Skip to main content
SpringerLink
Log in

Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A new non-iterative mesh generation algorithm named conforming to interface structured adaptive mesh refinement (CISAMR) is introduced for creating 3D finite element models of problems with complex geometries. CISAMR transforms a structured mesh composed of tetrahedral elements into a conforming mesh with low element aspect ratios. The construction of the mesh begins with the structured adaptive mesh refinement of elements in the vicinity of material interfaces. An r-adaptivity algorithm is then employed to relocate selected nodes of nonconforming elements, followed by face-swapping a small fraction of them to eliminate tetrahedrons with high aspect ratios. The final conforming mesh is constructed by sub-tetrahedralizing remaining nonconforming elements, as well as tetrahedrons with hanging nodes. In addition to studying the convergence and analyzing element-wise errors in meshes generated using CISAMR, several example problems are presented to show the ability of this method for modeling 3D problems with intricate morphologies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31

Similar content being viewed by others

References

  1. Young PG, Bresford-West TBH, Coward SRL, Notarberardino B, Walker B, Abdud-Aziz A (2008) An efficient approach to converting three-dimensional image data into highly accurate computational model. Philos Trans R Soc A 355:3155–3173

    Article  MathSciNet  Google Scholar 

  2. Geuzaine C, Remacle JF (2009) Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331

    Article  MathSciNet  Google Scholar 

  3. Berzins M (1999) Mesh quality: a function of geometry, error estimates or both? Eng Comput 15(3):236–247

    Article  Google Scholar 

  4. Shewchuk JR (2002) What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measures, vol 73. University of California, Berkeley

    Google Scholar 

  5. Vallet MG, Manole CM, Dompierre J, Dufour S, Guibault F (2007) Numerical comparison of some Hessian recovery techniques. Int J Numer Methods Eng 72(8):987–1007

    Article  MathSciNet  Google Scholar 

  6. Mosler J, Ortiz M (2007) Variational h-adaption in finite deformation elasticity and plasticity. Int J Numer Methods Eng 72(5):505–523

    Article  MathSciNet  Google Scholar 

  7. Xie D, Waas AM (2006) Discrete cohesive zone model for mixed-mode fracture using finite element analysis. Eng Fract Mech 73(13):1783–1796

    Article  Google Scholar 

  8. Elman HC, Silvester DJ, Wathen AJ (2014) Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Oxford University Press, Oxford

    Book  Google Scholar 

  9. Kamenski L, Huang W, Xu H (2014) Conditioning of finite element equations with arbitrary anisotropic meshes. Math Comput 83(289):2187–2211

    Article  MathSciNet  Google Scholar 

  10. Shewchuk JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom 22(1):21–74

    Article  MathSciNet  Google Scholar 

  11. Si H (2010) Constrained Delaunay tetrahedral mesh generation and refinement. Finite Elem Anal Des 46(1):33–46

    Article  MathSciNet  Google Scholar 

  12. Schöberl J (1997) NETGEN an advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci 1(1):41–52

    Article  Google Scholar 

  13. Yerry MA, Shephard MS (1984) Automatic three-dimensional mesh generation by the modified-octree technique. Int J Numer Methods Eng 20(11):1965–1990

    Article  Google Scholar 

  14. Baehmann PL, Wittchen SL, Shephard MS, Grice KR, Yerry MA (1987) Robust, geometrically based, automatic two-dimensional mesh generation. Int J Numer Methods Eng 24(6):1043–1078

    Article  Google Scholar 

  15. Shephard MS, Georges MK (1991) Automatic three-dimensional mesh generation by the finite octree technique. Int J Numer Methods Eng 32(4):709–749

    Article  Google Scholar 

  16. Gawlik ES, Lew AJ (2014) High-order finite element methods for moving boundary problems with prescribed boundary evolution. Comput Methods Appl Mech Eng 278:314–346

    Article  MathSciNet  Google Scholar 

  17. Gawlik ES, Kabaria H, Lew AJ (2015) High-order methods for low Reynolds number flows around moving obstacles based on universal meshes. Int J Numer Methods Eng 104(7):513–538

    Article  MathSciNet  Google Scholar 

  18. Gawlik ES, Lew AJ (2015) Unified analysis of finite element methods for problems with moving boundaries. SIAM J Numer Anal 53(6):2822–2846

