DVRlib: A C++ library for geometric mesh improvement using Directional Vertex Relaxation

The success of finite element simulations in physical sciences, applied mathematics, and com- puter graphics relies on generating high-quality unstructured meshes. In general, well-shaped elements are essential to ensure accurate numerical approximations, to improve the condi- tioning of systems of equations to be resolved, and to choose reasonable step sizes in time integration schemes.

DVRlib is a C++ library that implements the directional vertex relaxation algorithm introduced in Rangarajan & Lew (2017) to improve qualities of unstructured meshes. DVRlib improves qualities of triangular and tetrahedral elements by iteratively and optimally perturb- ing a selected set of vertices along prescribed directions. During the process, the connectivity of the mesh remains unaltered; just the locations of vertices may change. DVRlib is straight- forward to couple with existing libraries for unstructured mesh generation by invoking the functionalities it provides as a simple post-processing step. Equally significantly, DVRlib enables engineers and researchers to simulate a challenging class of moving boundary problems by helping to maintain good element qualities in deforming meshes.