Numerical integration technique in computation of extended finite element method

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.