nearly independent of the power of the microwave interferences, which means the speed degradation phenomenon of the conventional method has almost been eliminated.

Originality/value

This paper proposes a modified Newton method to speed up the simulation of the semiconductor components under high‐power microwave interferences.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 27 March 2023

Xiao Xiao, Fabian Müller, Martin Marco Nell and Kay Hameyer

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects…

Abstract

Purpose

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.

Design/methodology/approach

To stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.

Findings

In this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.

Originality/value

In this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 2 May 2017

Bogdan Fabianski and Krzysztof Zawirski

The paper is concerned about parameter adaptation of a novel, simplified and nonlinear switched reluctance motor (SRM) model. The purpose of the presented on-line procedure is to…

Abstract

Purpose

The paper is concerned about parameter adaptation of a novel, simplified and nonlinear switched reluctance motor (SRM) model. The purpose of the presented on-line procedure is to give an opportunity to set the model parameters’ values to obtain a relatively good convergence with the real control object. This is important when a reference model is used for control (e.g. optimal) or object state classification (e.g. fault detection) purposes. The more convergent the real object model is, the better operation quality may be expected.

Design/methodology/approach

In the paper, a 12/8 pole’s SRM as a control object is analyzed. The model equations were verified experimentally by comparing phase current model estimations with reference (measured) ones at different operational points. Differential equations of motor winding currents were chosen as an approximation function in the fitting (parameter adaptation) process using the Newton and Gauss–Newton methods. The structure of the adaptation system is presented along with the implementation in simulation environment.

Findings

It was confirmed in the simulation tests that Newton and Gauss–Newton methods of nonlinear model parameters’ adaptation may be used for the SRM. The introduced fitting structure is well suited for implementation in real-time, embedded systems. The proposed approximation function could be used in process as an expansion to Jacobian and Hessian matrices. The χ2 (chi2) coefficient (commonly used to measure the quality of the signal fitting) reduced to a low value during the adaptation process. Another introduced quality coefficient shows that the Newton method is slightly better in scope of the entire adaptation process time; however, it needs more computational power.

Research limitations/implications

The proposed structure and approximation function formula in the parameters’ adaptation system is appropriate for sinusoidal distribution of the motor phase inductance value along the rotor angle position. The inductance angular shape is an implication of the mechanical construction – with appropriate dimensions and materials used. In the presented case, the referenced model is a three-phase SRM in 12/8 poles configuration used as a main drive part of Maytag Neptune washing machine produced by Emerson Motors.

Practical implications

The presented method of parameter adaptation for novel, simplified and nonlinear SRM model provides an opportunity for its use in embedded, real-time control systems. The convergent motor model, after the fitting procedure (when the estimations are close to the measurements from real object), may be used for solving many well-known control challenges such as detection of initial rotor position, sensorless control, optimal control, fault-tolerant control end in fault detection (FD) systems. The reference model may be used in FD in the way of deducing signals from the difference between the estimated and measured ones.

Originality/value

The paper proposed a new system of parameter adaptation for the evaluated nonlinear, simplified 12/8 poles SRM model. The relative simplicity of the proposed model equations provides the possibility of implementing an adaptation system in an embedded system that works in a real-time regime. A Two adaptation methodsNewton and Gauss–Newton – have been compared. The obtained results shown that the Newton fitting method is better in the way of the used quality indicator, but it consumes more computational power.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Open Access
Article
Publication date: 1 March 2022

Jaehyuk Choi and Rong Chen

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to…

1535

Abstract

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. The authors enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. The authors also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

Details

Journal of Derivatives and Quantitative Studies: 선물연구, vol. 30 no. 2
Type: Research Article
ISSN: 1229-988X

Keywords

Article
Publication date: 1 April 1987

CONOR J. FITZSIMONS

This paper examines several modifications to Newton's method for the numerical solution of the nonlinear Poisson equation which describes the electrostatic potential distribution…

Abstract

This paper examines several modifications to Newton's method for the numerical solution of the nonlinear Poisson equation which describes the electrostatic potential distribution in a semiconductor device. Two methods for a more efficient solution of the equation when the device is a Metal‐Oxide‐Semiconductor Field Effect Transistor are proposed. Their extension to the solution of the fully coupled system of equations is also discussed. The modifications to Newton's method are also compared numerically.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 6 no. 4
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 25 May 2012

