The Extended Finite Element Method

Abstract

Abstract.This chapter discusses level-set topology optimization methods where the governing state equations are discretized by the Extended Finite Element Method (XFEM). In contrast to conventional methods that map the level-set function into a density distribution of a fictitious material, the XFEM allow preserving the crisp geometry information of level-sets in the mechanical model. A brief introduction into the XFEM will be provided and its application to topology optimization will be illustrated with problems in fluid mechanics.