Engineering with Computers

, Volume 30, Issue 2, pp 161–174 | Cite as

RBF morphing techniques for simulation-based design optimization

  • Daniel SiegerEmail author
  • Stefan Menzel
  • Mario Botsch
Original Article


Morphing an existing simulation mesh according to updated geometric parameters in the underlying computer-aided design model is a crucial technique within fully automatic design optimization. By avoiding costly automatic or even manual meshing, it enables the automatic and parallel generation and evaluation of new design variations, e.g., through finite element or computational fluid dynamics simulations. In this paper, we present a simple yet versatile method for high-quality mesh morphing. Building upon triharmonic radial basis functions, our shape deformations minimize distortion and thereby implicitly preserve shape quality. Moreover, the same unified code can morph tetrahedral, hexahedral, or arbitrary polyhedral meshes. We compare our method to other recently proposed techniques and show that ours yields superior results in most cases. We analyze how to explicitly prevent inverted mesh elements by successively splitting the deformation into smaller steps. Finally, we investigate the performance of different linear solvers as well as the use of an incremental least squares solver for the sake of improved scalability.


Mesh morphing Design optimization Radial basis functions 



The authors kindly thank Matthew Staten from Sandia National Laboratories for providing us with the Bore, Pipe, and Courier models from [35]. We also thank the anonymous reviewers for their useful comments and suggestions. Daniel Sieger gratefully acknowledges the financial support from Honda Research Institute Europe (HRI-EU). Mario Botsch is supported by the German National Research Foundation (DFG CoE 277: CITEC).


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Bielefeld UniversityBielefeldGermany
  2. 2.Honda Research Institute Europe GmbHOffenbach/MainGermany

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