Triangular Bzier surface patches in modeling shape of boundary geometry for potential problems in 3D
This paper presents a new boundary shape representation for 3D boundary value problems based on parametric triangular Bzier 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.
triangular bzier surface patches potential problems parametric integral equation system (pies) boundary integral equations (bie) laplaces equation