메뉴 건너뛰기




Volumn 14, Issue 1, 2011, Pages 17-25

The least squares AMG Solver for the one-dimensional Helmholtz operator

Author keywords

Adaptive; Helmholtz equations; Indefinite; Least squares; Multigrid; Wave ray

Indexed keywords

ADAPTIVE; INDEFINITE; LEAST SQUARE; MULTI-GRID; WAVE-RAY;

EID: 80054892824     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-011-0159-3     Document Type: Conference Paper
Times cited : (4)

References (23)
  • 1
    • 0001350531 scopus 로고
    • An iterative method for the helmholtz equation
    • 701181 0524.65068 10.1016/0021-9991(83)90139-0
    • A. Bayliss C.I. Goldstein E. Turkel 1983 An iterative method for the helmholtz equation J. Comput. Phys. 49 3 443 457 701181 0524.65068 10.1016/0021-9991(83)90139-0
    • (1983) J. Comput. Phys. , vol.49 , Issue.3 , pp. 443-457
    • Bayliss, A.1    Goldstein, C.I.2    Turkel, E.3
  • 2
    • 0031234450 scopus 로고    scopus 로고
    • A domain decomposition method for the Helmholtz equation and related optimal control problems
    • DOI 10.1006/jcph.1997.5742, PII S0021999197957429
    • J.D. Benamou 1997 A domain decomposition method for the helmholtz equation and related optimal control problems J. Comput. Phys. 136 1 68 82 1468624 0884.65118 10.1006/jcph.1997.5742 (Pubitemid 127170091)
    • (1997) Journal of Computational Physics , vol.136 , Issue.1 , pp. 68-82
    • Benamou, J.-D.1    Despres, B.2
  • 3
    • 0034884436 scopus 로고    scopus 로고
    • Preconditioning highly indefinite and nonsymmetric matrices
    • 1787298 0985.65036 10.1137/S1064827599361308
    • M. Benzi J.C. Haws M. Tuma 2000 Preconditioning highly indefinite and nonsymmetric matrices SIAM J. Sci. Comput. 22 4 1333 1353 1787298 0985.65036 10.1137/S1064827599361308
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.4 , pp. 1333-1353
    • Benzi, M.1    Haws, J.C.2    Tuma, M.3
  • 6
    • 0142096515 scopus 로고    scopus 로고
    • Multiscale scientific computation: Review 2001
    • Barth, T.J.; Chan, T.F.; Haimes, R. (eds.)
    • Brandt, A.: Multiscale scientific computation: review 2001. In: Barth, T.J.; Chan, T.F.; Haimes, R. (eds.) Multiscale and Multiresolution Methods: Theory and Applications, pp. 1-96 (2001)
    • (2001) Multiscale and Multiresolution Methods: Theory and Applications , pp. 1-96
    • Brandt, A.1
  • 8
    • 79957581762 scopus 로고    scopus 로고
    • A least squares based algebraic multigrid solver for hermitian and positive definite systems
    • 2785964 10.1137/090752973
    • A. Brandt J. Brannick K. Kahl I. Livshits 2010 A least squares based algebraic multigrid solver for hermitian and positive definite systems SIAM J. Sci. Comput. 33 2 612 632 2785964 10.1137/090752973
    • (2010) SIAM J. Sci. Comput. , vol.33 , Issue.2 , pp. 612-632
    • Brandt, A.1    Brannick, J.2    Kahl, K.3    Livshits, I.4
  • 10
    • 29144485795 scopus 로고    scopus 로고
    • Higher-order fourier approximation in scattering by two-dimensional, inhomogeneous media
    • DOI 10.1137/S0036142903425811
    • O.P. Bruno E.M. Hyde 2005 Higher-order fourier approximation in scattering by two-dimensional, inhomogeneous media SIAM J. Numer. Anal. 42 6 2298 2319 2139394 1128.65106 10.1137/S0036142903425811 (Pubitemid 41812884)
    • (2005) SIAM Journal on Numerical Analysis , vol.42 , Issue.6 , pp. 2298-2319
    • Bruno, O.P.1    Hyde, E.M.2
  • 11
    • 0036344991 scopus 로고    scopus 로고
    • A multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations
    • 1885602 1004.65134 10.1137/S1064827501357190
    • H.C. Elman O.G. Ernst D.P. O'Leary 2001 A multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations SIAM J. Sci. Comput. 23 4 1291 1315 1885602 1004.65134 10.1137/S1064827501357190
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.4 , pp. 1291-1315
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3
  • 12
    • 48249115600 scopus 로고    scopus 로고
    • Fast directional multilevel algorithms for oscillatory kernels
    • 2341809 1180.65006 10.1137/07068583X
