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Abstract

For the administration of adaptive mesh refinement on (hyper-)rectangular meshes, we provide a method. Our method is an efficient, easy-to-use method for h-refinement on 1-, 2-, and 3-D domains that does not need navigating the connectivity graph of the ancestry of mesh cells. The use of a rectangular mesh structure substantially facilitates the detection of siblings and nearby cells [1-15]. The administration method is especially made for meshes that are smooth since matrix operations use smoothness on an as-needed basis. It is inexpensive for a variety of mesh resolutions over a broad class of issues thanks to its modest memory footprint. We provide three uses for this method, one of which discusses the advantages of h-refinement in a 2D setting.

Adaptive mesh refinement (AMR) has frequently been used to increase the precision of numerical techniques and lessen their computing weight. AMR is frequently used in the domains of engineering, astronomy, and fluid dynamics, where the related techniques have become an essential part of the total numerical inquiry. Mathematical biology, on the other hand, has not yet seen much of their use. Examples are available.