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Volumn 30, Issue 3-4, 2002, Pages 199-239

A fast algorithm for two-dimensional elliptic problems

Author keywords

Helmholtz equation; Numerical algorithm; Poisson equation

Indexed keywords


EID: 0036374085     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020176803736     Document Type: Article
Times cited : (7)

References (34)
  • 1
    • 0001361205 scopus 로고    scopus 로고
    • A fast Poisson solver of arbitrary order accuracy in rectangular regions
    • A. Averbuch, M. Israeli and L. Vozovoi, A fast Poisson solver of arbitrary order accuracy in rectangular regions, SIAM J. Sci. Comput. 19 (1998) 933-952.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 933-952
    • Averbuch, A.1    Israeli, M.2    Vozovoi, L.3
  • 2
    • 0031321552 scopus 로고    scopus 로고
    • On fast direct elliptic solver by modified Fourier method
    • L. Badea and P. Daripa, On fast direct elliptic solver by modified Fourier method, Numer. Algorithms 15 (1997) 287-313.
    • (1997) Numer. Algorithms , vol.15 , pp. 287-313
    • Badea, L.1    Daripa, P.2
  • 4
    • 0027574205 scopus 로고
    • A fast domain decomposition Poisson solver on a rectangle for Hermite bicubic orthogonal spline collocation
    • B. Bialecki, A fast domain decomposition Poisson solver on a rectangle for Hermite bicubic orthogonal spline collocation, SIAM J. Numer. Anal. 30 (1993) 425-434.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 425-434
    • Bialecki, B.1
  • 6
    • 0034386253 scopus 로고    scopus 로고
    • A parallel version of a fast algorithm for singular integral transforms
    • L. Borges and P. Daripa, A parallel version of a fast algorithm for singular integral transforms, Numer. Algorithms 23 (2000) 71-96.
    • (2000) Numer. Algorithms , vol.23 , pp. 71-96
    • Borges, L.1    Daripa, P.2
  • 7
    • 0001018671 scopus 로고    scopus 로고
    • A fast parallel algorithms for the Poisson equation on a disk
    • L. Borges and P. Daripa, A fast parallel algorithms for the Poisson equation on a disk, J. Comput. Phys. 169 (2001) 151-192.
    • (2001) J. Comput. Phys. , vol.169 , pp. 151-192
    • Borges, L.1    Daripa, P.2
  • 9
    • 0042296776 scopus 로고
    • A domain-decomposed fast Poisson solver on a rectangle
    • T.F. Chan and D.C. Resasco, A domain-decomposed fast Poisson solver on a rectangle, SIAM J. Sci. Statist. Comput. 8 (1987) S14-S26.
    • (1987) SIAM J. Sci. Statist. Comput. , vol.8
    • Chan, T.F.1    Resasco, D.C.2
  • 10
    • 0141467957 scopus 로고
    • A comparison of elliptic solvers for general two-dimensional regions
    • T.F. Chan and F. Saied, A comparison of elliptic solvers for general two-dimensional regions, SIAM J. Sci. Statist. Comput. 6 (1985) 742-760.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 742-760
    • Chan, T.F.1    Saied, F.2
  • 11
    • 38249040450 scopus 로고
    • Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor
    • S.C. Chang, Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor, J. Comput. Phys. 67 (1986) 91-123.
    • (1986) J. Comput. Phys. , vol.67 , pp. 91-123
    • Chang, S.C.1
  • 12
    • 0041580048 scopus 로고
    • On applications of a complex variable method in compressible flows
    • P. Daripa, On applications of a complex variable method in compressible flows, J. Comput. Phys. 88 (1990) 337-361.
    • (1990) J. Comput. Phys. , vol.88 , pp. 337-361
    • Daripa, P.1
  • 13
    • 0000097604 scopus 로고
    • A fast algorithm to solve nonhomogeneous Cauchy-Riemann equations in the complex plane
    • P. Daripa, A fast algorithm to solve nonhomogeneous Cauchy-Riemann equations in the complex plane, SIAM J. Sci. Statist. Comput. 13 (1992) 1418-1432.
    • (1992) SIAM J.Sci. Statist. Comput. , vol.13 , pp. 1418-1432
    • Daripa, P.1
  • 14
    • 0042582033 scopus 로고
    • A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings
    • P. Daripa, A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings, J. Comput. Phys. 106 (1993) 355-365.
    • (1993) J. Comput. Phys. , vol.106 , pp. 355-365
    • Daripa, P.1
  • 15
    • 22444452805 scopus 로고    scopus 로고
    • Singular integral transforms and fast numerical algorithms
    • P. Daripa and D. Mashat, Singular integral transforms and fast numerical algorithms, Numer. Algorithms 18 (1998) 133-157.
    • (1998) Numer. Algorithms , vol.18 , pp. 133-157
    • Daripa, P.1    Mashat, D.2
  • 16
    • 22444455007 scopus 로고    scopus 로고
    • An efficient numerical method for quasiconformal mappings of doubly connected domains
