November 3, 2012 17:58 WSPC/INSTRUCTION FILE paper International Journal of Computational Methods c  World Scientific Publishing Company Performance of different integration schemes in facing discontinuities in the Finite Cell Method Alireza Abedian Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran abedian@me.iut.ac.ir Jamshid Parvizian Department of Industrial Engineering, Isfahan University of Technology, Isfahan, Iran japa@cc.iut.ac.ir Alexander D¨ uster Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik (M-10), Technische Universit¨ at Hamburg-Harburg, Hamburg, Germany alexander.duester@tu-harburg.de Hassan Khademyzadeh Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran hkhademyza@me.iut.ac.ir Ernst Rank Lehrstuhl f¨ ur Computation in Engineering, Fakult¨ at f¨ ur Bauingenieur- und Vermessungswesen Technische Universit¨ at M¨ unchen, M¨ unchen, Germany rank@bv.tum.de Received (Day Month Year) Revised (Day Month Year) In many extended versions of the Finite Element Method the mesh does not conform to the physical domain. Therefore, discontinuity of variables is expected when some elements are cut by the boundary. Thus, the integrands are not continuous over the whole integration domain. Apparently, none of the well developed integration schemes such as Gauss quadrature can be used readily. This paper investi- gates several modifications of the Gauss quadrature to capture the discontinuity within an element and to perform a more precise integration. The extended method used here is the Finite Cell Method, an extension of a high order approximation space with the aim of simple meshing. Several examples are included to evaluate different modifications. Keywords: Finite Cell Method; discontinuous integration; Gauss quadrature; quadtree; octree. 1. Introduction Simulation problems quite often involve discontinuous and complex geometries. Discretis- ing with standard finite element methods should respect complex boundaries and disconti- 1