Higher-order multi-resolution topology optimization using the finite cell method

Jeroen Peter Groen (Speaker), Martin Ruess (Other), Mathijs Langelaar (Other), Sigmund, O. (Other)

Activity: Talks and presentationsConference presentations


The objective of this work is to present a detailed study on the potential and limitations of performing topology optimization using the Finite Cell Method (FCM) [1]. In previous work the possibility of performing topology optimization with the FCM has been demonstrated [2], furthermore, reductions in computational cost have been reported when analysis- and geometry-mesh are decoupled [3, 4]. In the current work, we shift part of our attention to the limits at which topology optimization with the FCM can be performed, since this will greatly help the maturation of the method.

It is known that the FCM shows superior convergence compared to linear finite elements for smooth structures, however, in topology optimization highly inhomogeneous topologies belong to the solution space [5]. Filter methods are employed to impose a length-scale on the solution, and we demonstrate that the
quality of the corresponding solution depends on both the filter and the properties of the analysis mesh.

Using a large number of numerical examples for both minimum compliance and minimum displacement problems we find parameters for which topology optimization using the FCM results in satisfying topologies. Finally, we present a detailed study on the computational cost of the method, and show its competitiveness compared to the use of linear finite elements. To do so, we present a modification to the FCM to include static condensation of the stiffness matrix, and show a significant gain in efficiency when high polynomial degrees are used.
Event titleECCOMAS Congress 2016: VII European Congress on Computational Methods in Applied Sciences and Engineering
Event typeConference
LocationHersonissos, Greece
Degree of RecognitionInternational


  • p-FEM
  • topology optimization
  • finite cell method