메뉴 건너뛰기




Volumn 27, Issue 1, 2005, Pages 346-367

Higher-order, cartesian grid based finite difference schemes for elliptic equations on irregular domains

Author keywords

Elliptic and parabolic equations on irregular domains; Fourth order finite difference schemes; Immersed interface method

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INTERFACES (COMPUTER); PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33144468552     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/03060120X     Document Type: Article
Times cited : (29)

References (24)
  • 2
    • 0037285958 scopus 로고    scopus 로고
    • Three-dimensional elliptic solvers for interface problems and applications
    • S. DENG, K. ITO, AND Z. LI, Three-dimensional elliptic solvers for interface problems and applications, J. Comput. Phys., 184 (2003), pp. 215-243.
    • (2003) J. Comput. Phys. , vol.184 , pp. 215-243
    • Deng, S.1    Ito, K.2    Li, Z.3
  • 3
    • 0037456931 scopus 로고    scopus 로고
    • A least square extrapolation method for improving solution accuracy of PDE computations
    • A. GARBEY AND W. SHYY, A least square extrapolation method for improving solution accuracy of PDE computations, J. Comput. Phys., 186 (2003), pp. 1-23.
    • (2003) J. Comput. Phys. , vol.186 , pp. 1-23
    • Garbey, A.1    Shyy, W.2
  • 4
    • 0037050814 scopus 로고    scopus 로고
    • A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
    • F. GIBOU, R. P. FEDKIW, L. T. CHENG, AND M. KANG, A second-order-accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys., 176 (2002), pp. 205-227.
    • (2002) J. Comput. Phys. , vol.176 , pp. 205-227
    • Gibou, F.1    Fedkiw, R.P.2    Cheng, L.T.3    Kang, M.4
  • 6
    • 0037059248 scopus 로고    scopus 로고
    • Autophobic spreading of drops
    • J. HUNTER, Z. LI, AND H. ZHAO, Autophobic spreading of drops, J. Comput. Phys., 183 (2001), pp. 335-366.
    • (2001) J. Comput. Phys. , vol.183 , pp. 335-366
    • Hunter, J.1    Li, Z.2    Zhao, H.3
  • 7
    • 0001827481 scopus 로고    scopus 로고
    • A cartesian grid embedded boundary method Poisson's equation on irregular domains
    • H. JOHANSEN AND P. COLELLA, A cartesian grid embedded boundary method Poisson's equation on irregular domains, J. Comput. Phys., 147 (1998), pp. 60-85.
    • (1998) J. Comput. Phys. , vol.147 , pp. 60-85
    • Johansen, H.1    Colella, P.2
  • 8
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • R. B. LEHOUCQ AND D. C. SORENSEN, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17, pp. 789-821.
    • SIAM J. Matrix Anal. Appl. , vol.17 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.C.2
  • 10
    • 33144455087 scopus 로고    scopus 로고
    • Finite difference methods for differential equations
    • University of Washington, Seattle, WA
    • R. J. LEVEQUE, Finite Difference Methods for Differential Equations, DRAFT VERSION for use in courses AMath 585-6, University of Washington, Seattle, WA, 1998.
    • (1998) Draft Version for Use in Courses AMath , vol.585 , Issue.6
    • LeVeque, R.J.1
  • 11
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • R. J. LEVEQUE AND Z. LI, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31 (1994), pp. 1019-1044.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1019-1044
    • LeVeque, R.J.1    Li, Z.2
  • 12
    • 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 (1998), pp. 230-254.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 230-254
    • Li, Z.1
  • 13
    • 0036208213 scopus 로고    scopus 로고
    • Maximum principle preserving schemes for interface problems with discontinuous coefficients
    • Z. LI AND K. ITO, Maximum principle preserving schemes for interface problems with discontinuous coefficients, SIAM J. Sci. Comput., 23 (2001), pp. 339-361.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 339-361
    • Li, Z.1    Ito, K.2
  • 14
