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Erschienen in: Engineering with Computers 2/2012

01.04.2012 | Original Article

DARSS: a hybrid mesh smoother for all hexahedral meshes

verfasst von: Dhaval Jani, Anoop Chawla, Sudipto Mukherjee, Raman Khattri

Erschienen in: Engineering with Computers | Ausgabe 2/2012

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Abstract

A method for smoothing hexahedral meshes has been developed. The method consists of two phases. In the first phase, the nodes are moved based on an explicit formulation. A constraint has also been implemented to prevent the deterioration of elements associated with the node being moved. The second phase of the method is optismoothing based on the Nelder–Mead simplex method. The summation of the Jacobian of all the elements sharing a node has been taken as the function to be maximized. The method has been tested on meshes up to 18,305 hexahedral elements and was found to be stable and improved the mesh in about 112.6 s on an Intel Centrino® 1.6 GHz, 1 GB RAM machine. The method thus has the advantage of being effective as well as being computationally efficient.

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Literatur
1.
Zurück zum Zitat White DR, Mingu L, Benzley SE, Sjaardema GD (1995) Automated hexahedral mesh generation by virtual decomposition. In: Proceedings of 4th international meshing roundtable. Sandia National Laboratories, California, pp 165–176 White DR, Mingu L, Benzley SE, Sjaardema GD (1995) Automated hexahedral mesh generation by virtual decomposition. In: Proceedings of 4th international meshing roundtable. Sandia National Laboratories, California, pp 165–176
2.
Zurück zum Zitat Knupp PM (1998) Next generation Sweep Tool: a method for generating all hex meshes on a two and one half dimensional geometries. In: Proceedings of 7th international meshing roundtable. Sandia National Laboratory, California, pp 505–513 Knupp PM (1998) Next generation Sweep Tool: a method for generating all hex meshes on a two and one half dimensional geometries. In: Proceedings of 7th international meshing roundtable. Sandia National Laboratory, California, pp 505–513
3.
Zurück zum Zitat Folwell NT, Mitchell SA (1999) Reliable whisker weaving via curve contraction. Eng Comput 15:292–302MATHCrossRef Folwell NT, Mitchell SA (1999) Reliable whisker weaving via curve contraction. Eng Comput 15:292–302MATHCrossRef
4.
Zurück zum Zitat Jankovich SR, Benzley SE, Shepherd JF, Mitchell SA (1999) The Graft Tool: an all-hexahedral transition algorithm for creating a multi-directional swept volume mesh. In: 8th international meshing roundtable. S. Lake Tahoe, CA, pp 387–392 Jankovich SR, Benzley SE, Shepherd JF, Mitchell SA (1999) The Graft Tool: an all-hexahedral transition algorithm for creating a multi-directional swept volume mesh. In: 8th international meshing roundtable. S. Lake Tahoe, CA, pp 387–392
5.
Zurück zum Zitat Owen SJ, Saigal S (2000) H-Morph: an indirect approach to advancing from hex meshing. Int J Numer Methods Eng 49:289–312MATHCrossRef Owen SJ, Saigal S (2000) H-Morph: an indirect approach to advancing from hex meshing. Int J Numer Methods Eng 49:289–312MATHCrossRef
6.
Zurück zum Zitat White D, Rodrigue G (1997) Improved vector FEM solutions of Maxwell’s equations using grid pre-conditioning. Int J Numer Meth Eng 40:3815–3837MathSciNetMATHCrossRef White D, Rodrigue G (1997) Improved vector FEM solutions of Maxwell’s equations using grid pre-conditioning. Int J Numer Meth Eng 40:3815–3837MathSciNetMATHCrossRef
7.
Zurück zum Zitat Shontz SM, Vavasis SA (2004) A linear weighted laplacian smoothing framework for warping tetrahedral meshes. CS.NA/0410045. October 2004 Shontz SM, Vavasis SA (2004) A linear weighted laplacian smoothing framework for warping tetrahedral meshes. CS.NA/0410045. October 2004
