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

Author

Ovando-Martínez, R. B B ; López, M. A Arjona ; Flores, C. Hernández

Author_Institution

Div. de Estudios de Posgrado e Investig., Inst. Tecnol. de La Laguna, Torreón, Mexico

Volume

48

Issue

2

fYear

2012

Firstpage

647

Lastpage

650

Abstract

This paper presents a new methodology for applying the Backward Differentiation Formula (BDF) and the Theta algorithm for the variable time-stepping finite-element discretization. The developed BDF-Theta formulation was implemented for solving the Electromagnetic Diffusion equation. An initial-guess prediction algorithm was adopted for convergence acceleration. An algorithm for the selection of the order and time-step size is also included. A minimum time step criterion is adopted. The proposed methodology was validated against an analytical solution and good results were obtained. The adaptive time-step (BDF) requires less computation time than using the fixed time-step implicit Euler.

Keywords

convergence of numerical methods; differential equations; electromagnetic wave scattering; finite element analysis; Theta algorithm; adaptive time-step; backward differentiation formula; convergence acceleration; electromagnetic diffusion equation; finite-element variable time-stepping algorithm; fixed time-step implicit Euler; initial-guess prediction algorithm; minimum time step criterion; Eddy currents; Finite element methods; Mathematical model; Polynomials; Prediction algorithms; Transient analysis; Backward differentiation formula; finite elements; numerical methods; time-stepping;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2011.2177448

Filename

6136589