Triangulation of p-Order Parametric Surfaces

Abstract

The generation of triangulations on p-order parametric surfaces is a fundamental first step to numerical solutions for multidomain problems involving complex geometries such as those encountered in biological fluid dynamics and other applications. In this study we develop a novel, computationally efficient method for generating triangulations in computational space, which, under parametric mapping, are of high geometric quality. Computational efficiency is maintained over parametric orders (p) through approximating the parametric surface by a grid of simplified vector functions. Unlike other length metric approximations, a maximum bound on the error introduced to the calculation of lengths by this approximation is defined to ensure the fidelity of the transformation. This technique is applied to three parametric functions which demonstrate its robustness in handling high mesh distortions, singularities, and high order surfaces. Further, three complex high-order biological finite element meshes are triangulated. High mesh quality and a linear relationship between triangle generation and CPU time is observed for each of these meshes.