Interior Penalty Galerkin Methods for Time Domain Eddy Current Problems

This paper proposes the family of interior penalty methods to solve an eddy current problem in the time domain. These methods use discontinuous basis functions to approximate the solution and penalize the jump of the solution by introducing an additional term. Using discontinuous basis functions and applying Galerkin's method leads to a block-diagonal mass matrix in conducting regions, which can be inverted easily. Therefore, an explicit time-stepping scheme can be used. Depending on the considered problem, the numerical scheme in the conducting region can be coupled with classical finite elements in the nonconducting region or described by an interior penalty method as well. The theory of the methods is illustrated by assuming the A-A formulation for a two-dimensional problem.