An integrated Davidson and multigrid solution approach for very large scale symmetric eigenvalue problems

Computer Methods in Applied Mechanics and Engineering

Volumn 190, Issue 28, 2001, Pages 3543-3563

  Feng, Y T ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Davidson's method; Jacobi Davidson; Large scale symmetric eigenvalue problem; Multigrid method; Newton correction equation; Rayleigh quotient

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF STATE;

DAVIDSON SOLUTION STRATEGY; LARGE SCALE EIGENVALUE PROBLEMS;

MECHANICAL ENGINEERING;

MATHEMATICAL METHOD;

EID: 0035970468     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(00)00283-8     Document Type: Article

References (34)

1. A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems
2. The multifrontal method for sparse matrix solution: Theory and practice
3. Preconditioned eigensolvers - An oxymoron?
4. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
5. Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices
6. Passing one-billion limit in full configuration-interaction (FCI) calculations
7. Jacobi-Davidson iteration method for linear eigenvalue problems
8. A inverse iteration using multigrid for quantum chemistry
9. A multilevel variational method for au = λbu on composite grids
10. Dynamic thick restarting of the Davidson and the implicitly restarted Arnoldi methods
11. Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue methods
12. A truncated RQ-iteration for large scale eigenvalue calculations
13. Alternative correction equations in the Jacobi-Davidson method
14. A block Rayleigh quotient iteration with local quadratic convergence
15. Inexact Newton preconditioning techniques for large symmetric eigenvalue problems
16. Multi-level adaptive solution to boundary-value problems
17. Algebraic multigrid
18. Multigrid methods in science and engineering
19. Node-nested multigrid with delaunay coarsening
20. An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems
21. Iterative methods on parallel computers for FE simulation of 3D sheet forming operations
22. A non-nested Galerkin multi-grid method for solving linear and nonlinear solid mechanics problems
23. A multi-grid enhanced GMRES algorithm for elasto-plastic problems
24. Coarse mesh evolution strategies in the Galerkin multigrid method with mesh adaptivity for geometrically nonlinear problems
25. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear equations
26. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
27. A flexible inner-outer preconditioned GMRES algorithm
28. Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems
29. Jacobi-Davidson type method for generalized eigenproblems and polynomial eigenproblems
30. Jacobi-Davidson style QR and QZ algorithm for the partial reduction of matrix pencils