1. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 1 A M odular D esign for a P arallel M ultifrontal M esh G enerator J.P. Boufflet, P. Breitkopf, C. Longeau, A. Rassineux, P. Villon Université de Technologie de Compiègne UMR CNRS 6599 HeuDiaSyC (department of computer science) UMR CNRS 6066 Roberval (department of computational mechanics)

2. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 2 Parallel volume mesh generator: parallelize a mesh generation code decompose the data Re-use of an existing sequential volume mesh generator Two strategies are possible:

3. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 3 The sequential volume mesh generator used the initial data: a triangular surface mesh needs a closed envelope generates the internal tetrahedrons less initial data than generated data

4. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 4 Splitting of a closed envelope (1) based on a Moving Least Square technique updating the cutting plane  position and direction by using an attenuation function only the points « close enough » to the current cutting plane  are taken into account balance the number of surface node 

5. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 5 Splitting of a closed envelope (2) We obtain a cutting plane  splitting the initial triangular surface mesh into two parts having roughly the same number of nodes 

6. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 6 geometric decomposition Triangular surface mesh (the domain envelope) Module 1

7. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 7 Interface mesh generation (1) define the interface surface nodes close to  with this boundary area define a border line C project the surface nodes of C to  generate a surface mesh using this geometry with a standard 2D mesh generator fit this new surface mesh to initials coordinates of the interface surface nodes

8. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 8 Interface mesh generation (2) define the interface surface nodes close to  (1) We obtain two open subdomains and a boundary area near the cutting plane    S 1 the triangular finite elements on one side of  S 2 the triangular finite elements on the other side of  S 3 the triangular finite elements near  distance criterion the boundary area

9. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 9 Interface mesh generation (3) define the interface surface nodes close to  (2) We assign the triangular finite elements of the boundary area  “crown”

10. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 10 Interface mesh generation (4) define the interface surface nodes close to  (3) That defines a border line C composed of interface surface nodes splitting the initial triangular surface mesh into two open subdomains C 

11. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 11 Interface mesh generation (4) project the surface nodes of C to  generate a surface mesh using this geometry with a standard 2D mesh generator We obtain a new plane surface mesh

12. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 12 Interface mesh generation (5) fit this new surface mesh to the initial coordinates of the interface surface nodes Merge this new surface mesh with the two open subdomains By restoring the initial coordinates of the surface nodes of C

13. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 13 Interface mesh generation (6) We obtain two new triangular surface meshes corresponding to two closed envelopes compatible with the sequential volume mesh generator used

14. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 14 geometric decomposition interface mesh generator Triangular surface mesh (the domain envelope) Module 2

15. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 15 Sequential volume mesh generator We apply the sequential volume mesh generator on each closed envelope of each subdomain We obtain two volume meshes

16. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 16 geometric decomposition interface mesh generator sequential volume mesh generator Triangular surface mesh (the domain envelope) Module 3

17. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 17 Volume mesh merging The interface surface mesh is the same

18. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 18 geometric decomposition 3D volume mesh interface mesh generator sequential volume mesh generator volume mesh merging Triangular surface mesh (the domain envelope) Module 4

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30. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 30 geometric decomposition 3D volume mesh interface mesh generator sequential volume mesh generator volume mesh merging scheduler Triangular surface mesh (the domain envelope) n=2 h Module 5

31. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 31 Complex geometry

32. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 32 Complex geometry

33. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 33 Complex geometry

34. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 34 More complex geometry Multiple contour Contour with hole inside we know where is the material detection of the connected components re-assigning strategy for small parts (intersection with 

35. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 35 re-assigning strategy for small parts

36. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 36 Two examples of interface mesh generated with two different 

37. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 37 geometric decomposition 3D volume mesh interface mesh generator sequential volume mesh generator volume mesh merging scheduler Triangular surface mesh (the domain envelope)

38. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 38 Conclusion the preliminary results have to be confirmed on other benchmarks the results have to be compared with the meshes computed with the sequential volume mesh generator alone several issues have to be addressed : piloting strategy for the cutting plane  according to the attenuation function and the shape of the initial surface mesh the behavior of each module has to be studied

39. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 39 Future works design of the scheduler coupling the parallel volume mesh generation with a solver

40. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 40 Questions ?

41. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 41 Clue (1.0) piloting strategy for the cutting plane  according to the attenuation function and the shape of the initial surface mesh X the first center of gravity  the first cutting plane material Two boundary areas  the first normal vector

42. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 42 Clue (1.1) We compute the weight: w i =w ref (distance(h(X i ),X)/r) Where : h(X i ) is the projection of surface node X i to the normal of  r is a radius (area of influence) w ref (d) is an attenuation function where : w ref (d) = 0.5 (1+cos(  d)) if d  [0,1] and 0 otherwise

43. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 43 Clue (1.2) detect the two boundary area for each, compute a new center of gravity for each boundary area, adjust a new quantity r according to each local geometry run the partitioning algorithm on each part

44. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 44 Clue (1.3) X1X1     X2X2 r1r1 r2r2

45. UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval 45 Clue (1.4) X1X1       X2X2 r1r1 r2r2