    Article  MathSciNet  Google Scholar 

  19. Lo SH (1985) A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng 21(8):1403–1426

    Article  Google Scholar 

  20. Lo SH (1991) Volume discretization into tetrahedra-II. 3D triangulation by advancing front approach. Comput Struct 39(5):501–511

    Article  Google Scholar 

  21. Shephard MS, Yerry M (1983) A modified Quadtree approach to finite element mesh generation. IEEE Comput Gr Appl 3(1):39–46

    Article  Google Scholar 

  22. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Gr 21(4):163–169

    Article  Google Scholar 

  23. Zhang YJ, Hughes TJR, Bajaj CL (2010) An automatic 3D mesh generation method for domains with multiple materials. Comput Methods Appl Mech Eng 199(5):405–415

    Article  Google Scholar 

  24. Liang XH, Zhang YJ (2014) An octree-based dual contouring method for triangular and tetrahedral mesh generation with guaranteed angle range. Eng Comput 30(2):211–222

    Article  Google Scholar 

  25. Zhang YG, Bajaj C (2006) Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Eng 195(9):942–960

    Article  Google Scholar 

  26. Rozavany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237

    Article  MathSciNet  Google Scholar 

  27. Phongthanapanich S, Dechaumphai P (2004) Adaptive Delaunay triangulaiton with object-oriented programming for crack propagation analysis. Finite Elem Anal Des 40:1753–1771

    Article  Google Scholar 

  28. Shakoor M, Bouchard PO, Bernacki M (2017) An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains. Int J Numer Methods Eng 109(4):555–576

    Article  MathSciNet  Google Scholar 

  29. Babuska I, Melnek JM (1997) The partition of unity method. Int J Numer Methods Eng 40(4):727–758

    Article  MathSciNet  Google Scholar 

  30. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150

    Article  Google Scholar 

  31. Duarte CA, Babuška I, Oden TJ (2000) Generalized finite element methods for three-dimensional structural mechanics. Comput Struct 77(2):215–232

    Article  MathSciNet  Google Scholar 

  32. Soghrati S (2014) Hierarchical interface-enriched finite element method: an automated technique for mesh-independent simulations. J Comput Phys 275:41–52

    Article  MathSciNet  Google Scholar 

  33. Soghrati S, Ahmadian H (2015) 3D hierarchical interface-enriched finite element method: implementation and applications. J Comput Phys 299:45–55

    Article  MathSciNet  Google Scholar 

  34. Karoui A, Mansouri K, Renard Y, Arfaoui M (2014) The extended finite element method for cracked hyperelastic materials: a convergence study. Int J Numer Methods Eng 100(3):222–242

    Article  MathSciNet  Google Scholar 

  35. Zi G, Belytschko T (2003) New crack-tip elements for XFEM and applications to cohesive cracks. Int J Numer Methods Eng 57(15):2221–2240

    Article  Google Scholar 

  36. Chahine E, Laborde P, Renard Y (2008) Crack tip enrichment in the XFEM using a cutoff function. Int J Numer Methods Eng 75(6):629–646

    Article  MathSciNet  Google Scholar 

  37. Lang C, Makhija D, Doostan A, Maute K (2014) A simple and efficient preconditioning scheme for heaviside enriched XFEM. Comput Mech 54(5):1357–1374

    Article  MathSciNet  Google Scholar 

  38. Belytschko T, Gracie R, Ventura G (2009) A review of extended/generalized finite element methods for material modeling. Modell Simul Mater Sci Eng 17(4):043001

    Article  Google Scholar 

  39. Omerović S, Fries TP (2017) Conformal higher-order remeshing schemes for implicitly defined interface problems. Int J Numer Methods Eng 109(6):763–789

    Article  MathSciNet  Google Scholar 

  40. Noble DR, Newren EP, Lechman JB (2010) A conformal decomposition finite element method for modeling stationary fluid interface problems. Int J Numer Methods Fluids 63(6):725–742

    MATH  Google Scholar 

  41. Fries TP, Schöllhammer D (2017) Higher-order meshing of implicit geometries-part II: approximations on manifolds. arXiv preprint arXiv:1706.00840

    Article  MathSciNet  Google Scholar 

  42. Fries TP (2017) Higher-order meshing of implicit geometries-part III: conformal decomposition FEM (CDFEM). arXiv preprint arXiv:1706.00919

