AUTOMATIC ADAPTIVE FINITE-ELEMENT MESH GENERATION OVER RATIONAL B-SPLINE SURFACES

A new approach is suggested for the generation of adaptive finite elem ent meshes over three-dimensional surfaces. The surfaces to be meshed are represented as the unions of rational B-spline surface (RBSS) patc hes such that the mesh generation process is reduced to the formation of nodes and elements in a parametric space. A robust and refined tria ngular element formation procedure is employed for the generation of h ighly skewed meshes in the parametric space such that well-shaped fini te elements are obtained after mapping back to the three-dimensional ( 3D) space. By carefully monitoring the geometrical distortion effect d ue to the parametric mapping, the suggested element formation procedur e can be used on convoluted and rough surfaces without impairing the q uality of the meshes generated. In fact, the proposed generation schem e can easily be extended to many other bivariate surfaces without majo r modification. A simple and effective conversion scheme is also devel oped for the generation of pure quadrilateral meshes. Numerical experi ments show that the operational complexity of the surface mesh generat or is exactly the same as in two-dimensional (2D) planar mesh generati on. High quality finite element meshes with element size grading compa tible with the specified node spacing requirement are generated within a reasonable time limit in a common small computing environment. (C) 1998 Elsevier Science Ltd. All rights reserved.