## 1 Introduction
The method models the body boundary using a single continuous NURBS function thus makes the geometry discretization independent of the evaluation points and separates the kernels calculation from the interpolation functions. These properties allow us to modify the boundary to solve problems like the contact between two bodies. The mechanical contact has been extensively studied. [PERSON] [13] described the best-known analytical contact models, such as the Hertz model, the JKR model, and the Bradley model, among others. The Hertz model relates the contact area and the material properties; the JKR model uses the same assumption but adds the interfacial interaction strength; and, finally, the Bradley model considers the external Van der Waals interactions that add load to the contact. In the numerical methods used in continuum mechanics, the most popular algorithm to analyze the contact is the master-slave. This method consists in projecting the nodes of an elastic body (slave) onto a rigid body (master) when a force is applied. If the slave-node penetrates the body of the master, a force is used in the contact area to return the slave-node to the outer surface of the master. Thereby, the deformation of two bodies in contact is found. This algorithm has been widely used with FEM [14, 15, 16] and has recently been combined with IGA [17, 18, 19, 20, 21, 22, 23, 24]. Nevertheless, the main disadvantage of this method is that applied contact force is not a real force. Additionally, every time this force is used, the contact zone must be found again and verified for penetration. In case penetration is found, another force must be applied, so the algorithm iterates until there is no penetration. When using BEM, the problem is solved differently [25]. The nodes that are in the contact zone must satisfy two general conditions: there must be continuity between their displacements (not overlapping), and their tractions must be the same but in the opposite direction [25, 26, 27, 28]. As the contact area is not known in advance, the analysis starts with a first contact zone, which is modified until the nodes satisfy the contact conditions. Although the contact is more easily modeled with BEM than with FEM, the analysis draws the disadvantages of BEM, such as the sensitivity to the analysis-points selection that leads to errors in the numerical calculation of the integrals. This investigation takes the best features of IGA and BEM to overcome the inconveniences of the conventional BEM. The analysis points of the geometry are separated from the bodies in contact, and the particle swarm optimization (PSO) algorithm is used to find the contact area. In this way, the control points of the NURBS are modified repeatedly, until a correct area is found. With the proposed method, the solution domain is closed (not discrete), by defining the boundary with a single NURBS, and with fewer analysis points in contrast to traditional FEM. This paper is arranged as follows: Section 2 presents the basis to understand the isogeometric boundary element method, such as the NURBS functions and conventional BEM. Section 3 sets the guidelines to implement the modified IGA-BEM, and later, it details the methodology to be implemented in conjunction with the optimization algorithm. The following section presents the results and properties of the analyzed bodies, as well as a comparison with FEM and BEM. Finally, Section 5 concludes the work and defines future work with the theory presented.