Mathematisches Seminar

Dr. Daniel Elfverson, Umeå University, Schweden: "Shape Optimization using Cut Finite Elements"

15.02.2018 von 14:00 bis 15:00

WR 383 - Raum 306/307

Abstract:

We present a shape and topology optimization method based on the cut finite element method, for the compliance problem in linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity field. The velocity field is defined to be the largest decreasing direction of the shape derivative that resides in a certain Hilbert space. We thus obtain a coupled problem involving three partial differential equations: (1) the elasticity problem, (2) the problem that determines the velocity field, and (3) the transport problem for the level set function along the velocity field. The elasticity problem is solved using a cut finite element method on a fixed back-ground mesh, which completely avoids re–meshing when the domain is updated. We also employ higher order cut approximations including isogeometric analysis for the elasticity problem. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements at the boundary, which provides control of the variation of the solution. We present numerical examples illustrating the performance of the method.

Einladende: J. Ahlkrona

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