From a direct solver to a parallel iterative solver in 3-D forming simulation

The industrial simulation code FORGES, devoted to three dimensional forming applications, has been equipped with a robust iterative solver. Using an implicit approach, this code carries out the large deformations of viscoplastic incompressible materials with unilateral contact conditions. It is based on a mixed-velocity/pressure finite element method using tetrahedral unstructured meshes. Central to the Newton iterations dealing with the nonlinearities, a conjugate residual method with a diagonal or block diagonal preconditioning has been implemented. The convergence rate of the iterative solver is given. The advantage and performance of this iterative method are compared to the direct solution. The complete parallel version of the code is performed by using a single-program multiple-data programming model. The scalability of the parallel iterative solver is shown on real complex applications. Several results of parallel computing are given for both a cluster of workstations and for an IBM SP2 up to 34 processors.