Simulation-based optimisation with dynamic domains

Computer-based optimisation is finding its way into nearly all disciplines of science and engineering. Already today, it is used to design more efficient cars and airplanes, to control large wind farms, to predict the dynamics of the atmosphere and the ocean, and to improve the extraction of oil from reservoirs. However, today's computer-based optimisation techniques typically assume a fixed, or nearly fixed simulation geometry. This assumption is a severe limitation for many real-world engineering and biological processes: for example wind and water turbines and the human cardiovascular system undergo great rotations and deformations that need to be captured in a representative computer model. Therefore, the grand challenge is to able to optimise systems with dynamic geometries, that is, geometries that change in time. The overall ambition of the OptCutCell project is to enable the solution of optimisation problems with dynamic geometries. To achieve this goal, we will develop the required mathematical and numerical methods, as well as generic, user-friendly, open-source simulation and optimisation software. The mathematical and numerical methods will be based on a multi-mesh approach, in which multiple, independent simulation geometries can overlap and interact with each other. The software will be developed within the FEniCS and the dolfin-adjoint framework, winner of the 2015 Wilkinson Prize for Numerical Software. The new software platform will be demonstrated and tested on two industrial and scientific applications: the optimal design of a stent to minimise risk of blood vessel rupture, and the optimisation of tidal stream turbine performance.

The project developed novel algorithms for the numerical simulation and optimisation of physical processes on multiple independent meshes. These methods have been integrated into the open-source software FEniCS and dolfin-adjoint.

Optimisation is the process of making something as fully perfect as possible. This proposal focuses on optimisation in the context of science and engineering. Optimisation constrained by mathematical models can be found across all scientific disciplines, for instance in design, inversion, and control problems. Many such systems involve domains that change in time, so-called dynamic domains. This class of problems is challenging for simulation and optimisation, and can generally not be solved using existing methods, tools and techniques. The overall ambition of this project is to enable the solution of general optimisation problems with dynamic domains. To achieve this goal, we seek to develop new mathematical and numerical methods, and a generic, user-friendly, open source optimisation platform. This platform will be demonstrated and tested on two large-scale scientific applications: the optimal design of a stent to minimise risk of blood vessel rupture, and the optimisation of tidal stream turbine performance. This project is headed by Dr. Simon Funke and brings together researchers from Simula Research Laboratory, Umeå University, Chalmers University of Technology, Technische Universität Darmstadt and two industrial partners: Stryker Corporation and Andritz Hydro Hammerfest. These partners join in a multidisciplinary collaboration involving computer science, applied mathematics, bioengineering, and perspectives from the medical and renewable energy industry sectors.