, Volume 18, Issue 2, pp 185-200

Local and Parallel Finite Element Algorithms for Eigenvalue Problems

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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.

* Partially supported by NSF DMS-0074299 through Penn State and Center for Computational Mathematics and Applications, The Pennsylvania State University.
** Subsidized by the Special Funds for Major State Basic Research Projects, and also partially supported by the National Natural Science Foundation ofChina and the Knowledge Innovation Program of the Chinese Academy of Sciences.