    • B. Engquist L. Ying 2007 Fast directional multilevel algorithms for oscillatory kernels SIAM J. Sci. Comput. 29 4 1710 1737 2341809 1180.65006 10.1137/07068583X
    • (2007) SIAM J. Sci. Comput. , vol.29 , Issue.4 , pp. 1710-1737
    • Engquist, B.1    Ying, L.2
  • 14
    • 33746033769 scopus 로고    scopus 로고
    • A novel multigrid based preconditioner for heterogeneous Helmholtz problems
    • DOI 10.1137/040615195
    • Y.A. Erlangga C.W. Oosterlee C. Vuik 2006 A novel multigrid based preconditioner for heterogeneous helmholtz problems SIAM J. Sci. Comput. 27 4 1471 1492 2199758 1095.65109 10.1137/040615195 (Pubitemid 44077336)
    • (2006) SIAM Journal of Scientific Computing , vol.27 , Issue.4 , pp. 1471-1492
    • Erlangga, Y.A.1    Oosterlee, C.W.2    Vuik, C.3
  • 15
    • 25644431975 scopus 로고    scopus 로고
    • An incomplete LU preconditioner for problems in acoustics
    • DOI 10.1142/S0218396X05002803
    • M.J. Gander F. Nataf 2005 An incomplete lu preconditioner for problems in acoustics J. Comput. Acoust. 13 3 455 476 2174402 1189.76362 10.1142/S0218396X05002803 (Pubitemid 41383139)
    • (2005) Journal of Computational Acoustics , vol.13 , Issue.3 , pp. 455-476
    • Gander, M.J.1    Nataf, F.2
  • 16
    • 55549128247 scopus 로고    scopus 로고
    • One-dimensional algorithm for finding eigenbasis of the schrodinger operator
    • 2377448 1159.65334 10.1137/070684197
    • I. Livshits 2008 One-dimensional algorithm for finding eigenbasis of the schrodinger operator SIAM J. Sci. Comput. 30 1 416 440 2377448 1159.65334 10.1137/070684197
    • (2008) SIAM J. Sci. Comput. , vol.30 , Issue.1 , pp. 416-440
    • Livshits, I.1
  • 18
    • 0033693515 scopus 로고    scopus 로고
    • First-order system least squares for the helmholtz equation
    • 1766016 0957.65097 10.1137/S1064827598339773
    • B. Lee T.A. Manteuffel S.F. McCormick J. Ruge 2000 First-order system least squares for the helmholtz equation SIAM J. Sci. Comput. 21 5 1927 1949 1766016 0957.65097 10.1137/S1064827598339773
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.5 , pp. 1927-1949
    • Lee, B.1    Manteuffel, T.A.2    McCormick, S.F.3    Ruge, J.4
  • 19
    • 34547199415 scopus 로고    scopus 로고
    • Accuracy properties of the wave-ray multigrid algorithm for helmholtz equations
    • DOI 10.1137/040620461
    • I. Livshits A. Brandt 2006 Accuracy properties of the wave-ray multigrid algorithm for helmholtz equations SIAM J. Sci. Comput. 28 4 1228 1251 2255454 1119.65109 10.1137/040620461 (Pubitemid 47109335)
    • (2006) SIAM Journal of Scientific Computing , vol.28 , Issue.4 , pp. 1228-1251
    • Livshits, I.1    Brandt, A.2
  • 21
    • 0027851427 scopus 로고
    • Diagonal forms of translation operators for the helmholtz equation in three dimensions
    • 1256528 0795.35021 10.1006/acha.1993.1006
    • V. Rokhlin 1993 Diagonal forms of translation operators for the helmholtz equation in three dimensions Appl. Comput. Harmon. Anal. 1 1 82 93 1256528 0795.35021 10.1006/acha.1993.1006
    • (1993) Appl. Comput. Harmon. Anal. , vol.1 , Issue.1 , pp. 82-93
    • Rokhlin, V.1
  • 22
    • 0040683523 scopus 로고    scopus 로고
    • A domain decomposition method for the exterior Helmholtz problem
    • DOI 10.1006/jcph.1998.6094, PII S0021999198960946
    • R.F. Susan-Resiga H.M. Atassi 1998 A domain decomposition method for the exterior helmholtz problem J. Comput. Phys. 147 2 388 401 1663559 0923.65084 10.1006/jcph.1998.6094 (Pubitemid 128343305)
    • (1998) Journal of Computational Physics , vol.147 , Issue.2 , pp. 388-401
    • Susan-Resiga, R.F.1    Atassi, H.M.2
  • 23
    • 0008858386 scopus 로고    scopus 로고
    • Two-level algebraic multigrid for the helmholtz problem
    • 1649630
    • P. Vanek J. Mandel M. Brezina 1998 Two-level algebraic multigrid for the helmholtz problem Cont. Math. 218 349 356 1649630
    • (1998) Cont. Math. , vol.218 , pp. 349-356
    • Vanek, P.1    Mandel, J.2    Brezina, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.