메뉴 건너뛰기




Volumn 43, Issue 2, 2003, Pages 387-411

Parallel solution of the Helmholtz equation in a multilayer domain

Author keywords

Domain decomposition; Helmholtz equation; Parallelization; Preconditioned iterative method

Indexed keywords


EID: 4043089115     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026087112862     Document Type: Article
Times cited : (5)

References (28)
  • 1
    • 0000455455 scopus 로고
    • Orthogonal grid generation for two-dimensional ducts
    • L. Abrahamsson, Orthogonal grid generation for two-dimensional ducts, J. Comput. Appl. Math., 34 (1991), pp. 305-314.
    • (1991) J. Comput. Appl. Math. , vol.34 , pp. 305-314
    • Abrahamsson, L.1
  • 3
    • 0021462701 scopus 로고
    • The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics
    • A. Bayliss, C. I. Goldstein, and E. Turkel, The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics, Comput. Math. Appl., 11 (1985), pp. 655-665.
    • (1985) Comput. Math. Appl. , vol.11 , pp. 655-665
    • Bayliss, A.1    Goldstein, C.I.2    Turkel, E.3
  • 4
    • 0000350889 scopus 로고
    • On accuracy conditions for the numerical computation of waves
    • A. Bayliss, C. I. Goldstein, and E. Turkel, On accuracy conditions for the numerical computation of waves, J. Comput. Phys., 59 (1985), pp. 396-404.
    • (1985) J. Comput. Phys. , vol.59 , pp. 396-404
    • Bayliss, A.1    Goldstein, C.I.2    Turkel, E.3
  • 5
    • 0000681145 scopus 로고    scopus 로고
    • Overlapping Schwarz algorithms for solving Helmholtz's equation
    • J. Mandel, C. Farhat, and X.-C. Cai, eds. of Contemp. Math., AMS, Providence, RI
    • X.-C. Cai, M. A. Casarin, F. W. Elliott, and O. B. Widlund, Overlapping Schwarz algorithms for solving Helmholtz's equation, in Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai, eds., vol. 218 of Contemp. Math., AMS, Providence, RI, 1998, pp. 391-399.
    • (1998) Domain Decomposition Methods 10 , vol.218 , pp. 391-399
    • Cai, X.-C.1    Casarin, M.A.2    Elliott, F.W.3    Widlund, O.B.4
  • 7
    • 17344387825 scopus 로고    scopus 로고
    • An optimized order 2 (OO2) method for the Helmholtz equation
    • P. Chevalier and F. Nataf, An optimized order 2 (OO2) method for the Helmholtz equation, C. R. Acad. Sci. Paris Sr. I Math., 326 (1998), pp. 769-774.
    • (1998) C. R. Acad. Sci. Paris Sr. I Math. , vol.326 , pp. 769-774
    • Chevalier, P.1    Nataf, F.2
  • 8
    • 0036344991 scopus 로고    scopus 로고
    • A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations
    • H. C. Elman, O. G. Ernst, and D. P. O'Leary, A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations, SIAM J. Sci. Comput., 23 (2001), pp. 1290-1314.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1290-1314
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3
  • 9
    • 0030369255 scopus 로고    scopus 로고
    • A finite-element capacitance matrix method for exterior Helmholtz problems
    • O. G. Ernst, A finite-element capacitance matrix method for exterior Helmholtz problems, Numer. Math., 75 (1996), pp. 175-204.
    • (1996) Numer. Math. , vol.75 , pp. 175-204
    • Ernst, O.G.1
  • 11
    • 0003070124 scopus 로고    scopus 로고
    • Fictitious domain methods for the numerical solution of two-dimensional scattering problems
    • E. Heikkola, Y. A. Kuznetsov, P. Neittaanmäki, and J. Toivanen, Fictitious domain methods for the numerical solution of two-dimensional scattering problems, J. Comput. Phys., 145 (1998), pp. 89-109.
    • (1998) J. Comput. Phys. , vol.145 , pp. 89-109
    • Heikkola, E.1    Kuznetsov, Y.A.2    Neittaanmäki, P.3    Toivanen, J.4
  • 12
    • 0002499049 scopus 로고
    • Fast transforms for tridiagonal linear equations
    • T. Huckle, Fast transforms for tridiagonal linear equations, BIT, 34 (1994), pp. 99-112.
    • (1994) BIT , vol.34 , pp. 99-112
    • Huckle, T.1
  • 13
    • 0001299857 scopus 로고    scopus 로고
    • Finite element solution of the Helmholtz equation with high wave number Part II: The h-p version of the FEM
    • F. Ihlenburg and I. Babuška, Finite element solution of the Helmholtz equation with high wave number Part II: The h-p version of the FEM, SIAM J. Numer. Anal., 34 (1997), pp. 315-358.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 315-358
