The finite cell method for polygonal meshes: poly-FCM

• Published in: Computational mechanics Vol. 58; no. 4; pp. 587 - 618
• Main Authors: Duczek, Sascha, Gabbert, Ulrich
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Engineering; Mathematical analysis; Numerical integration; Original Paper; Theoretical and Applied Mechanics; Finite cell method; Polygonal finite element methods; Fictitious domain method; Generalized barycentric coordinates
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-016-1307-x

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.