A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection
Linbo Zhang · Numerical Mathematics Theory Methods and Applications · 2009
Local mesh refinement is one of the key steps in implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. The algorithm is part of PHG, Parallel Hierarchical Grid, a toolbox under development for parallel adaptive multigrid solution of PDEs. The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Some general properties on local refinement of conforming tetrahedral meshes using bisec-tion are also discussed which are useful in analysing and validating the parallel refinement algorithm as well as in simplifying the implementation.