抄録
The conjugate projected gradient method is applied for solving large-scale contact problems. The finite element discretization of contact problems results in linear algebraic equations with a set of linear multipoint constraints. When the penalty method is adopted for incorporating the constraints, the linear equations without the constraints are derived. However, they are ill-conditioned and difficult to be solved by using the conjugate gradient method with a simple preconditioner such as the diagonal scaling. In the present study, the constraints due to the contact are formulated by using the Lagrange multiplier method, and the linear equations are solved by the conjugate projected gradient method. The projection matrices for the node-to-node and master-slave contact strategies are derived. The performance study of the algorithm is conducted by solving linear contact problems with 0.2-0.7 million degrees of freedom. The latter problem can be solved within 768 seconds by using one Alpha 21164 (433MHz) processor with 448MB memory.
