Numerical
solution of a transient eddy current problem with current intensities as boundary data
The objective of this work is to analyze a
time-dependent eddy current problem defined in a 3D bounded domain including
conducting and dielectric materials and giving the current source in terms of
current intensities. The input current intensities will be introduced in the
model as non-local boundary conditions (see, for instance, [1]). Thus, by
following [2], we will analyze a formulation based on the magnetic field in the
conductor regions and a multivalued scalar magnetic potential in the dielectric
part.
From a mathematical point of view, we will obtain a
parabolic problem and prove its well posedness as well as some regularity
results. We will propose a finite element combined with an implicit Euler time
discretization to numerically solve the problem. Concerning the space
discretization, the magnetic field is approximated by the lowest N´ed´elec edge
finite elements and the magnetic potential by standard piecewise linear
continuous elements. The current intensities are imposed as jumps of the
multivalued magnetic potential on some prescribed cut surfaces. We will obtain
convergence results for the main physical quantities, namely, the magnetic
field and the current density. Finally, we will present some numerical results
corresponding to the simulation of an application of electromagnetic forming.
This is a joint work with A. Bermúdez, B. López-Rodríguez, R. Rodríguez, P. Salgado.
References
[1] A. Bossavit, Most general non-local boundary
conditions for the Maxwell equation in a bounded region, COMPEL (2000), 19, pp. 239–245.
[2] A. Berm´udez, R. Rodr´ıguez and P. Salgado,
Numerical solution of eddy current problems in bounded domains using realistic boundary conditions, Comput.
Methods Appl. Mech. Engrg.
