SpringerLink
Log in

Automatic unstructured mesh generation approach for simulation of electronic packaging system

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

An automatic unstructured mesh generation approach is presented to discretize complex electronic packaging systems for finite element analysis. Various novel schemes are developed to resolve the common issues (models contain geometrical defects, models contain small but necessary features, simulation properties are predefined on models, etc.) to automate the entire mesh generation pipeline. These schemes include employing Boolean operations with a few technical considerations to resolve the geometrical defects of the original model, defining a sizing function that can adapt to small features, and develo** a new data structure named the unified topology model to connect a CAD model and the mesh resulting from the model. The proposed approach can generate quality meshes on certain models with geometrical defects, while state-of-the-art open-source tools (Netgen and Gmsh) generate nonconforming meshes on those models. Tests on complex configurations show that the proposed approach can achieve a speed-up of 3–5 times in comparison with state-of-the-art commercial tools (e.g., COMSOL Multiphysics). Simulation results are provided to demonstrate that the proposed approach can create a mesh with satisfactory quality.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. ** J (2015) The finite element method in electromagnetics, 17–36

  2. Ismail F, Sarker P, Mohamed M, Kim K, Ravaioli U (2018) Moving mesh adaptation for si and gan-based power device simulation. J Comput Electron 17(4):1621–1629

    Google Scholar 

  3. Zuo S, Zhang Y, Doñoro DG, Zhao X, Liu Q (2019) A novel finite element mesh truncation technology accelerated by parallel multilevel fast multipole algorithm and its applications. Appl Comput Electromagn Soc J (ACES) 2:1671–1678

    Google Scholar 

  4. Li C, Pan Z, Di M, Zhang F, Li Z, Jiang N, Wang A (2020) Esd device layout design guidelines by 3d tcad simulation. In: 2020 4th IEEE Electron Devices Technology & Manufacturing Conference (EDTM), pp. 1–4 . IEEE

  5. Liu QQ, Zhuang M, Zhan W, Liu N, Liu QH (2022) An efficient thin layer equivalent technique of setd method for thermo-mechanical multi-physics analysis of electronic devices. Int J Heat Mass Transf 192:122816

    Google Scholar 

  6. Li B, Tang M, Yue H, Tang Y, Mao J (2019) Efficient transient thermal simulation of ics and packages with laguerre-based finite-element method. IEEE Trans Components Packag Manuf Technol 10(2):203–211

    Google Scholar 

  7. Li J, Tang M, Mao J (2021) Efficient transient thermal simulation with laguerre-based finite-element method and domain decomposition. Numer Heat Transf Part B: Fundam 80(1–2):14–28

    Google Scholar 

  8. Wang Y, Lu C, Li J, Tan X, Tse Y (2005) Simulation of drop/impact reliability for electronic devices. Finite Elem Anal Des 41(6):667–680

    Google Scholar 

  9. Ho-Le K (1988) Finite element mesh generation methods: a review and classification. Comput Aided Des 20(1):27–38

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  11. Shewchuk J (2002) What is a good linear finite element? interpolation, conditioning, anisotropy, and quality measures (preprint). University of California at Berkeley 2002

  12. Guo J, Ding F, Jia X, Yan D-M (2019) Automatic and high-quality surface mesh generation for cad models. Comput Aided Des 109:49–59

    Google Scholar 

  13. Bawin A, Henrotte F, Remacle J-F (2021) Automatic feature-preserving size field for three-dimensional mesh generation. Int J Numer Meth Eng 122(18):4825–4847

    Google Scholar 

  14. Slotnick JP, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis DJ (2014) Cfd vision 2030 study: a path to revolutionary computational aerosciences. Technical report

  15. Bowyer A (1981) Computing dirichlet tessellations. Comput J 24(2):162–166

    MathSciNet  Google Scholar 

  16. Watson DF (1981) Computing the n-dimensional delaunay tessellation with application to voronoi polytopes. Comput J 24(2):167–172

    MathSciNet  Google Scholar 

  17. Shewchuk JR (1998) Tetrahedral mesh generation by delaunay refinement. In: Proceedings of the Fourteenth Annual Symposium on Computational Geometry, pp. 86–95

  18. Chen J, Zhao D, Huang Z, Zheng Y, Gao S (2011) Three-dimensional constrained boundary recovery with an enhanced steiner point suppression procedure. Comput struct 89(5–6):455–466

    Google Scholar 

  19. Chen J, Zhao D, Huang Z, Zheng Y, Wang D (2012) Improvements in the reliability and element quality of parallel tetrahedral mesh generation. Int J Numer Meth Eng 92(8):671–693

    MathSciNet  MATH  Google Scholar 

  20. Shewchuk JR, Si H (2014) Higher-quality tetrahedral mesh generation for domains with small angles by constrained delaunay refinement. In: Proceedings of the Thirtieth Annual Symposium on Computational Geometry. SOCG’14, pp. 290–299. Association for Computing Machinery, New York, NY, USA. https://doi.org/10.1145/2582112.2582138

