Publications

Articles in journals and refereed proceedings volumes

K. Welker:Suitable spaces for shape optimization, 2018. (arXiv:1702.07579)

B. Führ, V. Schulz and K. Welker:Shape optimization for interface identification with obstacle problems. Vietnam Journal of Mathematics, 2018. DOI: 10.1007/s10013-018-0312-0

A. Panotopoulou, E. Ross, K. Welker, E. Hubert and G. Morin:Scaffolding a skeleton. In: A. Gençtav et al., editors, Research in Shape Analysis, Association for Woman in Mathematics, pages 17-35, Springer, 2018. DOI: 10.1007/978-3-319-77066-6 (PDF)

V. Schulz and K. Welker: On optimization transfer operators in shape spaces, Appears in: V. Schulz and D. Seck, editors, Shape Optimization, Homogenization and Optimal Control, International Series of Numerical Mathematics, Volume 169, pages 259–275. Springer, 2018.

M. Siebenborn and K. Welker:Computational aspects of multigrid methods for optimization in shape spaces, SIAM Journal on Scientific Computing, 39(6):B1156-B1177, 2017. (arXiv:1611.05272)

K. Welker:Optimization in the space of smooth shapes, In: F. Nielsen and F. Barbaresco, editors, Geometric Science of Information, Lecture Notes in Computer Science, Volume 10589, pages 65-72, Springer, 2017. DOI: 10.1007/978-3-319-68445-1_8.

V. Schulz, M. Siebenborn and K. Welker:Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics, SIAM Journal on Optimization, 26(4):2800-2819, 2016. (arXiv:1506.02244)

V. Schulz, M. Siebenborn and K. Welker:PDE constrained shape optimization as optimization on shape manifolds, In: F. Nielsen and F. Barbaresco, editors, Geometric Science of Information, Lecture Notes in Computer Science, Volume 9389, pages 499-508, Springer, 2015. DOI: 10.1007/978-3-319-25040-3_54.

V. Schulz, M. Siebenborn and K. Welker:Structured inverse modeling in parabolic diffusion problems, SIAM Journal on Control and Optimization, 53(6):3319-3338, 2015. (arXiv:1409.3464)

V. Schulz, M. Siebenborn and K. Welker:Towards a Lagrange-Newton approach for PDE constrained shape optimization, In: A. Pratelli and G. Leugering, editors, Trends in PDE Constrained Shape Optimization, International Series of Numerical Mathematics, Volume 166, pages 229-249, Springer, 2015. DOI: 10.1007/978-3-319-17563-8. (arXiv:1405.3266)

Thesis

K. Welker:Efficient PDE constrained shape optimization in shape spaces, PhD Thesis, Trier University, 2016. (PDF)

K. Welker:Riemannian metrics on the shape space (in german), Diploma Thesis, Trier University, 2013.