Archives of Acoustics, 31, 1, pp. 99-111, 2006

A solution of 3D Helmholtz equation for boundary geometry modeled by Coons patches using the Parametric Integral Equation System

E. ZIENIUK
University of Białystok, Department of Mathematics and Physics Institute of Computer Science

K. SZERSZEŃ
University of Białystok, Department of Mathematics and Physics Institute of Computer Science

In this paper, the authors propose an algorithm for numerical solution of the 3D Helmholtz equation using the Parametric Integral Equation System (PIES). The PIES, unlike the traditional Boundary Integral Equation (BIE), is characterized by the fact that the boundary geometry has been considered in its mathematical formalism. Polygonal Coons surfaces have been used to describe the 3D domain. This makes it possible to obtain continuous solutions without any discretization of the 3D domain.
Keywords: Helmholtz equation, Boundary Integral Equation (BIE), Parametric Integral Equation System (PIES)
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