Archives of Acoustics, 34, 1, pp. 51–61, 2009

Triangular Bezier patches in modelling smooth boundary surface in exterior Helmholtz problems solved by the PIES

Eugeniusz ZIENIUK
University of Białystok, Faculty of Mathematics and Computer Science

Krzysztof SZERSZEŃ
University of Białystok, Faculty of Mathematics and Computer Science

The paper proposes the use of triangular parametric Bezier
patches as a new and effective way to generate three-dimensional boundaries in
acoustics problems. The boundary geometry composed of triangular Bezier patches
has been directly linked to the parametric integral equation system (PIES) to
numerical solving exterior Helmholtz problems. A primary advantage of the
proposed approach is to avoid the necessity of conventional domain or boundary
discretization. The obtained numerical solutions compared with literature exacts
results are characterized by high accuracy and convergence.
Keywords: Helmholtz equation; acoustics problems; the parametric integral equation system (PIES); triangular Bezier patches
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