Alternating direction method of multiplier for a unilateral contact problem in electro-elastostatics

We study an alternating direction method of multiplier (ADMM) applied to a unilateral frictional contact problem between an electro-elastic material and an electrically non conductive foundation. The frictional contact is modeled by the Tresca friction law. The resulting coupled problem is non symmetric and non coercive. By eliminating the electric potential, we obtain a symmetric and coercive problem which can be reformulated as a convex minimization problem. We then apply an alternating direction method of multiplier for the numerical approximation. To avoid explicit matrices inverse (due to the elimination of the electric potential) we use a preconditioned conjugate gradient algorithm as an inner solver. Numerical experiments are proposed to illustrate the efficiency of the proposed approach.