A Finite-Element Variable Time-Stepping Algorithm for Solving the Electromagnetic Diffusion Equation

Ovando-Martinez, R. B. B.; Lopez, Mario; Flores, Concepción Hernández

doi:10.1109/tmag.2011.2177448

Cited by 5 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The temperature for all the material components was constantly kept as 293.15 K. The time‐dependent solving started from 0 to 320 days, with the time step of 10 days. Implicit backward differentiation formula (BDF) was used in solving the differential equations of transport in time stepping, for getting stable numerical approximation (Ovando‐Martinez, Arjona Lopez, & Hernandez Flores, 2012). Besides, the damped Newton method was applied to facilitate the convergent solution of the nonlinear problem (Stute, Krupp, & Von Lieres, 2013), which was thought to address the stable calculation issue with varying magnitudes of diffusion coefficients.…”

Section: Model Descriptionmentioning

confidence: 99%

Meso‐scale modeling of chloride diffusivity in mortar subjected to corrosion‐induced cracking

Qiu

2021

Computer aided Civil Eng

View full text Add to dashboard Cite

This paper presents a methodology for numerically simulating the chloride diffusivity in mortar subjected to corrosion‐induced cracking with the aid of X‐ray microcomputed tomography (X‐ray µCT). In the research, the mortar sample with embedded steel rod was subjected to accelerated corrosion and then scanned by X‐ray µCT at consecutive corrosion periods of 0, 1,000, and 2,000 minutes. Upon the scanned CT images, a meso‐scale model consisting of multiple material phases with their intrinsic structures was built up and implemented into a finite element method for diffusion simulation. In the numerical simulation, the effects of multiple phases (void, crack, aggregate, rust, and interfacial transition zone between cement and aggregate) on the chloride diffusion of mortar are studied. Since the X‐ray µCT facilitates accurate local material information in time‐dependent and in situ manner, the diffusivity of mortar under different corrosion time and its spatial distribution characteristics (e.g., at different locations from the mortar surface) can be evaluated.

show abstract

Section: Model Descriptionmentioning

confidence: 99%

Meso‐scale modeling of chloride diffusivity in mortar subjected to corrosion‐induced cracking

Qiu

2021

Computer aided Civil Eng

View full text Add to dashboard Cite

show abstract

“…However, an implicit s-step linear multi-step method involves solving m algebraic equations [21] Backward differentiation formulae (BDF) are another kind of multi-step numerical method for solving stiff systems. They involve variable time-steps, are A-stable, and are thus recommended for solving stiff problems [22], [23]. The BDF methodology has been treated as an implicit Euler technique for solving ODEs [24].…”

Section: Introductionmentioning

confidence: 99%

Optimizing the Coefficients of Numerical Differentiation Formulae Using Neural Networks

et al. 2021

View full text Add to dashboard Cite

The use of a numerical differentiation formula (NDF) is an excellent method for solving stiff ordinary differential equations. However, the NDF method cannot fully adapt to all stiff systems. An optimal general method for optimizing NDF coefficients using a back-propagation neural network is proposed in this work that can be used for different systems of stiff equations. The ranges of stability of the first-to fourthorder coefficients are obtained by analyzing the definition of stability. In order to solve the different stiff systems by changing the NDF coefficients, the relationship between the eigenvalues of the Jacobian matrix and NDF coefficients is analyzed. The back-propagation neural network is used to describe the relationship between them and predict the optimal parameters of different stiff systems. Compared with the NDF coefficients, the absolute and mean square errors of the numerical solutions are smaller. The simulation results show that the numerical solution's accuracy is higher. Because optimizing the NDF coefficients improves the accuracy of the simulation results, the new approach is more suitable for solving stiff ordinary differential equations.INDEX TERMS Numerical differentiation formulae, stiff ordinary differential equations, optimized coefficients, back-propagation neural network, accuracy.

show abstract

“…In this paper, the coupled field-circuit equations form the basis for electromagnetic finite element analysis. A finite-element variable time-stepping algorithm for solving the electromagnetic diffusion equation has been proposed by OvandoMartínez et al [5].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Analysis of a Bridge Configured Winding Cage Induction Machine Using Finite Element Method

Konwar¹,

Kalita²,

Banerjee³

et al. 2013

PIER B

View full text Add to dashboard Cite

Abstract-A 2D finite element electromagnetic model that permits the simulation of a cage induction machine, involving the effects of eddy currents and coupling the field equation with the stator fieldcircuit equation, has been presented in this paper. Transformation matrix has been derived to incorporate specialized stator winding scheme called the bridge configured winding (BCW) in the coupled field circuit equation. The bridge configured winding scheme is capable of producing controllable transverse force by deliberately imparting asymmetric flux distribution in the machine air-gap. Steady state stator currents have been calculated using the time-stepping scheme with the rotor motion at constant speed allowing the FE model to take into account the harmonics due to the eccentricity (static) of the rotor. This work has furnished us with the 2D magnetic flux distribution in the whole finite element domain as well as sets out an electromagnetic model to study the electromechanical interaction between the eccentric rotor motion and the electromagnetic field. The results, in terms of variation of terminal currents (phase and bridge) and unbalanced magnetic pull (UMP) due to rotor eccentricity as well as asymmetric field (deliberately imparted by exciting the bridge), obtained from the simulation have been compared with analytical formulations as well as already published experimental results.

show abstract

A Finite-Element Variable Time-Stepping Algorithm for Solving the Electromagnetic Diffusion Equation

Cited by 5 publications

References 12 publications

Meso‐scale modeling of chloride diffusivity in mortar subjected to corrosion‐induced cracking

Meso‐scale modeling of chloride diffusivity in mortar subjected to corrosion‐induced cracking

Optimizing the Coefficients of Numerical Differentiation Formulae Using Neural Networks

Electromagnetic Analysis of a Bridge Configured Winding Cage Induction Machine Using Finite Element Method

Contact Info

Product

Resources

About