Calculs Intensifs en Mise en Forme des Métaux. L. Fourment, H. Digonnet, M. Ramadan CEMEF, Mines ParisTech UMR CNRS n 7635
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1 Calculs Intensifs en Mise en Forme des Métaux L. Fourment, H. Digonnet, M. Ramadan CEMEF, Mines ParisTech UMR CNRS n 7635
2 Calculs Intensifs en Mise en Forme des Métaux Verrous simulations calculs intensifs Micro / macro Optimisation Procédés incrémentaux
3 Micro / macro Loi d évolution micro comportement macro Friction Stir Welding Texture evolution Spécifique non abordé Sensor1 Sensor 5
4 Calculs Intensifs en Mise en Forme des Métaux Verrous simulations calculs intensifs Micro / macro Optimisation Procédés incrémentaux
5 Optimisation Calculs coûteux Calculs parallèles Partitionnement de maillage Solveur itératif, R lage parallèle, Plusieurs heures / jours Optimisation Nombreux calculs 100
6 Optimisation Calculs coûteux Calculs parallèles Partitionnement de maillage Solveur itératif, R lage parallèle, Plusieurs heures Optimisation Nombreux calculs 100 calculs Algorithme évolutionnaire Global Parallélisation: chaque individu est évalué indépendamment Métamodèle N u population P parents (P) offsprings (E) - selection - crossover - mutation evaluation of f(e) improvement meta-model ( ) f ɶ E F.E. calculations ψ max
7 Closed die forging optimization problem Minimize: Weight & Unfilling weighted average function Parameters: height & diameter Workpiece / die distance 2 parameters shape Final shape
8 Closed die forging optimization problem Minimize: Weight & Unfilling weighted average function Parameters: height & diameter 5 parameters Workpiece / die distance 2 parameters shape Final shape 5 parameters shape N par N evatot N eva N Proc CPU TOT It best F best h 24 h kg 5.62 kg 5 %
9 Calculs Intensifs en Mise en Forme des Métaux Verrous simulations calculs intensifs Micro / macro Optimisation Procédés incrémentaux
10 Procédé incrémentaux Déformation locale, progressive nombreux coups >500 ou nombreux tours martelage laminage circulaire
11 Procédé incrémentaux Déformation locale, progressive nombreux coups >500 ou nombreux tours Reduced Contact Area martelage laminage circulaire Temps de calcul: plusieurs jours/semaines sur 9 processeurs Caractère multi-échelles de la déformation
12 Bibliographic overview Adaptive meshing: refinement / derefinement Refinement follows tool movement Derefinement behind A. Hadoush and A.H. van den Boogaard (2008), Time reduction in implicit single point incremental sheet forming simulation by refinement - derefinement, Int. J. Material Forming, vol. suppl. 1, pp Loss of information in the derefined zone
13 Bibliographic overview Adaptive meshing: refinement / derefinement Efficient solver: Multi-grid method Algebraic approach Different meshes 3 levels Computational time Reference mesh Intermediate mesh CPU [S] ICP-GR (reference) Multi-grid Weak speed-up 2 Parallel efficiency? Coarser mesh Nb of nodes
14 Bibliographic overview Adaptive meshing: refinement / derefinement Efficient solver: Multi-grid method Multi-mesh method storage Two meshes: calculation / storage Transfer: calculation storage Storage mesh Calculation mesh Hirt, G., R. Kopp, et al. (2007). "Implementing a high accuracy Multi-Mesh Method for incremental Bulk Metal Forming." CIRP Annals - Manufacturing Technology 56(1): Multi-physics features not taken into account (thermal calculations)
15 Bibliographic overview Adaptive meshing: refinement / derefinement Efficient solver: Multi-grid method Multi-mesh method storage Multi-mesh method coupled One mesh for each physics & coupled resolutions Embedded meshes Di, Y. and X.-P. Wang (2009). "Precursor simulations in spreading using a multi-mesh adaptive finite element method." Journal of Computational Physics 228(5): Complex Weak efficiency Parallelization? Velocity Phase field Couette flow Phase field mesh Velocity mesh
16 Outline Motivations Bibliographic overview Multi-mesh method Application to cogging Conclusion
17 Multi-mesh method Presentation Multi-physics problem Domain Ω Physics 1 Physics 2 Physics 3 incremental coupling for t=t beg, t end for i=1, Nb phys resolution of Pi update M _B
18 Multi-mesh method Presentation Multi-mesh / multi-physics Domain Based mesh M _B Ω Physics 1 Physics 2 Physics 3 Mesh1 M _P1 Mesh2 M _P2 Mesh3 M _P3 incremental coupling for t=t beg, t end For any i, M _Pi is optimal for Pi for i=1, Nb phys resolution of Pi update M _B M _B is the disjunction of all M _Pi or a reference mesh
