Numerical Algorithms

, Volume 80, Issue 3, pp 753–780

# A separation between the boundary shape and the boundary functions in the parametric integral equation system for the 3D Stokes equation

• Eugeniusz Zieniuk
• Krzysztof Szerszeń
Open Access
Original Paper

## Abstract

The paper introduces the analytical modification of the classic boundary integral equation (BIE) for Stokes equation in 3D. The performed modification allows us to obtain separation of the approximation boundary shape from the approximation of the boundary functions. As a result, the equations, called the parametric integral equation system (PIES) with formal separation between the boundary geometry and the boundary functions, are obtained. It enables us to independently choose the most convenient methods of boundary geometry modeling depending on its complexity without any intrusion into the approximation of boundary functions and vice versa. Furthermore, we investigated the possibility of the modeling of the domains bounded by rectangular and triangular parametric Bézier patches. The boundary functions are approximated by generalized Chebyshev series. In addition, numerical techniques for solving the obtained PIES have been developed. The effectiveness of the presented strategy for boundary representation by surface patches in connection with PIES has been studied in numerical examples.

## Keywords

Parametric integral equation system (PIES) Boundary integral equation (BIE) Stokes equation Bézier surface patches

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