A boundary element method (BEM) designed for solving the symmetric generalized Wagner formulation is presented. The flow field is parameterized with analytical functions and can describe the kinematics at any free surface or body location using a small set of parameters obtained from a collocation scheme. The method is fast and robust for all deadrise angles, even for flat plate impacts where classical BEMs usually fail. The method is easy to implement and is easy to apply. Given a smooth body contour the only additional input is the requested accuracy. There is no mesh involved. When solving the temporal problem, we exploit the analytical distribution of free surface velocities and apply an integral equation formalism consistent with the Wagner formulation. The output of the spatial and temporal scheme is a set of functions and parameters suitable for fast computation of the complete kinematics for any impact trajectory given the position of the keel and the body velocity. The method is developed to be combined with seakeeping programs for statistical impact and whipping assessment.