SURFACE DISCRETIZATION OF R-FUNCTIONS DEFINED GEOMETRICAL OBJECTS

Abstract

This article describes actual problem of an automatic generation of finite elements for complex geometrical objects defined by implicit R-functions of V. L. Rvachev. Rvachev’s approach of geometrical objects description is universal. R-functions allow create models of complex solids in constructive manner. Author describes functional approach for modeling of solids and methods of surface meshing in the first section of the article. This section also contains mathematical model of the surface finite elements mesh. Section II describes approaches for the surface mesh optimization. Author describes new some functions of quality of the mesh. Proposed approaches based on minimization of deviation between functional and mesh representations of geometrical objects. Proposed approaches allow define regular and irregular elements of the mesh for local refinement of the mesh. Author uses differential characteristics of the mesh for the non-uniform mesh generation. Surface curvature used for control of the non-uniform mesh generation.