Shape Optimization for Time-dependent Domains

Brügger, R. C. . Shape Optimization for Time-dependent Domains. 2021, Doctoral Thesis, University of Basel, Faculty of Science.


Official URL: https://edoc.unibas.ch/87017/

Downloads: Statistics Overview


In this thesis, we treat shape optimization for parabolic equations on time-dependent domains. As a theoretical foundation we extend the solution theory of parabolic boundary integral equations in the canonical Sobolev spaces from the cylindrical to the time-dependent case. The results imply existence and uniqueness of solutions. This is followed by a review of shape optimization theory on time-dependent domains, where we complement a few proofs which seem to be missing in the literature. Building on these foundations we give general formulae for shape gradients of functionals. These theoretical results are complemented by two numerical examples. The first example is concerned with a time-dependent shape detection problem, reformulated as a time-dependent shape optimization problem. The second example is a time-dependent one-phase Stefan problem in multiple dimensions, also reformulated as a shape optimization problem.
Advisors:Harbrecht, Helmut and Grote, Marcus J. and Dambrine, Marc
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Grote, Marcus J.
Item Type:Thesis
Thesis Subtype:Doctoral Thesis
Thesis no:14590
Thesis status:Complete
Number of Pages:117
Identification Number:
  • urn: urn:nbn:ch:bel-bau-diss145903
edoc DOI:
Last Modified:15 Feb 2022 10:54
Deposited On:10 Feb 2022 13:10

Repository Staff Only: item control page