## 6 Conclusions  
The CISAMR algorithm has been extended to generate conforming meshes for polycrystalline microstructures in 2D. This non-iterative algorithm, named PolyCISAMR, uses a segregated meshing strategy to discretize individual grains independently of other grains and then merge them to build the FE model, which makes it suitable for meshing huge microstructures and allows for efficient parallelization in the future. An automated image processing algorithm has been presented for converting low-resolution pixelated images of a polycrystal to a NURBS representation of grains for use as an input file to the PolyCISAMR meshing algorithm. This manuscript further addresses new algorithmic aspects of CISAMR such as the treatment of extremely sharp corners of grains by using an element collapse approach to preserve the mesh quality. A detailed mesh refinement study and several example problems have been presented to demonstrate the application of the proposed framework in modeling polycrystalline microstructures. Two alloy systems were adopted from the previous modeling work of the co-authors, and the computed macroscale trends were in agreement with these prior results. Additionally, in stark contrast to the pixelated meshes that we investigated, the elemental contour fields computed from the high-quality meshes generated using PolyCISAMR were free of oscillations and captured stress localizations near grain boundaries. Key insights from this work include:  
Figure 31: CPFEM simulation results in the slice with hydrides at a strain level of 0.0026: (**a**) Axial stress \(\sigma_{xx}\) (**b**) Axial strain \(\epsilon_{xx}\). Figure 32: CPFEM simulation results in the slice with hydrides at a strain level of 0.008: (**a**) Axial stress \(\sigma_{xx}\) (**b**) Axial strain \(\epsilon_{xx}\). * Our numerical examples show that the presented framework is suitable for modeling polycrystalline microstructures. * The CPFE simulations performed on conforming meshes generated using PolyCISAMR are superior to those obtained using pixelated meshes, as the artificial stress concentrations along the jagged boundaries in the latter are eliminated when using PolyCISAMR conforming meshes. Future work involves the extension of the proposed image processing and segregated meshing algorithms to 3D, which requires further modifications to the latest version of the CISAMR algorithm [57] to ensure conformity of the nodes along neighboring grain boundaries, especially along their sharp edges/corners. When this is accomplished, it will be possible to merge individual grain meshes to generate conforming meshes for the 3D polycrystals. Moreover, as mentioned earlier, the PolyCISAMR algorithm in its current form is segregated in nature, enabling efficient parallelization without any communication overhead. Future efforts will be devoted to developing a parallel version of PolyCISAMR, which can then be used to mesh massive polycrystalline microstructures. Conceptualization, S.S. and T.T. ; methodology, B.V., A.N., S.P. and W.H.I. ; software, B.V., A.N., S.P. and W.H.I. ; validation, W.H.I. and T.T. ; formal analysis, B.V., W.H.I., S.P. and T.T. ; investigation, B.V., W.H.I. and T.T. ; resources, S.S. and T.T. ; data curation, B.V. and A.N. ; writing--original draft preparation, B.V., T.T., S.P. and S.S.; writing--review and editing, S.S. and T.T. ; visualization, B.V., S.S., W.H.I., and T.T. ; supervision, S.S. and T.T. ; project administration, S.S.; funding acquisition, S.S. All authors have read and agreed to the published version of the manuscript. This work has been supported by the Air Force Office of Scientific Research (AFOSR) under grant number FA9550-21-1-0245. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to ongoing research utilizing the same data. The authors acknowledge the allocation of computing resources by The Ohio State University Simulation Innovation and Modeling Center (SIMCenter) and the Ohio Supercomputer Center (OSC).