Summary
In manufacturing a common objective is to find the optimal shape of the manufactured product. For instance, in aircraft manufacturing, it is desired to minimize the air resistance around an airplane. To find the optimal shape, a combination of computer simulations and experiments are required. The computer simulations consist of two main steps. The first step is to create a discrete approximation of the object. This can be a time consuming and complex task, requiring manual work.
In this thesis, I present and analyze an alternative finite element discretization scheme aiming to simplify this procedure. The key idea of this discretization scheme is to split the discretization into multiple overlapping geometries, which are then coupled in the physical description of the problem.
The second step is to approximate the physical quantities of interest and decide how to change the object to obtain the desired design. This step is particularly difficult in the setting of time-dependent problems. To this end, I present an automated framework for computation of shape sensitivities in the finite element framework FEniCS. The framework is capable of computing discretely consistent shape sensitivities for non-linear time-dependent partial differential equations.
Before the defence, Jørgen Dokken presentedhis trial lecture "High-performance computing and finite element methods".
The PhD defence and trial lecture were fully digital.
Adjudication committee
- Professor Nicolas Gauger,TU Kaiserslautern, Germany
- Associate Professor Sara Zahedi,KTH Royal Institute of Technology, Sweden
- Professor Xing Cai,Department of Informatics, University of Oslo, Norway
Supervisors
- Dr. Simon Wolfgang Funke,Simula Research Laboratory, Norway
- Professor Kent-Andre Mardal,Department of Mathematics, UiO / Simula Research Laboratory, Norway
- Dr. August Johansson,SINTEF, Norway
Chair of defence
- Associate Professor Petter Nielsen, Department of Informatics, UiO