Original Papers

Acta Mathematicae Applicatae Sinica

, Volume 18, Issue 2, pp 185-200

First online:

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

  • Jinchao Xu*Affiliated withCenter for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University Email author 
  • , Aihui Zhou**Affiliated withInstitute for Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences

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Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.


Eigenvalue finite element local algorithm parallel algorithm

2000 MR Subject Classification

65N15 65N30 65N55