Solution of 3-dimensional eddy current problems: The T-Ω method

Three Dimensional Finite Element Modeling

“…To overcome the first problem, the use of two scalar potentials was suggested [3] while the second can only be treated by a vector potential. The natural outcome of this was the use of a vector potential in current regions and a scalar potential in the rest of the solution region [5]. This approach seems to be optimal but the interface between vector regions and scalar regions has not yet been solved satisfactorily.…”

“…This approach seems to be optimal but the interface between vector regions and scalar regions has not yet been solved satisfactorily. Among the many methods suggested are the coupling of the magnetic vector potential with the magnetic scalar-potential [7] and the electric vector potential and the magnetic scalar potential [5] to mention but two. Another method is to solve directly for H or B [6].…”

“…The formulation of Maxwell's equations is in itself more complex and the type of formulation has important implications. Formulations rang ing from single and double scalar potentials [3] through magnetic vector potentials [4] to combinations of scalar and vector potentials [5] abound. Far more significant than the choice available is the fact that these formulations are not necessarily equivalent and their applicability is not universal.…”

Field synthesis for the optimal treatment planning in Magnetic Fluid Hyperthermia

“…In order to compute the temperature as a function of time and space in the treated region, a thermal transient problem coupled with a time-harmonics magnetic problem is solved. In the magnetic problem Maxwell equations are solved subject to appropriate boundary conditions [16], whereas in the thermal problem the Fourier equation [17], taking into account the blood perfusion [18], is solved.…”

The Second Order Finite Element Analysis of Eddy Currents Based on the T-Ω Method

“…Based on the finite element method, the T-Ω method is one of the most effective methods for the numerical analysis of eddy currents [2]. In this method, the magnetic field intensity is expressed as the sum of two parts: the gradient of a magnetic scalar potential Ω and electric vector potential T. In order to maintain tangential continuity, the electric vector potential can be interpolated by Whitney edge elements [3].…”