Geodesic
Comparison of adaptive mesh refinement approaches on distributed computational system
Numerical methods and programming, Tome 26 (2025) no. 1, pp. 33-49.

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The article discusses block-based and tree-based approaches to adaptive mesh refinement on regular meshes. Our goal is to compare the efficiency of approaches in solving problems on a distributed computational system. Descriptions of the approaches and features of the implementation of difference schemes using them are given. A comparison of the efficiency of the approaches in terms of speed and number of mesh elements when performing three-dimensional calculations of the development of Rayleigh–Taylor instability is made. The modeling used a predictor-corrector scheme, a Godunov-type scheme using linear interpolation, and the HLL method. Grid adaptation is applied in the area of mixing of substances. Experiments compliance of a priori estimates of the effectiveness of the approaches obtained as a result of the experiments.
Keywords: adaptive mesh refinement; octree-mesh; parallel computations. 
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     author = {S. K. Grigorjev and A. A. Bay},
     title = {Comparison of adaptive mesh refinement approaches on distributed computational system},
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     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2025_26_1_a4/}
}
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S. K. Grigorjev; A. A. Bay. Comparison of adaptive mesh refinement approaches on distributed computational system. Numerical methods and programming, Tome 26 (2025) no. 1, pp. 33-49. http://geodesic.mathdoc.fr/item/VMP_2025_26_1_a4/