Bezier curves in the modification of boundary integral equations (BIE) for potential boundary-values problems

The paper presents a modification of the classical boundary integral equation method (BIEM) for two-dimensional potential boundary values problems. The proposed modification consists in describing the boundary geometry by means of Bézier curves. As a result of this analytical modification of the BIEM, a new parametric integral equation system (PIES) was obtained. The kernels of these equations include the geometry of the boundary. This new PIES is no longer defined on the boundary, as in the case of the BIEM, but on the straight line for any given domain. The solution of the new PIES does not require a boundary discretization since it can be reduced merely to an approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with exact solutions.