19 Multi-mesh method Presentation Multi-mesh / multi-physics For any i, M _Pi is optimal for Pi M _B is the disjunction of all M _Pi or a reference mesh Domain Based mesh M _B Ω Physics 1 Physics 2 Physics 3 Mesh1 M _P1 Mesh2 M _P2 Mesh3 M _P3 incremental coupling for t=t beg, t end for i=1, Nb phys resolution of Pi update M _B for t=t beg, t end for i=1, Nb phys projection: M _B M _Pi resolution of Pi onm _Pi interpolation: M _Pi M _B update M _B and then M _Pi, for any i
20 Multi-mesh method Key points For any i, M _Pi is optimal for Pi M _B is the disjunction of all M _Pi or a reference mesh Domain Based mesh M _B Physics 1 Physics 2 Physics 3 Mesh1 M _P1 Mesh2 M _P2 Mesh3 M _P3 Key points Transfer accuracy: : M _B M _Pi ; M _Pi M _B Parallel implementation & efficiency
21 Multi-mesh method Key points Transfer accuracy Embedded meshes: i, k M_Pi, k M_B M _B transfer M _Pi M _B M _Pi exact transfer M _Pi M _B : inverse interpolation M _B is finer & M _Pi is optimal interpolation error < F.E. error Practice: compute M _B thenm _Pi is obtained by derefinement of M _B
22 Multi-mesh method Key point Parallel implementation Construction of M _Pi from M _B Load balancing Resolution on M _Pi Data transfer M M _B _Pi iterative parallel refinement / derefinement transfer
23 Outline Motivations Bibliographic overview Multi-mesh method Application to cogging Conclusion
24 Application to Cogging Two physics: mechanics & thermics / incrementally coupled Only two meshes: M _M & M _T M _B = M _T
25 Application to Cogging Multi-mesh method M_T_ construction of M _ M M _ T from - Deformation Box M_T_ M_M_ Derefinement
26 Application to Cogging Multi-mesh method M _T M _M M _T construction of M_ for t=t beg,t transfer of χ, from M_ T to M resolution of update of end M resolution of R RM ( χm,v,p ) ( ) ( χ,t ) from T - Deformation Box = 0 on transfer of v,p, from M_ M to M_ χ χ T on M T T on M _ T M M M_ update of T, of T and of M M = 0 on M construction of if necessary, re M from _ T M M_ M_ M_ M _ T M _ T
27 Application to Cogging Accuracy of the Multi-mesh method test problem Nb nodes Thermal Mesh Mechanical Mesh Derefinement rate
28 Application to Cogging Accuracy of the Multi-mesh method qualitative results Single mesh Single mesh Equivalent strain rate Multi-mesh Multi-mesh Cumulated strain Single mesh Temperature Multi-mesh
29 Application to Cogging Accuracy of the Multi-mesh method quantitative results Variables Max Error Euclidien Error Finite Element Error X V ε bar
30 Application to Cogging Efficiency of the Multi-mesh method Influence of the number of degrees of freedom Computational time Single mesh Speed-up Multi-mesh Nb of nodes Nb of nodes
31 Application to Cogging Efficiency of the Multi-mesh method Influence of the problem configuration beginning end of cogging Configuration Nb elements Thermal Mesh Nb elements Mechanical Mesh Derefinement rate Speed-up Beginning End
32 Application to Cogging Parallel efficiency of the Multi-mesh method Multi-mesh speed-up for nodes in the parallel context Nb nodes Thermal Mesh Mechanical Mesh M _T 64 processors nodes M _M
33 Application to Cogging Parallel efficiency of the Multi-mesh method Multi-mesh speed-up for nodes in the parallel context Computational time Nb of processors CPU Multi-mesh CPU Single mesh Multi-mesh Single mesh Nb of processors Multi-mesh(4processors) < Single-mesh(64processors)
34 Application to Cogging Parallel efficiency of the Multi-mesh method Multi-mesh speed-up for nodes in the parallel context Computational time Multi-mesh Single mesh Always more efficient Nb of processors Nb of processors Multi-mesh speed-up
35 Application to Cogging Parallel efficiency of the Multi-mesh method Multi-mesh speed-up for nodes in the parallel context Nb of processors Parallel Efficiency - Multi-mesh Parallel Efficiency - Single mesh Thermal Mesh Mechanical Mesh Nb nodes p 4p 8p 16p p p Scalability?
36 Application to Cogging Parallel efficiency of the Multi-mesh method Multi-mesh speed-up for nodes in the parallel context Parallel speed-up Single mesh nodes Multi-mesh nodes & nodes Nb of processors Nb of processors 2p 4p 8p 16p 32p 64p Proper scalability: of the mechanical mesh Parallel Efficiency - Multi-mesh Thermal Mesh Mechanical Mesh Parallel Efficiency - Single mesh Nb nodes
37 Conclusions Méthode multi-maillages Accélérations excellentes de 3 à 20, environ 10 pour les applications industrielles Bonne scalabilité celle de la physique la plus coûteuse à résoudre Toujours plus rapide (quel que soit le nombre de processeurs) permet d utiliser 8 à 16 fois moins de processeurs optimisation Calcul intensif: pas seulement pour les millions de ddl Optimisation cas plus complexe Méthode multi-maillage plus de physique, problèmes multi-échelles Multi-échelles en temps
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