Geometric modeling, isogeometric analysis and the finite cell method

E. Rank, M. Ruess, S. Kollmannsberger, D. Schillinger, A. Düster

Research output: Contribution to journalArticlepeer-review

111 Scopus citations


The advent of isogeometric analysis (IGA) using the same basis functions for design and analysis constitutes a milestone in the unification of geometric modeling and numerical simulation. However, an important class of geometric models based on the CSG (Constructive Solid Geometry) concept such as trimmed NURBS surfaces do not fully support the isogeometric paradigm, since basis functions do not explicitly represent the boundary. The finite cell method (FCM) is a high-order fictitious domain method, which offers simple meshing of potentially complex domains into a structured grid of cuboid cells, while still achieving exponential rates of convergence for smooth problems. In the present paper, we first discuss the possibility to directly couple the finite cell method to CSG, without any necessity for meshing the three-dimensional domain, and then explore a combination of the best of the two approaches IGA and FCM, closely following ideas of the recently introduced shell FCM. The resulting . finite cell extension to isogeometric analysis achieves a truly straightforward transfer of a trimmed NURBS surface into an analysis suitable NURBS basis, while benefiting from the favorable properties of the high-order and high-continuity basis functions. Accuracy and efficiency of the new approach are demonstrated by a numerical benchmark, and its versatility is outlined by the analysis of different trimmed design variants of a brake disk.

Original languageEnglish (US)
Pages (from-to)104-115
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Dec 1 2012

Bibliographical note

Funding Information:
This work has partially been supported by the Excellence Initiative of the German Federal and State Governments via the TUM International Graduate School of Science and Engineering. Schillinger has been supported by the Munich Centre for Advanced Computing (MAC) . This support is gratefully acknowledged.

Copyright 2012 Elsevier B.V., All rights reserved.


  • Embedding domain method
  • Fictitious domain method
  • Finite cell method
  • High-order methods
  • Isogeometric analysis
  • Thin-walled structures

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