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A multi-domain BEM based on the dual interpolation boundary face method for 3D potential problems

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Abstract

In this paper, a multi-domain method, based on the dual interpolation boundary face method with Hermite-type moving-least-squares approximation (DiBFM-HMLS) and the matrix condensation technique, is firstly proposed for the 3D potential problems. This method is superior in the discontinuous field simulation (such as the corner problem) and can implement accurate interpolation in geometric structures with thin walls. Matrix condensation and reassembly reduce the overall system of linear algebraic equations to the interfacial ones with sparsity. This blocked-sparse-dominated multi-domain DiBFM-HMLS takes fewer CPU operations than its single-domain counterparts. Additionally, the interfacial conditions are not in the node-to-node format anymore, and instead, a node-to-element projective scheme built on the dual interpolation element of DiBFM-HMLS is presented for free mesh division in the interfaces (such as in self-adaption problems). Several numerical experiments from different aspects illustrate the feasibility and reliability of our multi-domain algorithms.

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References

  1. Zhang, J.M.: Multidomain thermal simulation of CNT composites by hybrid BNM. Numer. Heat Transf. Part B Fundam. 53(3), 246–258 (2008)

    Article  Google Scholar 

  2. Davı̀, G., Milazzo, A.: Multidomain boundary integral formulation for piezoelectric materials fracture mechanics. Int. J. Solids Struct. 38(40–41), 7065–7078 (2001)

    Article  MATH  Google Scholar 

  3. Ahmad, S., Banerjee, P.K.: Multi-domain BEM for two-dimensional problems of elastodynamics. Int. J. Numer. Meth. Eng. 26(4), 891–911 (1988)

    Article  MATH  Google Scholar 

  4. Kane, J.H.: Boundary Element Analysis in Engineering Continuum Mechanics. Prentice Hall, Englewood Cliffs (1994)

    Google Scholar 

  5. Layton, J.B., Guanguly, S., Balakrishna, C., Kane, J.H.: A symmetric Galerkin multi-zone boundary element formulation. Int. J. Numer. Methods Eng. 40(16), 2913–2931 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kallivokas, L.F., Juneja, T., Bielak, J.: A symmetric Galerkin BEM variational framework for multi-domain interface problems. Comput. Methods Appl. Mech. Eng. 194(34–35), 3607–3636 (2005)

    Article  MATH  Google Scholar 

  7. Chen, T.Z., Wang, B., Gen, Z.Z., Wu, Z.S.: A symmetric Galerkin multi-zone boundary element method for cohesive crack growth. Eng. Fract. Mech. 63(5), 591–609 (1999)

    Article  Google Scholar 

  8. Ramšak, M., Škerget, L., Hriberšek, M., Žunič, Z.: A multidomain boundary element method for unsteady laminar flow using stream function-vorticity equations. Eng. Anal. Bound. Elem. 29(1), 1–14 (2005)

    Article  MATH  Google Scholar 

  9. Baumann, M., van Gijzen, M.B.: Convergence and complexity study of GMRES variants for solving multi-frequency elastic wave propagation problems. J. Comput. Sci. 26, 285–293 (2018)

    Article  Google Scholar 

  10. Zhang, J.M., Zhuang, C., Qin, X.Y., Li, G.Y., Sheng, X.M.: FMM-accelerated hybrid boundary node method for multi-domain problems. Eng. Anal. Bound. Elem. 34(5), 433–439 (2010)

    Article  MATH  Google Scholar 

  11. Chaillat, S., Bonnet, M., Semblat, J.F.: A new fast multi-domain BEM to model seismic wave propagation and amplification in 3-D geological structures. Geophys. J. Int. 177(2), 509–531 (2009)

    Article  Google Scholar 

  12. Huang, S., Liu, Y.J.: A new simple multidomain fast multipole boundary element method. Comput. Mech. 58(3), 533–548 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liang, Y., Gao, X.W., Xu, B.B., Zhu, Q.H., Wu, Z.Y.: A new alternating iteration strategy based on the proper orthogonal decomposition for solving large-scaled transient nonlinear heat conduction problems. J. Comput. Sci. 45, 101206 (2020)

    Article  MathSciNet  Google Scholar 

  14. Peng, H.F., Bai, Y.G., Yamg, K., Gao, X.W.: Three-step multi-domain BEM for solving transient multi-media heat conduction problems. Eng. Anal. Bound. Elem. 37(11), 1545–1555 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zheng, Y.T., Gao, X.W., Peng, H.F., Xu, B.B.: The coupled method of multi-domain BEM and element differential method for solving multi-scale problems. Eng. Anal. Bound. Elem. 113, 145–155 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gao, X.W., Guo, L., Zhang, C.: Three-step multi-domain BEM solver for nonhomogeneous material problems. Eng. Anal. Bound. Elem. 31(12), 965–973 (2007)

    Article  MATH  Google Scholar 

  17. Zhang, J.M., Lin, W.C., Dong, Y.Q., Ju, C.M.: A double-layer interpolation method for BIE implementation for potential problems. Appl. Math. Model. 51, 250–269 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, J.M., Lin, W.C., Dong, Y.Q.: A dual interpolation boundary face method for elasticity problems. Eur. J. Mech. A Solids 73, 500–511 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang, J.M., Chi, B.T., Lin, W.C., Ju, C.M.: A dual interpolation boundary face method for three-dimensional potential problems. Int. J. Heat Mass Transf. 140, 862–876 (2019)

    Article  Google Scholar 

  20. Zhang, J.M., He, R., Chi, B.T., Lin, W.C.: A dual interpolation boundary face method with Hermite-type approximation for potential problems. Appl. Math. Model. 81, 457–472 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, J.M., He, R., Lin, W.C., Yang, L., Chi, B.T., Ju, C.M.: A dual interpolation boundary face method with Hermite-type approximation for elasticity problems. Eur. J. Mech. A Solids 82, 104005 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, Y.: Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  23. Xie, G., Wang, L., Zhang, J., et al.: Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction. Eng. Anal. Bound. Elem. 60, 137–143 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Xie, G., Zhou, F., Zhong, Y., Geng, H., Wu, C.: Bi-directional sinh transformations based on the generalized Duffy space for nearly singular integrals. J. Comput. Appl. Math. 380, 112981 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China under grant numbers 11772125 and 11972010.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

    Pengfei Chai, Jianming Zhang, Rongxiong Xiao, Rui He & WeiCheng Lin

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  1. Pengfei Chai
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  2. Jianming Zhang
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  3. Rongxiong Xiao
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Correspondence to Jianming Zhang.

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Chai, P., Zhang, J., Xiao, R. et al. A multi-domain BEM based on the dual interpolation boundary face method for 3D potential problems. Acta Mech 234, 451–469 (2023). https://doi.org/10.1007/s00707-022-03414-0

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