The motion of surfaces with a velocity depending on the Dirichlet-to-Neumann operator for a given elliptic problem appear in various practical applications ranging from the motion of cells to the geometrical optimisation of mechanical structures. The level-set framework is particularly interesting in this context of moving surfaces. In this work we focus on the computation of the Dirichlet-to-Neumann operator calculation for the Laplace equation, following the ideas developed by C.Kublik et. al. in [1] for the computation of the bulk solution. [1] Catherine Kublik, Nicolay M. Tanushev, Richard Tsai, An implicit interface boundary integral method for Poisson's equation on arbitrary domains, JCP, 2013.