A two-grid discretization scheme

for eigenvalue problems

Authors:
Jinchao Xu and Aihui Zhou

Journal:
Math. Comp. **70** (2001), 17-25

MSC (2000):
Primary 65L15, 65N15, 65N25, 65N30, 65N55

DOI:
https://doi.org/10.1090/S0025-5718-99-01180-1

Published electronically:
August 17, 1999

MathSciNet review:
1677419

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Abstract | References | Similar Articles | Additional Information

Abstract: A two-grid discretization scheme is proposed for solving eigenvalue problems, including both partial differential equations and integral equations. With this new scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid, and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy.

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Additional Information

**Jinchao Xu**

Affiliation:
Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

Email:
xu@math.psu.edu

**Aihui Zhou**

Affiliation:
Institute of Systems Science, Academia Sinica, Beijing 100080, China

Email:
azhou@bamboo.iss.ac.cn

DOI:
https://doi.org/10.1090/S0025-5718-99-01180-1

Keywords:
Eigenvalue problems,
finite elements,
partial differential equations,
integral equations,
two-grid method

Received by editor(s):
December 16, 1998

Received by editor(s) in revised form:
February 25, 1999

Published electronically:
August 17, 1999

Additional Notes:
This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236 through Penn State, and the Center for Computational Mathematics and Applications, The Pennsylvania State University, and by NSF ASC 9720257 through UCLA. The second author was also partially supported by National Science Foundation of China.

Article copyright:
© Copyright 1999
American Mathematical Society