2020/11/04 by Stefan A. Funken, Anja Schmidt, Funken, Stefan A. +1
Computer Science · Engineering · #3D Shape Modeling and Analysis #65M50 #Advanced Numerical Analysis Techniques #Advanced Surface Polishing Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2011.02537
openalex publication_date 2020/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Adaptive meshing includes local refinement as well as coarsening of meshes.\nTypically, coarsening algorithms are based on an explicit refinement history.\nIn this work, we deal with local coarsening algorithms that build on the\nrefinement strategies for triangular and quadrilateral meshes implemented in\nthe ameshref package (Funken and Schmidt 2018, 2019). The ameshref package is a\nMATLAB-toolbox for research and teaching purposes which offers the user a\ncertain flexibility in the REFINE step of an adaptive finite element method but\ncan also be used in other contexts like computer graphics. This toolbox is now\nbe extended by the coarsening option. In ameshref, no explicit information\nabout the refinement process is stored, but is instead implicit in the data\nstructure. In this work, we present coarsening algorithms that use\neasy-to-verify criteria to coarsen adaptively generated meshes by exploiting\nthe data structure. Thereby, the desired properties are guaranteed and\ncomputational efficiency is maintained. A MATLAB implementation and some\nnumerical examples are discussed in this work and are included in full in the\ntoolbox ameshcoars (Funken and Schmidt 2020).\n