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On hp refinements of independent cover numerical manifold method—some strategies and observations

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Abstract

In this paper, strategies are provided for a powerful numerical manifold method (NMM) with h and p refinement in analyses of elasticity and elasto-plasticity. The new NMM is based on the concept of the independent cover, which gets rid of NMM’s important defect of rank deficiency when using higher-order local approximation functions. Several techniques are presented. In terms of mesh generation, a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement. As to the condition number, a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch; an overlapping width of 1%–10% can ensure a good condition number for 2nd, 3rd, and 4th order local approximation functions; the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch. On numerical accuracy, local approximation using complete polynomials is necessary for the optimal convergence rate. Two issues that may damage the convergence rate should be prevented. The first is to approximate the curved boundary of a higher-order element by overly few straight lines, and the second is excessive overlapping width. Finally, several refinement strategies are verified by numerical examples.

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Authors and Affiliations

  1. School of Civil Engineering, Qinghai University, Qinghai, 810016, China

    Ning Zhang

  2. Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing, 100081, China

    Hong Zheng & WenAn Wu

  3. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100091, China

    Xu Li

Authors
  1. Ning Zhang
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  2. Hong Zheng
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  3. Xu Li
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  4. WenAn Wu
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Corresponding author

Correspondence to Ning Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52130905 and 52079002).

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Zhang, N., Zheng, H., Li, X. et al. On hp refinements of independent cover numerical manifold method—some strategies and observations. Sci. China Technol. Sci. 66, 1335–1351 (2023). https://doi.org/10.1007/s11431-022-2221-5

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  • DOI: https://doi.org/10.1007/s11431-022-2221-5

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