A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection |
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Authors: | LinBo Zhang |
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Institution: | 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. |
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Abstract: | 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/J, 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 |
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Keywords: | Adaptive refinement bisection tetrahedral mesh parallel algorithm MPI |
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