A flexible multidimensional rectangular mesh administration and refinement technique with application in cancer invasion models

We present a mesh-structure data administration technique for the bookkeeping of adaptive mesh refinement, in particular h-refinement, of rectangular parallelepiped meshes. Our technique is a unified approach for 1-, 2- and 3D domains, that can be extended to even higher dimensions. It is easy to use and avoids the traversing of the connectivity graph for the ancestry. Due to the rectangular structure of the mesh, the identification of the siblings and the neighboring cells is also greatly simplified. It is particularly designed for smooth meshes, and uses their smoothness dynamically 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; most notably, the first application of an h-refinement a 2D cancer growth and invasion problem.