9.
Zurück zum Zitat Canann SA, Stephenson MB, Blacker T (1993) Optismoothing: an optimization-driven approach to mesh smoothing. Finite Elem Anal Des 13:185–190MathSciNetMATHCrossRef Canann SA, Stephenson MB, Blacker T (1993) Optismoothing: an optimization-driven approach to mesh smoothing. Finite Elem Anal Des 13:185–190MathSciNetMATHCrossRef
10.
Zurück zum Zitat Cannan SA, Tristano JR, Staten ML (1998) An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes 7th international meshing roundtable, October 26–28, 1998, Dearborn, Michigan, USA Cannan SA, Tristano JR, Staten ML (1998) An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes 7th international meshing roundtable, October 26–28, 1998, Dearborn, Michigan, USA
11.
Zurück zum Zitat Hansbo P (1995) Generalized Laplacian smoothing of unstructured grids. Commun Numer Methods Eng 11:455–464MATHCrossRef Hansbo P (1995) Generalized Laplacian smoothing of unstructured grids. Commun Numer Methods Eng 11:455–464MATHCrossRef
12.
Zurück zum Zitat Amenta N, Bern M, Eppstein D (1997) Optimal point placement for mesh smoothing. In 8th ACM–SIAM symposium on discrete algorithms. New Orleans, pp 528–537 Amenta N, Bern M, Eppstein D (1997) Optimal point placement for mesh smoothing. In 8th ACM–SIAM symposium on discrete algorithms. New Orleans, pp 528–537
13.
Zurück zum Zitat Freitag L (1997) On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation, July 1997, ASME, pp 37–43 Freitag L (1997) On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation, July 1997, ASME, pp 37–43
14.
Zurück zum Zitat Xu H, Newman TS (2006) An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem Anal Des 42:1150–1164MathSciNetCrossRef Xu H, Newman TS (2006) An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem Anal Des 42:1150–1164MathSciNetCrossRef
15.
Zurück zum Zitat Khattri S (2006) A new smoothing algorithm for quadrilateral and hexahedral meshes, LNCS, ICCS 2006, pp 239–246 Khattri S (2006) A new smoothing algorithm for quadrilateral and hexahedral meshes, LNCS, ICCS 2006, pp 239–246
16.
17.
Zurück zum Zitat Herrmann LR (1976) Laplacian–isoparametric grid generation scheme. J Eng Mech Div 102(5):749–756 Herrmann LR (1976) Laplacian–isoparametric grid generation scheme. J Eng Mech Div 102(5):749–756
18.
Zurück zum Zitat Knupp PM (1999) Winslow smoothing on two-dimensional unstructured meshes. Eng Comput 15:263–268MATHCrossRef Knupp PM (1999) Winslow smoothing on two-dimensional unstructured meshes. Eng Comput 15:263–268MATHCrossRef
19.
Zurück zum Zitat Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25:287–301CrossRef Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25:287–301CrossRef
20.
Zurück zum Zitat Semonova I, Kozhekin N, Savchenko V, Hagiwara I (2005) A general framework for analysis and comparison of surface mesh optimization techniques. Eng Comput 21:91–100CrossRef Semonova I, Kozhekin N, Savchenko V, Hagiwara I (2005) A general framework for analysis and comparison of surface mesh optimization techniques. Eng Comput 21:91–100CrossRef
21.
22.
Zurück zum Zitat Parthasarathy V, Kodiyalam S (1991) A constrained optimization approach to finite element mesh smoothing. Finite Elem Anal Des 9:309–320MATHCrossRef Parthasarathy V, Kodiyalam S (1991) A constrained optimization approach to finite element mesh smoothing. Finite Elem Anal Des 9:309–320MATHCrossRef
23.
Zurück zum Zitat Calvo NA, Ideslohn SR (2001) All hexahedral mesh smoothing with a node based measure of mesh quality. Int J Numer Methods Eng 50:1957–1967MATHCrossRef Calvo NA, Ideslohn SR (2001) All hexahedral mesh smoothing with a node based measure of mesh quality. Int J Numer Methods Eng 50:1957–1967MATHCrossRef
24.
Zurück zum Zitat Knupp PM (2003) A method for hexahedral mesh shape optimization. Int J Numer Methods Eng 58:319–332MATHCrossRef Knupp PM (2003) A method for hexahedral mesh shape optimization. Int J Numer Methods Eng 58:319–332MATHCrossRef
