Computational Morphogenesis: Morphologic constructions using polygonal discretizations. (22nd October 2020)

• Record Type: Journal Article
• Authors: Choi, Habeun; Chi, Heng; Park, Kyoungsoo; Paulino, Glaucio H.
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 1(2021)
• Page Start: 25
• Page End: 52
• Publication Date: 2020-10-22
• Subjects: adaptive mesh coarsening -- error estimation -- polygonal elements -- unstructured mesh -- virtual element method; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6519
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: To consistently coarsen arbitrary unstructured meshes, a computational morphogenesis process is built in conjunction with a numerical method of choice, such as the virtual element method with adaptive meshing. The morphogenesis procedure is performed by clustering elements based on a posteriori error estimation. Additionally, an edge straightening scheme is introduced to reduce the number of nodes and improve accuracy of solutions. The adaptive morphogenesis can be recursively conducted regardless of element type and mesh generation counting. To handle mesh modification events during the morphogenesis, a topology‐based data structure is employed, which provides adjacent information on unstructured meshes. Numerical results demonstrate that the adaptive mesh morphogenesis effectively handles mesh coarsening for arbitrarily shaped elements while capturing problematic regions such as those with sharp gradients or singularity.