Nonlinear graded Delaunay meshes

Abstract

Starting with a boundary triangulation an algorithm automatically generates graded densities of triangular elements inside arbitrary polygonal domains. Interior nodes generated inside acute triangles receive spacing values from Bezier based nonlinear spacing functions defined on interior edges and a nonlinear interpolant defined over triangles. Nodal spacing values, adaptive breakpoints and a single G-value control densities of nodes and offer a range of graded meshes. Predetermined nodes with spacing values and internal boundaries provide additional initial control of nodal densities.