An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models
Abstract
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing the connectivity graph of the ancestry of mesh cells. Due to the employed rectangular mesh structure, the identification of the siblings and the neighbouring cells is greatly simplified. The administration technique is particularly designed for smooth meshes, where the smoothness is dynamically used in the matrix operations. It has a small memory footprint that makes it affordable for a wide range of mesh resolutions over a large class of problems. We present three applications of this technique, one of which addresses h-refinement and its benefits in a 2D tumour growth and invasion problem.
Citation
Kolbe , N & Sfakianakis , N 2022 , ' An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models ' , Journal of Computational and Applied Mathematics , vol. 416 , 114442 . https://doi.org/10.1016/j.cam.2022.114442
Publication
Journal of Computational and Applied Mathematics
Status
Peer reviewed
ISSN
0377-0427Type
Journal article
Description
NK was supported by the Postdoctoral Fellowships for Research in Japan (Standard) of the Japan Society for the Promotion of Science. NS was partly funded from the German Science Foundation (DFG) under the grant SFB 873: “Maintenance and Differentiation of Stem Cells in Development and Disease”.Collections
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