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Article History

Received: 23 November 2022

Revised: 2 May 2023

Accepted: 13 September 2023

First Online: 9 October 2023

Declarations

:

: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors that could have appeared to influence the work reported in this paper.

: Concerning the reproducibility of the numerical results, we remark on the following: We run the numerical experiments of Sect.  using the following standard ingredients: (i) Gmsh code to define the geometry, mesh, and mesh attributes for imposing the boundary conditions Geuzaine and Remacle ; (ii) Mfem code to assemble the elasticity system and support the adaptivity functionalities Anderson et al. ; (iii) Hypre code to support the manipulation of vector and matrices of coefficients using the ParCSR format Falgout et al. ; (iv) ParMeTis code to obtain the subdomains for the parallel execution using graph partitioning Karypis and Schloegel ; (v) Vtk code to store the results efficiently using Xdmf (eXtensible Data Model and Format) for HPC codes Schroeder et al. ). We develop an in-house code using the functionalities of Mfem and Hypre libraries to generate the mesh transfer operators between the non-conforming meshes to improve the computing performance of the adaptive GMG preconditioner. The authors are happy to be contacted by those readers interested in more details about the functionalities of Mfem and Hypre libraries used by our in-house code.