Abstract
Adaptive mesh refinement (AMR) is a dynamic approach to non-uniform grids which is commonly used to cut the simulation costs of multiscale problems in mathematical modeling of physical phenomena.
In this work, we propose a new dynamic data structure for AMR implementations which is based on a Z-order curve and tiles with variable size. It is a generalization of classical octree and various tile-based octrees, which can be seen as special cases of it. The tree height is dynamically decreased wherever possible by adjusting the number of children of nodes, increasing the size of tiles. Thus, the events of access to neighboring tiles become less frequent, and the complexity of access becomes less. Trivial data serialization presents another advantage of the data structure. In a specific case where the refinement level is constant over some region, the sub-tree height is equal to one, thus the neighbor access is just as simple as in a uniform multidimensional mesh. The structure inherits the locality properties of the Z-order space-filling curve.
In the text, the detailed description of the structure, algorithms for traversal, random access, neighbor search, and mesh adaptation are described.
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Ivanov, A., Perepelkina, A. (2021). Zipped Data Structure for Adaptive Mesh Refinement. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2021. Lecture Notes in Computer Science(), vol 12942. Springer, Cham. https://doi.org/10.1007/978-3-030-86359-3_19
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