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dca.iusiani.ulpgc.es/proyecto2012-2014

Tetrahedral Mesh Optimization Combining Boundary and Inner Node Relocation and Adaptive Local Refinement. Socorro G.V. (1) , Ruiz- Gironés E. (2) , Oliver A. (1) , Cascón J.M. (3) , Escobar J.M. (1) , Sarrate J. (2) and Montenegro R. (1).

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dca.iusiani.ulpgc.es/proyecto2012-2014

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  1. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement Socorro G.V.(1), Ruiz-Gironés E.(2), Oliver A.(1), Cascón J.M.(3), Escobar J.M.(1), Sarrate J.(2)and Montenegro R.(1) (1) University Institute SIANI, University of Las Palmas de Gran Canaria, Spain (2)Laboratoride CàlculNumèric(LaCàN), UniversitatPolitècnicade Catalunya– BarcelonaTech, Spain (3) Department of Economics and Economic History, University of Salamanca, Spain http://www.dca.iusiani.ulpgc.es/proyecto2012-2014

  2. Motivation MeshGenus-Zero Solids • Meshgenus-zerosolids and get a validvolumetricparameterization • Improvethequality of meshesgeneratedussingtheMeccanomethod • Maindrawback: boundarynodesattached at theirlocation • Smooth of bondarynodes (b) parametricdomain (a) boundarysurfaces 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 2

  3. TheMeccanoMethod Surface Parameterization Mapphysicalboundarysurface to meccanoboundary (a) solidboundarysurfaces (b) parametricdomain 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 3

  4. TheMeccanoMethod Surface Capture Mesh and refine themeccano to capture solidsurfaces (a) refinedmeccanomesh (b) solidmesh 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 4

  5. TheMeccanoMethod InnerNodesLocation ApplyCoonspatches to get a reasonablelocationforinnernodes (a) solidmeshbeforeCoonspatches (b) solidmeshafterCoonspatches 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 5

  6. TheMeccanoMethod Untangle and Smoothing Simultaneousuntangle and smoothing to get a validmesh (a) tangledsolidmesh (b) untangled and smoothedsolidmesh 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 6

  7. TheMeccanoMethod ResultingVolumeParameterization • VolumetricparameterizationfromuniformstructureKossasckymesh to solid in physicaldomain (a) uniformKossasckymeccanomesh (b) solidmesh in physicaldomain 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 7

  8. TetrahedralMeshSmoothing InnerNodeSmoothing • Unconstrainedoptimizationproblem in 3D physicaldomain • Physicalcoordinates as optimization variables • Qualitymeasurement in physicaldomain • Parametriccounterpart as ideal reduce thedistortion (b) afteroptimization (a) beforeoptimization 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 8

  9. TetrahedralMeshSmoothing BoundaryNodeSmoothing. Parameterizations • Exploitmeshparametrization to simplifytheoptimizationproblem 3D (physical) surfaceconstrained 2D (parametric) rectangleconstrained meshparameterization (a) parametricdomain (b) physicaldomain 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 9

  10. TetrahedralMeshSmoothing BoundaryNodeSmoothing. Optimization • Optimization • Parametriccoordinatesas optimizationvariables • Qualitymeasurement in physicaldomain (a) Initiallocations (b) locationsaftersmoothing 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 10

  11. TetrahedralMeshSmoothing BoundaryNodeSmoothing. ParametricDomains • Creatinganadditionalparametricdomainforsmoothingporpouseonly volumetric parameterization parametricdomain R (regular Kossasckymesh) physicaldomain Floater’s parameterization parametricdomain S (no regular Kossasckymesh) 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 11

  12. TetrahedralMeshSmoothing Validity of BoundaryMesh • Geometry preservation • The resulting mesh is tangled. There are no inverted tetrahedral but some of them are overlapped no valid mesh (b) physicaldomain (a) parametricdomain 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 12

  13. TetrahedralMeshSmoothing BoundaryNodeSmoothing • Imposing validity for boundary faces of the meccano • over star area • Extra term in the objective function • that penalties tetrahedral collapse in • the parametric domain. 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 13

  14. TetrahedralMeshSmoothing BoundaryNodeSmoothing • Analogous procedure for edge (1D) optimization • Boundary nodes smoothing could cause loose of both volume and geometry • Iterative Refinement, untangle and smoothing stages 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 14

  15. TetrahedralMeshSmoothing BoundSmoothingArea(Bufferingalgorithm) • Meshmust be smoothedafterrefinement • Bufferingalgorithmfocussmoothing in areaswhererefinementtoke place • Initializewith new nodes a buffer of pendingnodes to smooth • Smoothfirstpendingnode • Ifdisplacement ≥ prescribedthresholdenqueueneighbornodes • Ifanypendingnodereturn to 2 • Drasticreduction in thenumber of star to smooth 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 15

  16. Aplications Oil Field Meshing 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 16

  17. Aplications Oil Field Meshing • Initialcoarsemesh 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 17

  18. Aplications Oil Field Meshing • Coonspatches 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 18

  19. Aplications Oil Field Meshing • Innernodessmoothing 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 19

  20. Aplications Oil Field Meshing • Boundarynodessmoothing 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 20

  21. Aplications Oil Field Meshing • Tetrahedralquality Nbr. of nodes 8213 Nbr of cells 33104Min quality 0.0043Mean quality 0.649Max quality 0.986 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 21

  22. Aplications TroposphereMeshingforWindForecast 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 22

  23. Conclusions • Conclusions • Aninnovativemethod has beendevelopedforboth, boundarysmoothing and volumetricparametrization of genus-zerosolid • ThisworkupgradesTheMeccanoMethodbyaddingboundarynodesrelocation • Theprocedureobtainsgoodqualitymeshes • The idea can be applied to anymeshgenerationmethodthat uses surfaceparameterization • Theprocedurerequiresminimumuserintervention • Thealgorithm has a lowcomputationalcost and admitsparalellization 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 23

  24. Questions? • Thanksforyourattention! 11th World Congress on Computational Mechanics (WCCM XI). 20 – 26 July 2014. TetrahedralMeshOptimizationCombiningBoundary and InnerNodeRelocation and Adaptive Local Refinement - 24

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