25.
Zurück zum Zitat Shimada K, Gossard DC (1995) Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing. Solid modelling ‘95 (conference proceedings), pp 409–419 Shimada K, Gossard DC (1995) Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing. Solid modelling ‘95 (conference proceedings), pp 409–419
26.
Zurück zum Zitat Shimada K, Yamada A, Itoh T (2000) Anisotropic triangular meshing of parametric surfaces via close packing of ellipsoidal bubbles. Int J Comput Geom Appl 10(4):400–424MathSciNetCrossRef Shimada K, Yamada A, Itoh T (2000) Anisotropic triangular meshing of parametric surfaces via close packing of ellipsoidal bubbles. Int J Comput Geom Appl 10(4):400–424MathSciNetCrossRef
27.
Zurück zum Zitat Zhou T, Shimada K (2000) An angle based approach to two dimensional mesh smoothing. In: Proceedings of the 9th international meshing roundtable, pp 373–384 Zhou T, Shimada K (2000) An angle based approach to two dimensional mesh smoothing. In: Proceedings of the 9th international meshing roundtable, pp 373–384
28.
Zurück zum Zitat Branets L, Carey GF (2005) A local cell quality metric and variational grid smoothing algorithm. Eng Comput 21:19–28CrossRef Branets L, Carey GF (2005) A local cell quality metric and variational grid smoothing algorithm. Eng Comput 21:19–28CrossRef
29.
Zurück zum Zitat Kober C, Muller-Hannemann M (2001) A case study in hexahedral mesh generation: simulation of the human mandible. Eng Comput 17:249–260MATHCrossRef Kober C, Muller-Hannemann M (2001) A case study in hexahedral mesh generation: simulation of the human mandible. Eng Comput 17:249–260MATHCrossRef
30.
Zurück zum Zitat Vartziotis D, Athanasiadis T, Goudas I, Wipper J (2008) Mesh smoothing using the geometric element transformation method. Comput Methods Appl Mech Eng 197(45–48):3760–3767 Vartziotis D, Athanasiadis T, Goudas I, Wipper J (2008) Mesh smoothing using the geometric element transformation method. Comput Methods Appl Mech Eng 197(45–48):3760–3767
31.
Zurück zum Zitat Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25(3):287–301CrossRef Vartziotis D, Wipper J (2009) The geometric element transformation method for mixed mesh smoothing. Eng Comput 25(3):287–301CrossRef
32.
Zurück zum Zitat Vartziotis D, Wipper J (2009) Classification of symmetry generating polygon transformations and geometric prime algorithms. Math Pannon 20(2):167–187MathSciNetMATH Vartziotis D, Wipper J (2009) Classification of symmetry generating polygon transformations and geometric prime algorithms. Math Pannon 20(2):167–187MathSciNetMATH
33.
Zurück zum Zitat Vartziotis D, Wipper J (2010) Characteristic parameter sets and limits of circulant Hermitian polygon transformations. Linear Algebra Appl 433(5):945–955MathSciNetMATHCrossRef Vartziotis D, Wipper J (2010) Characteristic parameter sets and limits of circulant Hermitian polygon transformations. Linear Algebra Appl 433(5):945–955MathSciNetMATHCrossRef
34.
Zurück zum Zitat Vartziotis D, Wipper J, Schwald B (2009) The geometric element transformation method for tetrahedral mesh smoothing. Comput Methods Appl Mech Eng 199(1–4):169–182MathSciNetMATHCrossRef Vartziotis D, Wipper J, Schwald B (2009) The geometric element transformation method for tetrahedral mesh smoothing. Comput Methods Appl Mech Eng 199(1–4):169–182MathSciNetMATHCrossRef
35.
Zurück zum Zitat Vartziotis D, Wipper J (2011) A dual element based geometric element transformation method for all-hexahedral mesh smoothing. Comput Methods Appl Mech Eng 200:1186–1203MathSciNetMATHCrossRef Vartziotis D, Wipper J (2011) A dual element based geometric element transformation method for all-hexahedral mesh smoothing. Comput Methods Appl Mech Eng 200:1186–1203MathSciNetMATHCrossRef
