An algebraic multigrid wave-ray algorithm to solve eigenvalue problems for the Helmholtz operator

Numerical Linear Algebra with Applications

Volumn 11, Issue 2-3, 2004, Pages 229-239

  Livshits, Irene ^a  

^a UNIVERSITY OF CENTRAL ARKANSAS   (United States)

Author keywords

Eigenvalue; Helmholtz; Multigrid; Wave ray

Indexed keywords

EID: 10044248632     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.379     Document Type: Article

References (9)

1. Brandt A, Ta'asan S. Multigrid methods for nearly singular and slightly indefinite problems. In Multigrid Methods II, Lecture Notes in Mathematics, vol. 1228, Hackbush W, Trottenberg U (eds). Springer: Berlin, 1985; 100-122.
2. Elman HC, Ernst OG, O'Leary DP. A multigrid method enhanced by krylov subspace iterations for discrete Helmholtz equations. SIAM Journal on Scientific Computing 2001; 23(4):129I-1315.
3. Friese T, Deuflhard P, Schmidt F. A multigrid method for the complex Helmholtz eigenvalue problem. Proceedings of the Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), Lai C-H, Bjorstad PE, Cross M, Widlund OB (eds). UK, 1999; 19-26.
4. Lee B, Manteuffel TA, McCormick SF, Ruge J. First-order system least squares for Helmholtz equations. SIAM Journal on Scientific Computing 2000; 21(5):1927-1949.
5. Vanek P, Mandel J, Brezina M. Two level algebraic multigrid for the Helmholtz problem. Contemporary Mathematics 1998; 218:349-356.
6. Livshits I. Multigrid methods for solving standing wave equations. Ph.D. Thesis, Bar Ilan University, Israel, 1997.
7. Brandt A, Livshits I. Wave-ray multigrid method for solving standing wave equations. Electronic Transactions on Numerical Analysis 1997; 6:162-181.
8. Brandt A, Ron D. Multigrid solvers and multilevel optimization strategies. In Multilevel Optimization and VLSICAD, Cong J, Shinnerl JR (eds). Kluwer Academic Publishers: Boston, 2002; 1-69.
9. Livne OE, Brandt A. O(N log N) calculation of N eigenfunctions. In Multiscalc Computational Methods in Chemistry and Physics, NATO Science Series III: Computer and Systems Sciences, NATO Science Series, Brandt A, Bernholc J, Binder K. (eds). IOS Press: The Netherlands, 2001; 177:123-148.