Kurzfassung

This project aims at developing, analyzing and numerically implementing combined phasefield and
sharp interface techniques in pde-constrained shape optimization, where the application focuses on
shape optimization in fluid flow. This will be achieved by utilizing on the one hand a phase-field ansatz
with non-smooth homogeneous free energy densities, which yields robust numerical approximations
on grids which are well aligned to the shape, and, by a Darcy-type approach also allows to...This project aims at developing, analyzing and numerically implementing combined phasefield and
sharp interface techniques in pde-constrained shape optimization, where the application focuses on
shape optimization in fluid flow. This will be achieved by utilizing on the one hand a phase-field ansatz
with non-smooth homogeneous free energy densities, which yields robust numerical approximations
on grids which are well aligned to the shape, and, by a Darcy-type approach also allows to simultaneously optimize the topology of the fluid domain. Then, on the other hand a novel, mesh-quality
conserving W 1,∞ −sharp interface approach is used to sharpen out the shapes obtained by the diffuse
interface method. With this approach we expect to overcome well known shortcomings in numerical
shape optimization, where many methods suffer from grid degeneration, in particular when the initial
guess for the optimization algorithm is very different from the final solution.» weiterlesen» einklappen