Discontinuous Galerkin formulation for eddy‐current problems

The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy‐current problems. This results in a block‐diagonal mass matrix allowing explicit time stepping without having to solve large algebraic systems.

The effect of the basis functions in the conducting region is limited to the respective finite element. This yields to a block‐diagonal mass matrix, whereas each block in this matrix belongs to one finite element. In the nonconducting region, traditional finite elements are used which leads to well‐conditioned system matrices. For the two regions, different time steps are used.

To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. A value for weighting this term is suggested and tested on a simple two dimensional example.

The proposed method leads to a potentially fast method for solving eddy‐current problems.