메뉴 건너뛰기




Volumn 197, Issue 1, 2004, Pages 364-386

A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions

Author keywords

Cartesian grid; Discontinuous coefficient; Elliptic interface problem; Finite difference method; Immersed interface method; Irregular domain; Level set method

Indexed keywords

ITERATIVE METHODS; NUMERICAL METHODS;

EID: 2942565816     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.12.003     Document Type: Article
Times cited : (100)

References (18)
  • 1
    • 0037246341 scopus 로고    scopus 로고
    • The immersed interface/multigrid methods for interface problems
    • L. Adams, Z. Li, The immersed interface/multigrid methods for interface problems, SIAM J. Sci. Comput. 24 (2) (2002) 463-479.
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 463-479
    • Adams, L.1    Li, Z.2
  • 2
    • 0026841035 scopus 로고
    • Analysis of a one-dimensional model for the immersed boundary method
    • R.P. Beyer, R.J. Leveque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29 (2) (1992) 332-364.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.2 , pp. 332-364
    • Beyer, R.P.1    Leveque, R.J.2
  • 3
    • 28144462923 scopus 로고
    • A continuum method for modeling surface tension
    • J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100 (1992) 335-354.
    • (1992) J. Comput. Phys. , vol.100 , pp. 335-354
    • Brackbill, J.U.1    Kothe, D.B.2    Zemach, C.3
  • 4
    • 0030584607 scopus 로고    scopus 로고
    • A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
    • Y.C. Chang, T.Y. Hou, B. Merriman, S. Osher, A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comput. Phys. 124 (1996) 449-464.
    • (1996) J. Comput. Phys. , vol.124 , pp. 449-464
    • Chang, Y.C.1    Hou, T.Y.2    Merriman, B.3    Osher, S.4
  • 5
    • 0346837922 scopus 로고    scopus 로고
    • A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method)
    • R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method), J. Comput. Phys. 152 (1999) 457-492.
    • (1999) J. Comput. Phys. , vol.152 , pp. 457-492
    • Fedkiw, R.P.1    Aslam, T.2    Merriman, B.3    Osher, S.4
  • 6
    • 0033239108 scopus 로고    scopus 로고
    • Convergence analysis of the immersed interface method
    • H. Huang, Z. Li, Convergence analysis of the immersed interface method, IMA J. Numer. Anal. 19 (1999) 583-608.
    • (1999) IMA J. Numer. Anal. , vol.19 , pp. 583-608
    • Huang, H.1    Li, Z.2
  • 7
    • 0034260316 scopus 로고    scopus 로고
    • A boundary condition capturing method for multiphase incompressible flow
    • M. Kang, R.P. Fedkiw, X.-D. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput. 15 (3) (2000) 323-360.
    • (2000) J. Sci. Comput. , vol.15 , Issue.3 , pp. 323-360
    • Kang, M.1    Fedkiw, R.P.2    Liu, X.-D.3
  • 8
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • R.J. Leveque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (4) (1994) 1019-1044.
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.4 , pp. 1019-1044
    • Leveque, R.J.1    Li, Z.2
  • 9
    • 0003050917 scopus 로고    scopus 로고
    • A note on immersed interface method for three-dimensional elliptic equations
    • Z. Li, A note on immersed interface method for three-dimensional elliptic equations, Comput. Math. Applic 31 (3) (1996) 9-17.
    • (1996) Comput. Math. Applic , vol.31 , Issue.3 , pp. 9-17
    • Li, Z.1
  • 10
    • 0000641836 scopus 로고    scopus 로고
    • A fast iterative algorithm for elliptic interface problems
    • Z. Li, A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal. 35 (1) (1998) 230-254.
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.1 , pp. 230-254
    • Li, Z.1
  • 11
    • 0001439074 scopus 로고    scopus 로고
    • The immersed interface method for the Navier-Stokes equations with singular forces
    • Z. Li, M.-C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys 171 (2001) 822-842.
    • (2001) J. Comput. Phys. , vol.171 , pp. 822-842
    • Li, Z.1    Lai, M.-C.2
  • 12
    • 0036208213 scopus 로고    scopus 로고
    • Maximum principle preserving schemes for interface problems with discontinuous coefficients
    • Z. Li, K. Ito, Maximum principle preserving schemes for interface problems with discontinuous coefficients, SIAM J. Sci. Comput. 23 (1) (2001) 330-361.
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.1 , pp. 330-361
    • Li, Z.1    Ito, K.2
  • 13
    • 0001491689 scopus 로고    scopus 로고
    • A boundary condition capturing method for Poisson's equation on irregular domains
    • X.-D. Liu, R.P. Fedkiw, M. Kang, A boundary condition capturing method for Poisson's equation on irregular domains, J. Comput. Phys. 160 (2000) 151-178.
    • (2000) J. Comput. Phys. , vol.160 , pp. 151-178
    • Liu, X.-D.1    Fedkiw, R.P.2    Kang, M.3
  • 14
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988) 12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 15
    • 0017424014 scopus 로고
    • Numerical analysis of blood flow in heart
    • C.S. Peskin, Numerical analysis of blood flow in heart, J. Comput. Phys. 25 (1977) 220-252.
    • (1977) J. Comput. Phys. , vol.25 , pp. 220-252
    • Peskin, C.S.1
  • 16
    • 28144444111 scopus 로고
    • A level set approach for computing solutions to incompressible two-phase flow
    • M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159.
    • (1994) J. Comput. Phys. , vol.114 , pp. 146-159
    • Sussman, M.1    Smereka, P.2    Osher, S.3
  • 17
    • 3242694679 scopus 로고
    • A front-tracking method for viscous, incompressible multi-fluid flows
    • S.O. Unverdi, G. Tryggvason, A front-tracking method for viscous, incompressible multi-fluid flows, J. Comput. Phys. 100 (1992) 25-37.
    • (1992) J. Comput. Phys. , vol.100 , pp. 25-37
    • Unverdi, S.O.1    Tryggvason, G.2
  • 18
    • 0009853243 scopus 로고    scopus 로고
    • The explicit-jump immersed interface method: Finite difference methods for PDEs with piecewise smooth solutions
    • A. Wiegmann, K.P. Bube, The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions, SIAM J. Numer. Anal. 37 (3) (2000) 827-862.
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 827-862
    • Wiegmann, A.1    Bube, K.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.