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The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out. MSC 2010: 35J25, 65N38, 49K10, 49Q10, 53A04

A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method