Commun. Comput. Phys.,
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Volume 4.


Parallel Mesh Refinement of Higher Order Finite Elements for Electronic Structure Calculations

Dier Zhang 1*, Aihui Zhou 2, Xin-Gao Gong 1

1 Department of Physics, Fudan University, Shanghai 200433, China.
2 LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.

Received 29 February 2008; Accepted (in revised version) 29 May 2008
Available online 16 July 2008

Abstract

The finite element method is a promising method for electronic structure calculations. In this paper, a new parallel mesh refinement method for electronic structure calculations is presented. Some properties of the method are investigated to make it more efficient and more convenient for implementation. Several practical issues such as distributed memory parallel computation, less tetrahedra prototypes, and the assignment of the mesh elements carried out independently in each sub-domain will be discussed. The numerical experiments on the periodic system, cluster and nano-tube are presented to demonstrate the effectiveness of the proposed method.

AMS subject classifications: 81Q05, 65L50

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Key words: Tetrahedral mesh, adaptive mesh refinement, parallel algorithms, electronic structure calculations.

*Corresponding author.
Email: dearzhang@fudan.edu.cn (D. Zhang), azhou@lsec.cc.ac.cn (A. Zhou), xggong@fudan.edu.cn (X.-G. Gong)
 

The Global Science Journal