    • 14544268369 scopus 로고    scopus 로고
    • A fast finite difference method for solving Navier-Stokes equations on irregular domains
    • Z. LI AND C. WANG, A fast finite difference method for solving Navier-Stokes equations on irregular domains, Comm. Math. Sci., l (2003), pp. 180-196.
    • (2003) Comm. Math. Sci. , vol.50 , pp. 180-196
    • Li, Z.1    Wang, C.2
  • 15
    • 0001046083 scopus 로고    scopus 로고
    • A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid
    • Z. LI, H. ZHAO, AND H. GAO, A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid, J. Comput. Phys., 152 (1999), pp. 281-304.
    • (1999) J. Comput. Phys. , vol.152 , pp. 281-304
    • Li, Z.1    Zhao, H.2    Gao, H.3
  • 16
    • 0001491689 scopus 로고    scopus 로고
    • A boundary condition capturing method for Poisson's equation on irregular domains
    • X. D. LIU, R. P. FEDKIW, AND M. KANG, A boundary condition capturing method for Poisson's equation on irregular domains, J. Comput. Phys., 160 (2000), pp. 151-178.
    • (2000) J. Comput. Phys. , vol.160 , pp. 151-178
    • Liu, X.D.1    Fedkiw, R.P.2    Kang, M.3
  • 17
    • 0039986943 scopus 로고
    • A decomposition finite difference method for the fourth order accurate solution of Poisson's equation on general regions
    • A. MAYO, A decomposition finite difference method for the fourth order accurate solution of Poisson's equation on general regions, Int. J. High Speed Comput., 3 (1991), pp. 89-106.
    • (1991) Int. J. High Speed Comput. , vol.3 , pp. 89-106
    • Mayo, A.1
  • 18
    • 33144473159 scopus 로고    scopus 로고
    • High order accurate particular solutions of the biharmonic equation on general regions
    • A. MAYO, High order accurate particular solutions of the biharmonic equation on general regions, Contemp. Math., 323 (2003), pp. 233-243.
    • (2003) Contemp. Math. , vol.323 , pp. 233-243
    • Mayo, A.1
  • 19
    • 0035505590 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for the heat equation on irregular domains
    • P. MCCORQUODALE, P. COLELLA, AND H. JOHANSEN, A Cartesian grid embedded boundary method for the heat equation on irregular domains, J. Comput. Phys., 173 (2001), pp. 620-635.
    • (2001) J. Comput. Phys. , vol.173 , pp. 620-635
    • Mccorquodale, P.1    Colella, P.2    Johansen, H.3
  • 20
    • 0003668379 scopus 로고    scopus 로고
    • Partial differential equations and boundary-value problems with applications, 3rd ed
    • Waveland Press, Lake Grove, IL
    • M. A. PINSKY, Partial Differential Equations and Boundary-Value Problems with Applications, 3rd ed., International Series in Pure and Applied Mathematics, Waveland Press, Lake Grove, IL, 2003.
    • (2003) International Series in Pure and Applied Mathematics
    • Pinsky, M.A.1
  • 21
    • 0029380108 scopus 로고
    • A high-order compact scheme for the steady stream-function vorticity equations
    • W. F. SPOTZ AND G. F. CAREY, A high-order compact scheme for the steady stream-function vorticity equations, Internat. J. Numer. Methods Engrg., 38 (1995), pp. 3497-3512.
    • (1995) Internat. J. Numer. Methods Engrg. , vol.38 , pp. 3497-3512
    • Spotz, W.F.1    Carey, G.F.2
  • 23
    • 84966241274 scopus 로고
    • High order fast Laplace solvers for the Dirichlet problem on general regions
    • V. PEREYRA, W. PROSKUROWSKI, AND O. WIDLUND, High order fast Laplace solvers for the Dirichlet problem on general regions, Math. Comput., 31 (1977), pp. 1-16.
    • (1977) Math. Comput. , vol.31 , pp. 1-16
    • Pereyra, V.1    Proskurowski, W.2    Widlund, O.3
  • 24
    • 49149143501 scopus 로고
    • Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
    • S. YUSEF, Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices, Linear Algebra Appl., 34 (1980), pp. 269-295.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 269-295
    • Yusef, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.