Finite element mesh multiplication with boundary smoothing

Abstract

A procedure to improve the boundary geometry of refined finite element meshes is presented. Initially, the coarse mesh is submitted to an uniform refinement by splitting the elements, but maintaining the coarse boundary. Then, the boundary nodes of the refined mesh are filtered. To avoid search overheads, a spatial subdivision technique is applied to the set of reference nodes. To repositionate the remaining nodes i.e., the internal nodes, a simple scheme widely used for moving boundary problems is applied. The capability of this procedure is illustrated showing the stages of the geometry during the process, as well as the mesh volumetric convergence for each level of refinement. This procedure aims to help generating meshes for large-scale problems at runtime instead of generating those meshes using traditional mesh generators.