Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms

The industrial simulation code Forge3J is devoted to three-dimensional metal forming applications. This 8nite element software is based on an implicit approach. It is able to carry out the large deformations of viscoplastic incompressible materials with unilateral contact conditions. The 8nite element discretization is based on a stable mixed velocity–pressure formulation and tetrahedral unstructured meshes. Central to the Newton iterations dealing with the non-linearities, a preconditioned conjugate residual method (PCR) is used. The parallel version of the code uses an SPMD programming model and several results on complex applications have been published. In order to reduce the CPU time computation, a new solver has been developed which is based on multigrid theory. A detailed presentation of the di>erent elements of the method is given: the geometrical approach based on embedded meshes, the direct resolution of the velocity–pressure system, the use of PCR method as an original smoother and for solving the coarse problem, the full multigrid method and the required preconditioning by an incomplete Cholesky factorization for problems with complex contact conditions. By considering di>erent forging cases, the theoretical properties of the multigrid method are numerically veri8ed, optimizations of the solver are presented and 8nally, the results obtained on several industrial problems are given, showing the eBciency of the new solver that provides speed-up larger than 5