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

TL;DR

This paper introduces a unified, memory-efficient adaptive mesh refinement technique for rectangular meshes applicable in 1D, 2D, and 3D, demonstrated on tumor growth models.

Contribution

It presents a novel, easy-to-use administration method for adaptive mesh refinement that simplifies neighbor and sibling identification on rectangular meshes.

Findings

Effective in 2D tumor invasion modeling

Reduces memory footprint of mesh management

Applicable across multiple dimensions

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.