Premium
Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms
Author(s) -
Mocellin K.,
Fourment L.,
Coupez T.,
Chenot J. L.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.304
Subject(s) - multigrid method , solver , cholesky decomposition , discretization , computational science , computer science , finite element method , computation , polygon mesh , mathematics , preconditioner , conjugate gradient method , algorithm , mathematical optimization , parallel computing , iterative method , partial differential equation , mathematical analysis , eigenvalues and eigenvectors , physics , computer graphics (images) , quantum mechanics , thermodynamics
The industrial simulation code Forge3 ® is devoted to three‐dimensional metal forming applications. This finite 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 finite 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 different 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 different forging cases, the theoretical properties of the multigrid method are numerically verified, optimizations of the solver are presented and finally, the results obtained on several industrial problems are given, showing the efficiency of the new solver that provides speed‐up larger than 5. Copyright © 2001 John Wiley & Sons, Ltd.