    • Ihlenburg, F.1    Babuška, I.2
  • 15
    • 0000271460 scopus 로고
    • Exact non-reflecting boundary conditions
    • J. B. Keller and D. Givoli, Exact non-reflecting boundary conditions, J. Comput. Phys., 82 (1989), pp. 172-192.
    • (1989) J. Comput. Phys. , vol.82 , pp. 172-192
    • Keller, J.B.1    Givoli, D.2
  • 16
    • 0039243579 scopus 로고    scopus 로고
    • Domain decomposition iterative procedures for solving scalar waves in the frequency domain
    • S. Kim, Domain decomposition iterative procedures for solving scalar waves in the frequency domain, Numer. Math., 79 (1998), pp. 231-259.
    • (1998) Numer. Math. , vol.79 , pp. 231-259
    • Kim, S.1
  • 17
    • 0033297033 scopus 로고    scopus 로고
    • A domain decomposition method for the Helmholtz equation in a multilayer domain
    • E. Larsson, A domain decomposition method for the Helmholtz equation in a multilayer domain, SIAM J. Sci. Comput., 20 (1999), pp. 1713-1731.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1713-1731
    • Larsson, E.1
  • 19
    • 0033693515 scopus 로고    scopus 로고
    • First-order system least-squares for the Helmholtz equation
    • B. Lee, T. A. Manteuffel, S. F. McCormick, and J. Ruge, First-order system least-squares for the Helmholtz equation, SIAM J. Sci. Comput., 21 (2000), pp. 1927-1949.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1927-1949
    • Lee, B.1    Manteuffel, T.A.2    McCormick, S.F.3    Ruge, J.4
  • 20
    • 0031554591 scopus 로고    scopus 로고
    • Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm
    • M. Malhotra, R. W. Freund, and P. M. Pinsky, Iterative solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual algorithm, Comput. Methods Appl. Mech. Engrg., 146 (1997), pp. 173-196.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.146 , pp. 173-196
    • Malhotra, M.1    Freund, R.W.2    Pinsky, P.M.3
  • 22
    • 0037875990 scopus 로고    scopus 로고
    • Iterative solution of the Helmholtz equation by a fourth-order method
    • K. Otto, Iterative solution of the Helmholtz equation by a fourth-order method, Boll. Geof. Teor. Appl., 40 suppl. (1999), pp. 104-105.
    • (1999) Boll. Geof. Teor. Appl. , vol.40 , Issue.SUPPL. , pp. 104-105
    • Otto, K.1
  • 23
    • 0033233449 scopus 로고    scopus 로고
    • Iterative solution of the Helmholtz equation by a second-order method
    • K. Otto and E. Larsson, Iterative solution of the Helmholtz equation by a second-order method, SIAM J. Matrix Anal. Appl., 21 (1999), pp. 209-229.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 209-229
    • Otto, K.1    Larsson, E.2
  • 24
    • 0001046616 scopus 로고    scopus 로고
    • Partitioning strategies for structured multiblock grids
    • J. Rantakokko, Partitioning strategies for structured multiblock grids, Parallel Computing, 12 (2000), pp. 1661-1680.
    • (2000) Parallel Computing , vol.12 , pp. 1661-1680
    • Rantakokko, J.1
  • 25
    • 0000954680 scopus 로고
    • A flexible inner-outer preconditioned GMRES algorithm
    • Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comput., 14 (1993), pp. 461-469.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 461-469
    • Saad, Y.1
  • 26
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 27
    • 0036229185 scopus 로고    scopus 로고
    • FQMR: A flexible quasi-minimal residual method with inexact preconditioning
    • D. Szyld and J. Vogel, FQMR: A flexible quasi-minimal residual method with inexact preconditioning, SIAM J. Sci. Comput., 23 (2001), pp. 363-380.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 363-380
    • Szyld, D.1    Vogel, J.2
  • 28
    • 0028196254 scopus 로고
    • Complex wavenumber Fourier analysis of the p-version finite element method
    • L. L. Thompson and P. M. Pinsky, Complex wavenumber Fourier analysis of the p-version finite element method, Comput. Mech., 13 (1994), pp. 255-275.
    • (1994) Comput. Mech. , vol.13 , pp. 255-275
    • Thompson, L.L.1    Pinsky, P.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.