Mehdi Dehghan and Masoud Hajarian

Solving the non‐linear equation f(x)=0 has nice applications in various branches of physics and engineering. Sometimes the applications of the numerical methods to solve…

275

Abstract

Purpose

Solving the non‐linear equation f(x)=0 has nice applications in various branches of physics and engineering. Sometimes the applications of the numerical methods to solve non‐linear equations depending on the second derivatives are restricted in physics and engineering. The purpose of this paper is to propose two new modified Newton's method for solving non‐linear equations. Convergence results show that the order of convergence of the proposed iterative methods for a simple root is four. The iterative methods are free from second derivative and can be used for solving non‐linear equations without computing the second derivative. Finally, several numerical examples are given to illustrate that proposed iterative algorithms are effective.

Design/methodology/approach

In this paper, first the authors introduce two new approximations for the definite integral arising from Newton's theorem. Then by considering these approximations, two new iterative methods are provided with fourth‐order convergence which can be used for solving non‐linear equations without computing second derivatives.

Findings

In this paper, the authors propose two new iterative methods without second derivatives for solving the non‐linear equation f(x)=0. From numerical results, it is observed that the new methods are comparable with various iterative methods. Also numerical results corroborate the theoretical analysis.

Originality/value

The best property of these schemes is that they are second derivative free. Also from numerical results, it is observed that the new methods are comparable with various iterative methods. The numerical results corroborate the theoretical analysis.

Details

Engineering Computations, vol. 29 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 15 November 2011

Xi Chen and Yong‐Gang Cheng

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is…

Abstract

Purpose

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is its slow convergence, even when it is used in conjunction with acceleration techniques. The Newton‐Raphson method has a rapid convergence rate, but its implementation resorts to non‐symmetric linear solvers, and hence the memory requirement may be high. The purpose of this paper is to develop more advanced solution techniques which may overcome the above problems associated with the initial stiffness method and the Newton‐Raphson method.

Design/methodology/approach

In this work, the accelerated symmetric stiffness matrix methods, which cover the accelerated initial stiffness methods as special cases, are proposed for non‐associated plasticity. Within the computational framework for the accelerated symmetric stiffness matrix techniques, some symmetric stiffness matrix candidates are investigated and evaluated.

Findings

Numerical results indicate that for the accelerated symmetric stiffness methods, the elasto‐plastic constitutive matrix, which is constructed by mapping the yield surface of the equivalent material to the plastic potential surface, appears to be appealing. Even when combined with the Krylov iterative solver using a loose convergence criterion, they may still provide good nonlinear convergence rates.

Originality/value

Compared to the work by Sloan et al., the novelty of this study is that a symmetric stiffness matrix is proposed to be used in conjunction with acceleration schemes and it is shown to be more appealing; it is assembled from the elasto‐plastic constitutive matrix by mapping the yield surface of the equivalent material to the plastic potential surface. The advantage of combining the proposed accelerated symmetric stiffness techniques with the Krylov subspace iterative methods for large‐scale applications is also emphasized.

Article
Publication date: 1 April 1988

E. Ramm and A. Matzenmiller

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the…

Abstract

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the derivation of an efficient computational strategy placing emphasis on consistent elasto‐plastic tangent moduli and stress integration with the radial return method under the restriction of ‘zero normal stress condition’ in thickness direction. The advantageous performance of the standard Newton iteration using a consistent tangent stiffness matrix is compared to the classical scheme with an iteration matrix based on the infinitesimal elasto‐plastic constitutive tensor. Several numerical examples also demonstrate the effectiveness of the standard Newton iteration with respect to modified and quasi‐Newton methods like BFGS and others.

Details

Engineering Computations, vol. 5 no. 4
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 31 July 2020

Jingyu Pei, Xiaoping Wang, Leen Zhang, Yu Zhou and Jinyuan Qian

This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into…

Abstract

Purpose

This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.

Design/methodology/approach

For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.

Findings

The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.

Originality/value

The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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