  43. Soghrati S, Nagarajan A, Liang BW (2017) Conforming to interface structured adaptive mesh refinement: new technique for the automated modeling of materials with complex microstructures. Finite Elem Anal Des 125:24–40

    Article  Google Scholar 

  44. Baden Scott B (2000) Structured adaptive mesh refinement (SAMR) grid methods. Springer, Berlin

    Book  Google Scholar 

  45. Saksono PH, Dettmer WG, Peric D (2007) An adaptive remeshing strategy for flows with moving boundaries and fluid-structure interaction. Int J Numer Methods Eng 71(9):1009–1050

    Article  MathSciNet  Google Scholar 

  46. Piggott MD, Pain CC, Gorman GJ, Power PW, Goddard AJH (2005) h, r, and hr adaptivity with applications in numerical ocean modelling. Ocean Model 10(1):95–113

    Article  Google Scholar 

  47. Soghrati S, Xiao F, Nagarajan A (2017) A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems. Comput Mech 59(4):667–684

    Article  MathSciNet  Google Scholar 

  48. Soghrati S, Chen Y, Mai W (2017) A non-iterative local remeshing approach for simulating moving boundary transient diffusion problems. Finite elements in analysis and design (in press)

  49. Coupez T, Digonnet H, Ducloux R (2000) Parallel meshing and remeshing. Appl Math Model 25(2):153–175

    Article  Google Scholar 

  50. Terada K, Hori M, Kyoya T, Kikuchi N (2000) Simulation of the multi-scale convergence in computational homogenization approaches. Int J Solids Struct 37(16):2285–2311

    Article  Google Scholar 

  51. Nguyen VP, Stroeven M, Sluys LJ (2011) Multiscale continuous and discontinuous modeling of heterogeneous materials: a review on recent developments. J Multiscale Modell 3(04):229–270

    Article  MathSciNet  Google Scholar 

  52. Sukumar N, Chopp DL, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190(46):6183–6200

    Article  MathSciNet  Google Scholar 

  53. Szabo BA, Babuška I (1991) Finite element analysis. Wiley, Hoboken

    MATH  Google Scholar 

  54. Soghrati S, Aragón AM, Duarte CA, Geubelle PH (2012) An interface-enriched generalized finite element method for problems with discontinuous gradient fields. Int J Numer Meth Eng 89(8):991–1008

    Article  Google Scholar 

  55. Soghrati S, Geubelle PH (2012) A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries. Comput Methods Appl Mech Eng 217–220:46–57

    Article  MathSciNet  Google Scholar 

  56. Moës N, Cloirec M, Cartraud P, Remacle JF (2003) A computational approach to handle complex microstructure geometries. Comput Methods Appl Mech Eng 192:3163–3177

    Article  Google Scholar 

  57. Hooputra H, Gese H, Dell H, Werner H (2004) A comprehensive failure model for crashworthiness simulation of aluminium extrusions. Int J Crashworthiness 9(5):449–464

    Article  Google Scholar 

  58. Sadowski T, Golewski P, Kneć M (2014) Experimental investigation and numerical modelling of spot welding-adhesive joints response. Compos Struct 112:66–77

    Article  Google Scholar 

  59. Fiedler B, Hojo M, Ochiai S, Schulte K, Ando M (2001) Failure behavior of an epoxy matrix under different kinds of static loading. Compos Sci Technol 61(11):1615–1624

    Article  Google Scholar 

  60. Hughes TJR (2012) The finite element method: linear static and dynamic finite element analysis. Courier Corporation, North Chelmsford

    Google Scholar 

Download references

Acknowledgements

This work has been supported by the Air Force Office of Scientific Research (AFOSR) under grant number FA9550-17-1-0350. The authors also acknowledge partial funding from the Ohio State Simulation and Innovation Modeling Center (SIMCenter) through support from Honda R&D Americas, Inc. and the allocation of computing time from the Ohio Supercomputer Center.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 West 19th Avenue, Columbus, OH, USA

    Anand Nagarajan & Soheil Soghrati

  2. Department of Materials Science and Engineering, The Ohio State University, 201 West 19th Avenue, Columbus, OH, USA

    Soheil Soghrati

Authors
  1. Anand Nagarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Soheil Soghrati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soheil Soghrati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nagarajan, A., Soghrati, S. Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation. Comput Mech 62, 1213–1238 (2018). https://doi.org/10.1007/s00466-018-1560-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-018-1560-2

Keywords

Search

Navigation