Constructing a Volume Geometry Map for Hexahedra with Curved Boundary Geometries

: In (dynamic) adaptive mesh refinement (AMR), a given input mesh is refined and coarsened during the computation to optimally adapt the resolution of the computational mesh to specific requirements. The input mesh is often the output of a mesh generator and provides information on the geometry of the domain. It is desired to keep its resolution as coarse as possible in order to benefit from the AMR mesh hierarchy and efficient mesh indexing algorithms. We present a novel approach to equip the coarse mesh with high-order geometry data and evaluate this geometry on the fine mesh elements in order to ensure geometric accuracy of the refined mesh elements, even for coarse input meshes. To this end, we construct a volume geometry map for hexahedral cells from given curved boundary geometry data and discuss our implementation in a state-of-the-art AMR library