A DOFs condensation based algorithm for solving saddle point systems in 2D contact computation

Abstract

In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. The mortar finite element method is usually employed to discretize the variational form on the meshed contact surfaces, yielding a large-scale discretized saddle point system. Due to the indefiniteness of the discretized system, it is a challenge to solve the saddle point algebraic system. For two-dimensional tied contact problem, we develop an efficient algorithm based on degree-of-freedom (DOF) condensation. In this approach, a DOFs elimination process is first performed by exploiting the tridiagonal structure of the mortar matrix. The reduced linear system, now smaller in scale and symmetric positive definite (SPD), is then solved using the preconditioned conjugate gradient (PCG) method. Numerical results demonstrate the effectiveness of the algorithm.