BÉZIER CURVES IN THE MODELING OF BOUNDARY GEOMETRY FOR 2D BOUNDARY PROBLEMS DEFINED BY HELMHOLTZ EQUATION

Abstract

The paper uses analytical modification of the classical boundary integral equations (BIEs) for the Helmholtz equation to facilitate the process of practical definition of the boundary geometry. Instead of defining the boundary by means of a boundary integral, the modification makes use of Bézier curves exclusively. As a result, a new parametric integral equation system (PIES) is obtained in which boundary geometry is taken into account in original fundamental boundary solutions. Such boundary definition makes it easy to approximate boundary functions. The proposed method to obtain numerical solution of the PIES for the Helmholtz equation is characterized by high effectiveness.