An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models

Journal of Computational and Applied Mathematics, vol. 416, pp. 114442

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.

Authors 2

1. Niklas Kolbe Aachen Institute of Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute of Geometry and Practical Mathematics, RWTH Aachen University, Germany

2. Nikolaos Sfakianakis corresponding

   University of St Andrews

   Affiliation as printed

   School of Mathematics and Statistics, University of St Andrews, UK