    • P. Daripa and D. Mashat, An efficient numerical method for quasiconformal mappings of doubly connected domains, Numer. Algorithms 18 (1998) 159-178.
    • (1998) Numer. Algorithms , vol.18 , pp. 159-178
    • Daripa, P.1    Mashat, D.2
  • 19
    • 0030137413 scopus 로고    scopus 로고
    • A direct adaptive Poisson solver of arbitrary order accuracy
    • L. Greengard and J.Y. Lee, A direct adaptive Poisson solver of arbitrary order accuracy, J. Comput. Phys. 125 (1996) 415-424.
    • (1996) J. Comput. Phys. , vol.125 , pp. 415-424
    • Greengard, L.1    Lee, J.Y.2
  • 20
    • 85011484616 scopus 로고    scopus 로고
    • A new version of the fast multipole method for the Laplace equation in three dimensions
    • L. Greengard and V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numerica (1997) 229-269.
    • (1997) Acta Numerica , pp. 229-269
    • Greengard, L.1    Rokhlin, V.2
  • 21
    • 84932220767 scopus 로고
    • A fast direct solution of Poisson's equation using Fourier analysis
    • R.W. Hockney, A fast direct solution of Poisson's equation using Fourier analysis, J. Assoc. Comput. Math. 12 (1965) 95-113.
    • (1965) J. Assoc. Comput. Math. , vol.12 , pp. 95-113
    • Hockney, R.W.1
  • 22
    • 0042894123 scopus 로고
    • Evaluation of numerical methods for ellipitic partial differential equations
    • E. Houstis, R. Lynch and J. Rice, Evaluation of numerical methods for ellipitic partial differential equations, J. Comput. Phys. 27 (1978) 323-350.
    • (1978) J. Comput. Phys. , vol.27 , pp. 323-350
    • Houstis, E.1    Lynch, R.2    Rice, J.3
  • 23
    • 0000339157 scopus 로고
    • A fast Poisson solver for complex geometries
    • A. McKenney, L. Greengard and A. Mayo, A fast Poisson solver for complex geometries, J. Comput. Phys. 118 (1995) 348-355.
    • (1995) J. Comput. Phys. , vol.118 , pp. 348-355
    • McKenney, A.1    Greengard, L.2    Mayo, A.3
  • 24
    • 0001390840 scopus 로고
    • Capacitance, matrix methods for the Helmholtz equation on general three-dimensional regions
    • D. O'Leary, and O. Widlund, Capacitance, matrix methods for the Helmholtz equation on general three-dimensional regions, Math. Comp. 33 (1979) 849-879.
    • (1979) Math. Comp. , vol.33 , pp. 849-879
    • O'Leary, D.1    Widlund, O.2
  • 27
    • 84966205561 scopus 로고
    • A poulation of linear, second order, elliptic partial differential equations on rectangular domains
    • J. Rice, E. Houstis and R. Dyksen, A population of linear, second order, elliptic partial differential equations on rectangular domains. I, II, Math. Comp. 36 (1981) 475-484.
    • (1981) I, II, Math. Comp. , vol.36 , pp. 475-484
    • Rice, J.1    Houstis, E.2    Dyksen, R.3
  • 28
    • 0031261340 scopus 로고    scopus 로고
    • Efficient Galerkin methods III: Polar and cylindrical geometries
    • J. Shen, Efficient Galerkin methods III: Polar and cylindrical geometries, SIAM J. Sci. Comput. 18 (1997) 1583-1604.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1583-1604
    • Shen, J.1
  • 29
    • 0141467959 scopus 로고
    • Fast Poisson solvers on general two-dimensional regions for the Dirichlet problem
    • A.S.L. Shieh, Fast Poisson solvers on general two-dimensional regions for the Dirichlet problem, Numer. Math. 31 (1978) 405-429.
    • (1978) Numer. Math. , vol.31 , pp. 405-429
    • Shieh, A.S.L.1
  • 30
    • 84966233044 scopus 로고
    • A Fourier method for the numerical solution of Poisson's equation
    • G. Sköllermo, A Fourier method for the numerical solution of Poisson's equation, Math. Comp. 29 (1975) 697-711.
    • (1975) Math. Comp. , vol.29 , pp. 697-711
    • Sköllermo, G.1
  • 31
    • 0000595101 scopus 로고
    • The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle
    • P.N. Swarztrauber, The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle, SIAM Rev. 19 (1977) 491-501.
    • (1977) SIAM Rev. , vol.19 , pp. 491-501
    • Swarztrauber, P.N.1
  • 32
    • 0005685975 scopus 로고
    • A direct method for the discrete Poisson equation on a disc
    • P.N. Swarztrauber and R.A. Sweet, A direct method for the discrete Poisson equation on a disc, SIAM J. Numer. Anal. 10 (1973) 900-907.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 900-907
    • Swarztrauber, P.N.1    Sweet, R.A.2
  • 33
    • 49149147751 scopus 로고
    • On the FACR(ℓ) algorithm for the discrete Poisson equation
    • C. Temperton, On the FACR(ℓ) algorithm for the discrete Poisson equation, J. Comput. Phys. 34 (1980) 315-329.
    • (1980) J. Comput. Phys. , vol.34 , pp. 315-329
    • Temperton, C.1


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