A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection
Lin-Bo Zhang 1*1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China.
Received 13 March 2008; Accepted (in revised version) 10 July 2008
Local mesh refinement is one of the key steps in the 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. This algorithm is used in PHG, Parallel Hierarchical Grid (http://lsec.cc.ac.cn/phg/), a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. 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. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the bisectioning refinement procedure.AMS subject classifications: 65Y05, 65N50
Key words: Adaptive refinement, bisection, tetrahedral mesh, parallel algorithm, MPI.
Email: firstname.lastname@example.org (L.-B. Zhang)