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,

UMR CNRS 6599 HeuDiaSyC, UMR CNRS 6066 Roberval

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A Modular Design for a Parallel Multifrontal

Mesh Generator

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)


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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:


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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


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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


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Splitting of a closed envelope (2)

We obtain a cutting plane splitting the initial triangular surface mesh into two parts havingroughly the same number of nodes


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geometric decomposition

Triangular surface mesh(the domain envelope)

Module 1


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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


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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

S1 the triangular finite elements on one side of

S2 the triangular finite elements on the other side of

S3 the triangular finite elements near

distance criterion the boundary area


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(2)

We assign the triangular finite elements of the boundary area

“crown”


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(3)

That defines a border line C composed of interface surface nodes splitting the initial triangular surface mesh into two open subdomains

C


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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


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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


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Interface mesh generation (6)

We obtain two new triangular surface meshescorresponding to two closed envelopes compatiblewith the sequential volume mesh generator used


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interface mesh generator


Module 2


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Sequential volume mesh generator

We apply the sequential volumemesh generator on each closed envelope of each subdomain

We obtain two volume meshes


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sequential volume mesh generator


Module 3


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Volume mesh merging

The interface surface mesh is the same


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3D volume mesh



volume mesh merging


Module 4


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3D volume mesh



volume mesh merging

scheduler


n=2 h

Module 5


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Complex geometry


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Complex geometry


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Complex geometry


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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


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re-assigning strategy for small parts


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Two examples of interface mesh generatedwith two different


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3D volume mesh



volume mesh merging

scheduler



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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


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Future works

• design of the scheduler• coupling the parallel volume mesh generation with a solver


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Questions ?


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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


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Clue (1.1)

We compute the weight: wi=wref(distance(h(Xi),X)/r)

Where : • h(Xi) is the projection of surface nodeXi to the normal of

• r is a radius (area of influence)• wref(d) is an attenuation function where :

wref(d) = 0.5 (1+cos(d)) if d [0,1] and 0 otherwise


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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


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Clue (1.3)

X1

X2r1 r2


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Clue (1.4)

X1

X2

r1

r2

Documents

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,