Original Article

Engineering with Computers

, Volume 29, Issue 4, pp 517-527

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Triangular Bézier surface patches in modeling shape of boundary geometry for potential problems in 3D

  • Eugeniusz ZieniukAffiliated withFaculty of Mathematics and Computer Science, University of Bialystok Email author 
  • , Krzysztof SzerszenAffiliated withFaculty of Mathematics and Computer Science, University of Bialystok


This paper presents a new boundary shape representation for 3D boundary value problems based on parametric triangular Bézier surface patches. Formed by the surface patches, the graphical representation of the boundary is directly incorporated into the formula of parametric integral equation system (PIES). This allows us to eliminate the need for both boundary and domain discretizations. The possibility of eliminating the discretization of the boundary and the domain in PIES significantly reduces the number of input data necessary to define the boundary. In this case, the boundary is described by a small set of control points of surface patches. Three numerical examples were used to validate the solutions of PIES with analytical and numerical results available in the literature.


Boundary integral equations (BIE) Parametric integral equation system (PIES) Laplace’s equation Potential problems Triangular Bézier surface patches