  Partition of unity methods, such as the extended finite element method (XFEM)
allow discontinuities to be simulated independently of the mesh [1]. This
eliminates the need for the mesh to be aligned with the discontinuity or
cumbersome re-meshing, as the discontinuity evolves. However, to compute the
stiffness matrix of the elements intersected by the discontinuity, a
subdivision of the elements into quadrature subcells aligned with the
discontinuity is commonly adopted. In this paper, we use a simple integration
technique, proposed for polygonal domains [2] to suppress the need for element
subdivision. Numerical results presented for a few benchmark problems in the
context of linear elastic fracture mechanics and a multi-material problem, show
that the proposed method yields accurate results. Owing to its simplicity, the
proposed integration technique can be easily integrated in any existing code.
