Discontinuous Galerkin formulation for eddy-current problems

Purpose - 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.Design methodology approach - 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.Findings - 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.Originality value - The proposed method leads to a potentially fast method for solving eddy-current problems.