An adaptive rectangular mesh administration and refinement technique with application in cancer invasion models. (English) Zbl 1503.65212
The authors present a new developed mesh structure data administration technique used as machinery for AMR (Aaaptive mesh refinement) on (hyper-)rectangular meshes. The 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. Thanks to the employed rectangular mesh structure, the identification of the siblings and the neighbouring cells is 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. The capabilities and flexibility of the technique are shown in three applications. The first is a generic experiment in the absence of physical or biological laws where the mesh refinement is dictated by synthetic monitor functions. The second is a physical application of the technique and the AMR in the classical case of the Euler equation. The third application is a biological problem: a 2D tumour growth and invasion of the of the ECM (Extra Cellular Matrix) model.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 92C50 | Medical applications (general) |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35Q31 | Euler equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
cancer invasion; mesh administration; adaptive mesh refinement; finite volume method; h-refinementSoftware:
Dendro; libMesh; p4est; ALUGrid; deal.ii; Vascular Modeling Toolkit; DUNE-ALUGrid; AHF; VTK; LAPACK; OpenVolumeMesh; CGAL; DUNEReferences:
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