Cut Finite Element Methods with Application Design Optimization

Daniel Elfverson
Department of Mathematics and Mathematical Statistics, Umeå University

Abstract:

We present both a shape and topology optimization procedures based on the cut finite element method (CutFEM) to optimize the design for a elasticity problem. The CutFEM is a fictitious domain method where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion. To stabilize the method on the cut boundary, certain terms are added which provide the necessary control of the variation in the solution.

In the optimization procedures the elasticity problem is solved using the CutFEM on a fixed background mesh, completely avoiding remeshing as the domain is evolved. We also employ higher order cut approximations including isogeometric methods based on B-spline approximations paces of maximum regularity. We present numerical examples both in 2D and 3D illustrating the behavior and performance of the optimization procedures.