Acta Mathematicae Applicatae Sinica

, Volume 18, Issue 2, pp 185–200

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

Authors

    • Center for Computational Mathematics and Applications and Department of MathematicsPennsylvania State University
  • Aihui Zhou**
    • Institute for Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System SciencesChinese Academy of Sciences
Original Papers

DOI: 10.1007/s102550200018

Cite this article as:
Xu*, J. & Zhou**, A. Acta Mathematicae Applicatae Sinica, English Series (2002) 18: 185. doi:10.1007/s102550200018

Abstract

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.

Keywords

Eigenvaluefinite elementlocal algorithmparallel algorithm

2000 MR Subject Classification

65N1565N3065N55
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002