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Hybrid parallel multigrid preconditioner based on automatic mesh coarsening for 3D metal forming simulations
Author(s) -
Vi Frederic,
Mocellin Katia,
Digonnet Hugues,
Perchat Etienne,
Fourment Lionel
Publication year - 2018
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.5756
Subject(s) - preconditioner , multigrid method , polygon mesh , computational science , rate of convergence , finite element method , computer science , mathematics , adaptive mesh refinement , linear system , mesh generation , convergence (economics) , conjugate gradient method , parallel computing , algorithm , mathematical optimization , iterative method , partial differential equation , key (lock) , mathematical analysis , physics , thermodynamics , computer graphics (images) , computer security , economics , economic growth
Summary A parallel multigrid (MG) method is developed to reduce the large computational costs involved by the finite element simulation of highly viscous fluid flows, especially those resulting from metal forming applications, which are characterized by using a mixed velocity/pressure implicit formulation, unstructured meshes of tetrahedra, and frequent remeshings. The developed MG method follows a hybrid approach where the different levels of nonnested meshes are geometrically constructed by mesh coarsening, while the linear systems of the intermediate levels result from the Galerkin algebraic approach. A linear O ( N ) convergence rate is expected (with N being the number of unknowns), while keeping software parallel efficiency. These objectives lead to selecting unusual MG smoothers (iterative solvers) for the upper grid levels and to developing parallel mesh coarsening algorithms along with parallel transfer operators between the different levels of partitioned meshes. Within the utilized PETSc library, the developed MG method is employed as a preconditioner for the usual conjugate residual algorithm because of the symmetric undefinite matrix of the system to solve. It shows a convergence rate close to optimal, an excellent parallel efficiency, and the ability to handle the complex forming problems encountered in 3‐dimensional hot forging, which involve large material deformations and frequent remeshings.