  21. Si H (2015) Tetgen, a delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):2–2. https://doi.org/10.1145/2629697

    Article  MathSciNet  MATH  Google Scholar 

  22. Chen J, Zheng J, Zheng Y, Si H, Hassan O, Morgan K (2017) Improved boundary constrained tetrahedral mesh generation by shell transformation. Appl Math Model 51:764–790

    MathSciNet  MATH  Google Scholar 

  23. Chen J, Zheng J, Zheng Y, **ao Z, Si H, Yao Y (2017) Tetrahedral mesh improvement by shell transformation. Eng Comput 33(3):393–414

    Google Scholar 

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

    MATH  Google Scholar 

  25. Löhner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing-front method. Int J Numer Meth Fluids 8(10):1135–1149

    MATH  Google Scholar 

  26. Nakahashi K, Sharov D (1995) Direct surface triangulation using the advancing front method. In: 12th Computational Fluid Dynamics Conference, p. 1686

  27. Lan T, Lo S (1996) Finite element mesh generation over analytical curved surfaces. Comput Struct 59(2):301–309

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  29. Thompson JF, Soni BK, Weatherill NP (1998) Handbook of grid generation, 524–543

  30. Tremel U, Deister F, Hassan O, Weatherill NP (2004) Automatic unstructured surface mesh generation for complex configurations. Int J Numer Meth Fluids 45(4):341–364

    MATH  Google Scholar 

  31. Zhao D, Chen J, Zheng Y, Huang Z, Zheng J (2015) Fine-grained parallel algorithm for unstructured surface mesh generation. Comput Struct 154:177–191

    Google Scholar 

  32. Yu K, Chen J, Fu K, He J, Zheng J, Zheng Y (2022) On the efficiency of the advancing-front surface mesh generation algorithm. Comput-Aided Des 2:103403

    MathSciNet  Google Scholar 

  33. Hu Y, Zhou Q, Gao X, Jacobson A, Zorin D, Panozzo D (2018) Tetrahedral meshing in the wild. ACM Trans Graph 37(4):60–1

    Google Scholar 

  34. Hu Y, Schneider T, Wang B, Zorin D, Panozzo D (2020) Fast tetrahedral meshing in the wild. ACM Trans Gr (TOG) 39(4):117–121

    Google Scholar 

  35. Zheng P, Yang Y, Liu Z, Xu Q, Wang J, Leng J, Liu T, Zhu Z, Chen J (2020) Parallel and automatic isotropic tetrahedral mesh generation of misaligned assemblies. CCF Trans High Perform Comput 2(2):149–163

    Google Scholar 

  36. Liu Z, Chen J, **a Y, Zheng Y (2021) Automatic sizing functions for unstructured mesh generation revisited. Eng Comput 38:3995–4023. https://doi.org/10.1108/EC-12-2020-0700

    Article  Google Scholar 

  37. Chen J, **ao Z, Zheng Y, Zou J, Zhao D, Yao Y (2018) Scalable generation of large-scale unstructured meshes by a novel domain decomposition approach. Adv Eng Softw 121:131–146

    Google Scholar 

  38. Marot C, Pellerin J, Remacle J-F (2019) One machine, one minute, three billion tetrahedra. Int J Numer Meth Eng 117(9):967–990

    MathSciNet  Google Scholar 

  39. Yu F, Zeng Y, Guan Z, Lo S (2020) A robust delaunay-aft based parallel method for the generation of large-scale fully constrained meshes. Comput Struct 228:106170

    Google Scholar 

  40. Geuzaine C, Remacle J-F (2009) Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Meth Eng 79(11):1309–1331

    MathSciNet  MATH  Google Scholar 

  41. Fabri A, Pion S (2009) Cgal: The computational geometry algorithms library. In: Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 538–539

  42. COMSOL I (2021) COMSOL Multiphysics 5.6. https://cn.comsol.com/

  43. S.A.S., O.C. (2021) Open CASCADE Technology. https://www.opencascade.com/open-cascade-technology/. Accessed

  44. **ao Z, Chen J, Zheng Y, Zeng L, Zheng J (2014) Automatic unstructured element-sizing specification algorithm for surface mesh generation. Proc Eng 82:240–252. https://doi.org/10.1016/j.proeng.2014.10.387

    Article  Google Scholar 

  45. Chen J, **ao Z, Zheng Y, Zheng J, Li C, Liang K (2017) Automatic sizing functions for unstructured surface mesh generation. Int J Numer Meth Eng 109(4):577–608

    MathSciNet  Google Scholar 

  46. Mäntylä M (1987) An introduction to solid modeling, 1–101

  47. Stroud I (2006) Boundary representation modelling techniques, 1–787

  48. Tautges TJ (2001) Cgm: A geometry interface for mesh generation, analysis and other applications. Eng Comput 17(3):299–314

