CAD-based Adaptive Mesh Refinement
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This research explores the need for and implementation of CAD-based Adaptive Mesh Refinement (AMR) in the context of tree-based AMR. Tree-based AMR is a semi-structured AMR approach using an unstructured input mesh (coarse mesh), whose cells are further refined via refinement trees into a fine mesh of computational elements. Using this scalable and memory-efficient approach, it is possible to scale to millions of MPI ranks and trillions of elements. The geometry of the fine elements does not need to be stored in memory, but is derived from the geometry information of the coarse mesh. This approach, while effective for many applications, encounters limitations in accurately representing curved geometries with commonly used methods like Lagrangian basis functions. Since the only geometrical information left in the mesh are the high-order nodes of the coarse mesh cells, any refined element will have the same geometrical resolution as the provided coarse mesh. In response to this challenge, we propose and implement a CAD-based mapping scheme that overcomes the limitations associated with the loss of geometrical information. The introduced mapping scheme leverages the CAD engine OpenCASCADE Technology, enabling the representation of curved elements with enhanced precision and fidelity. By integrating CAD into our AMR library t8code, our methodology not only preserves the efficiency and adaptability of the forest-of-trees approach but also extends its applicability to complex geometries and scenarios.
