Adaptive time integration for electromagnetic models with sinusoidal excitation

Abstract

Purpose

To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.

Design/methodology/approach

The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge‐Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.

Findings

Standard error‐controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.

Originality/value

Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.

Citation

Benderskaya, G., De Gersem, H., Ackermann, W. and Weiland, T. (2008), "Adaptive time integration for electromagnetic models with sinusoidal excitation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 1, pp. 122-132. https://doi.org/10.1108/03321640810836690