    MATH  Google Scholar 

  49. Cuillière J-C, Francois V (2014) Integration of cad, fea and topology optimization through a unified topological model. Computer-Aided Des Appl 11(5):493–508

    Google Scholar 

  50. Beall MW, Shephard MS (1997) A general topology-based mesh data structure. Int J Numer Meth Eng 40(9):1573–1596

    MathSciNet  Google Scholar 

  51. Pirzadeh SZ (2010) Advanced unstructured grid generation for complex aerodynamic applications. AIAA J 48(5):904–915

    Google Scholar 

  52. Quadros WR, Vyas V, Brewer M, Owen SJ, Shimada K (2010) A computational framework for automating generation of sizing function in assembly meshing via disconnected skeletons. Eng Comput 26(3):231–247

    Google Scholar 

  53. Alexandre Cunha SS, Canann Scott (1997) Automatic boundary sizing for 2d and 3d meshes. AMD Trends Unstruct Mesh Gen, ASME 220:65–72

    Google Scholar 

  54. **e L, Chen J, Liang Y, Zheng Y (2012) Geometry-based adaptive mesh generation for continuous and discrete parametric surfaces. J Inf Comput Sci 9(8):2327–2344

    Google Scholar 

  55. Dapogny C, Dobrzynski C, Frey P (2014) Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. J Comput Phys 262:358–378

    MathSciNet  MATH  Google Scholar 

  56. Bartoň M, Hanniel I, Elber G, Kim M-S (2010) Precise hausdorff distance computation between polygonal meshes. Computer Aided Geometric Design 27(8):580–591

    MathSciNet  MATH  Google Scholar 

  57. Borouchaki H, Hecht F, Frey PJ (1998) Mesh gradation control. Int J Numer Meth Eng 43(6):1143–1165

    MathSciNet  MATH  Google Scholar 

  58. Pippa S, Caligiana G (2005) Gradh-correction: guaranteed sizing gradation in multi-patch parametric surface meshing. Int J Numer Meth Eng 62(4):495–515

    MATH  Google Scholar 

  59. Wald I, Boulos S, Shirley P (2007) Ray tracing deformable scenes using dynamic bounding volume hierarchies. ACM Trans Gr (TOG) 26(1):6

    Google Scholar 

  60. Eberly D (1999) Distance between point and triangle in 3d. Magic Software, http://www.magic-software.com/Documentation/pt3tri3.pdf

  61. Aubry R, Karamete BK, Mestreau EL, Dey S (2014) A three-dimensional parametric mesher with surface boundary-layer capability. J Comput Phys 270:161–181

    MATH  Google Scholar 

  62. ANSYS I (2021) Ansys Electronics 2021 R1. https://www.ansys.com/products/electronics

  63. Pébay P, Baker T (2003) Analysis of triangle quality measures. Math Comput 72(244):1817–1839

    MathSciNet  MATH  Google Scholar 

  64. Parthasarathy V, Graichen C, Hathaway A (1994) A comparison of tetrahedron quality measures. Finite Elem Anal Des 15(3):255–261

    Google Scholar 

  65. Knupp PM (2000) Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities. part ii–a framework for volume mesh optimization and the condition number of the jacobian matrix. Int J Numer Meth Eng 48(8):1165–1185

    MATH  Google Scholar 

  66. Knupp PM (2003) Algebraic mesh quality metrics for unstructured initial meshes. Finite Elem Anal Des 39(3):217–241

    MATH  Google Scholar 

  67. Cadence Design Systems I (2021) Equiangle Skewness. https://www.pointwise.com/doc/user-manual/examine/functions/equiangle-skewness.html

Download references

Acknowledgements

The authors would like to thank the support Zhejiang Provincial Science and Technology Program in China (Grant No.2021C01108) and the Innovative Research Foundation of Ship General Performance in China (Grant No.14022105).

Author information

Authors and Affiliations

  1. School of Aeronautics and Astronautics, Zhejiang University, Hang Zhou, 310027, China

    Kejie Fu, Jianjun Chen, Kaixin Yu & Yao Zheng

  2. State Key Lab of CAD&CG, Zhejiang University, Hang Zhou, 310027, China

    Jianjun Chen

  3. Key Laboratory of Ministry of Education of China for Research of Design and Electromagnetic Compatibility of High Speed Electronic Systems, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jie Li & Min Tang

  4. School of Software Technology, Zhejiang University, Hang Zhou, 310027, China

    Jiangda He

Authors
  1. Kejie Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianjun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kaixin Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiangda He
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Min Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yao Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianjun Chen.

Ethics declarations

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, K., Chen, J., Li, J. et al. Automatic unstructured mesh generation approach for simulation of electronic packaging system. Engineering with Computers 39, 3527–3559 (2023). https://doi.org/10.1007/s00366-022-01764-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01764-w

Keywords

Search

Navigation