Abstract
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.
Highlights
Computer methods have proved to be a versatile and effective approach for solving boundary value problems
This paper presents a new boundary shape representation for 3D boundary value problems based on parametric triangular Bezier 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)
Summary
Computer methods have proved to be a versatile and effective approach for solving boundary value problems. There have been several attempts to use the domain or boundary decryptions by parametric patches directly in solving boundary value problems This trend is seen especially in the context of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields. It should be pointed out that the proposed boundary shape representation by triangular Bezier surface patches does not need to be divided into any elements, but directly used in the process of solving boundary value problems. To find a solution in the domain, we need to obtain an integral identity known for BIE that makes use of the solution on the boundary obtained by PIES Based on these considerations, computer software has been developed and practically tested on the potential problems modeled by Laplace’s equation. The analysis is concerned with the compatibility of the obtained results with known analytical and numerical solutions available in the literature
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