Novel Graph-based Adaptive Triangular Mesh Refinement for Finite-volume Discretizations

Abstract

A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve time-dependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical and analytical tests were carried out in order to study the required execution time and the data storage cost. These tests confirmed the advantages of the approach proposed in elliptic and parabolic problems.