| dc.description.abstract | We consider topology optimisation of two-dimensional Stokes flow. The objective
is to distribute a certain amount of solid material in a given domain, such that
the total power dissipation is minimised. A generalised Stokes problem acts as
the governing PDE, and both existence of solutions to the state equations and the
optimisation problem is shown. The optimisation problem is solved using the optimality
criteria method, and the MINRES method is used for solving the algebraic
linear system arising from discretising the governing PDE with the finite element
method. Residual estimates are used in order to prematurely stop MINRES, and
the results indicate that the residual related to the momentum part of the Stokes
equations is sufficient for formulating a meaningful stopping criterion. Through
testing the algorithm on several different numerical examples, we propose a tolerance
such that the total number of MINRES iterations is low, while largest observed
error in the resulting objective value is 3.5% compared to when the linear system is
solved exactly. Adaptive mesh refinement based on the elementwise residual estimates
is performed during the course of the optimisation, and it was found that this
approach yields a significant reduction in the residuals when compared to starting
with a fine mesh. | |
