Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes

Arne Nägel, Volker Schulz, Martin Siebenborn*, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this work we consider inverse modeling of the shape of cells in the outermost layer of human skin. We propose a novel algorithm that combines mathematical shape optimization with high-performance computing. Our aim is to fit a parabolic model for drug diffusion through the skin to data measurements. The degree of freedom is not the permeability itself, but the shape that distinguishes regions of high and low diffusivity. These are the cells and the space in between. The key part of the method is the computation of shape gradients, which are then applied as deformations to the finite element mesh, in order to minimize a tracking type objective function. Fine structures in the skin require a very high resolution in the computational model. We therefor investigate the scalability of our algorithm up to millions of discretization elements.

Original languageEnglish (US)
Pages (from-to)79-88
Number of pages10
JournalComputing and Visualization in Science
Issue number2
StatePublished - Aug 13 2015


  • High performance optimization
  • Inverse problems
  • Shape optimization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics


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