36.
Zurück zum Zitat Savchenko M, Egorova O, Hagiwara I, Savchenko V (2005) Hexahedral mesh improvement algorithm. JSME Int J Ser C 48(2):130–136CrossRef Savchenko M, Egorova O, Hagiwara I, Savchenko V (2005) Hexahedral mesh improvement algorithm. JSME Int J Ser C 48(2):130–136CrossRef
37.
Zurück zum Zitat Savchenko V, Savchenko M, Egorova O, Hagiwara I (2008) Mesh quality improvement radial basis functions approach. Int J Comput Math 85(10):1589–1607MathSciNetMATHCrossRef Savchenko V, Savchenko M, Egorova O, Hagiwara I (2008) Mesh quality improvement radial basis functions approach. Int J Comput Math 85(10):1589–1607MathSciNetMATHCrossRef
38.
Zurück zum Zitat Taubin G (1995) A signal processing approach to fair surface design. Proc SIGGRPH’95 29:351–358 Taubin G (1995) A signal processing approach to fair surface design. Proc SIGGRPH’95 29:351–358
39.
Zurück zum Zitat Riccius J, Schweizerhof K, Baumann M (1997) Combination of adaptivity and mesh smoothing for the finite element analysis of shells with intersections. Int J Numer Meth Eng 40:2459–2474MATHCrossRef Riccius J, Schweizerhof K, Baumann M (1997) Combination of adaptivity and mesh smoothing for the finite element analysis of shells with intersections. Int J Numer Meth Eng 40:2459–2474MATHCrossRef
40.
Zurück zum Zitat Bank RE, Smith RK (997) 1997. Mesh smoothing using a posteriori error estimates SIAM J Numer Anal(34):3–979MathSciNet Bank RE, Smith RK (997) 1997. Mesh smoothing using a posteriori error estimates SIAM J Numer Anal(34):3–979MathSciNet
41.
Zurück zum Zitat Jacquotte OP, Coussement G (1992) Structured mesh adaption: space accuracy and interpolation methods. Comput Methods Appl Mech Eng 101:397–432MathSciNetMATHCrossRef Jacquotte OP, Coussement G (1992) Structured mesh adaption: space accuracy and interpolation methods. Comput Methods Appl Mech Eng 101:397–432MathSciNetMATHCrossRef
42.
Zurück zum Zitat Yin J, Teodosiu C (2008) Constrained mesh optimization on boundary. Eng Comput 24:231–240CrossRef Yin J, Teodosiu C (2008) Constrained mesh optimization on boundary. Eng Comput 24:231–240CrossRef
43.
Zurück zum Zitat Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optim 9(1):112–147MathSciNetMATHCrossRef Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J Optim 9(1):112–147MathSciNetMATHCrossRef
44.
Zurück zum Zitat Mathews J, Fink KK (2004) Numerical methods using Matlab, 4th edn. Prentice Hall Inc., New Jersey, pp 430–433 Mathews J, Fink KK (2004) Numerical methods using Matlab, 4th edn. Prentice Hall Inc., New Jersey, pp 430–433
45.
Zurück zum Zitat Knupp PM (2000) Hexahedral mesh untangling and algebraic mesh quality metrics. In: Proceedings of 9th international meshing roundtable, pp 173–183 Knupp PM (2000) Hexahedral mesh untangling and algebraic mesh quality metrics. In: Proceedings of 9th international meshing roundtable, pp 173–183
46.
Zurück zum Zitat Deng B (2007) Human model for real-world vehicle–pedestrian impact simulations. Human modeling and simulation in automotive safety. Technical Report, ENSAM de Paris, Paris Deng B (2007) Human model for real-world vehicle–pedestrian impact simulations. Human modeling and simulation in automotive safety. Technical Report, ENSAM de Paris, Paris
47.
Zurück zum Zitat Untaroiu CD (2005) Development and validation of a finite element model of human lower limb. PhD thesis, UVA Untaroiu CD (2005) Development and validation of a finite element model of human lower limb. PhD thesis, UVA
Metadaten
Titel
DARSS: a hybrid mesh smoother for all hexahedral meshes
verfasst von
Dhaval Jani
Anoop Chawla
Sudipto Mukherjee
Raman Khattri
Publikationsdatum
01.04.2012
Verlag
Springer-Verlag
Erschienen in
Engineering with Computers / Ausgabe 2/2012
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-011-0235-9

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