TY - JOUR
T1 - A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection
AU - Lin-Bo Zhang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 65
EP - 89
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6016.html
KW - Adaptive refinement, bisection, tetrahedral mesh, parallel algorithm, MPI.
AB - <p style="text-align: justify;">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.</p>