메뉴 건너뛰기




Volumn 196, Issue 4-6, 2007, Pages 766-781

A fictitious domain approach with spread interface for elliptic problems with general boundary conditions

Author keywords

Elliptic problems; Embedded boundary conditions; Fictitious domain method; Local adaptive mesh refinement; Spread interface method

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; FINITE ELEMENT METHOD; PROBLEM SOLVING;

EID: 33751037366     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.05.012     Document Type: Article
Times cited : (141)

References (41)
  • 1
    • 0012532648 scopus 로고
    • On the solution of some boundary value problems on high performance computers by fictitious domain method
    • (in Russian)
    • Saul'ev V.K. On the solution of some boundary value problems on high performance computers by fictitious domain method. Siberian Math. J. 4 4 (1963) 912-925 (in Russian)
    • (1963) Siberian Math. J. , vol.4 , Issue.4 , pp. 912-925
    • Saul'ev, V.K.1
  • 2
    • 33751045659 scopus 로고
    • Springer Verlag, New York (first ed., 1975)
    • Marchuk G.I. Methods of Numerical Mathematics. Application of Math. vol. 2 (1982), Springer Verlag, New York (first ed., 1975)
    • (1982) Application of Math. , vol.2
    • Marchuk, G.I.1
  • 3
    • 33751033224 scopus 로고    scopus 로고
    • Ph. Angot, J.-P. Caltagirone, K. Khadra, A comparison of locally adaptive multigrid methods: L.D.C., F.A.C. and F.I.C. NASA Conf. Publ. CP-3224, vol. 1, 1993, pp. 275-292.
  • 4
    • 0034521747 scopus 로고    scopus 로고
    • Fictitious domain approach for numerical modelling of Navier-Stokes equations
    • Khadra K., Angot Ph., Parneix S., and Caltagirone J.-P. Fictitious domain approach for numerical modelling of Navier-Stokes equations. Int. J. Numer. Methods Fluids 34 8 (2000) 651-684
    • (2000) Int. J. Numer. Methods Fluids , vol.34 , Issue.8 , pp. 651-684
    • Khadra, K.1    Angot, Ph.2    Parneix, S.3    Caltagirone, J.-P.4
  • 5
    • 0001123374 scopus 로고    scopus 로고
    • The blob projection method for immersed boundary problems
    • Cortez R., and Minion M. The blob projection method for immersed boundary problems. J. Comput. Phys. 161 (2000) 428-463
    • (2000) J. Comput. Phys. , vol.161 , pp. 428-463
    • Cortez, R.1    Minion, M.2
  • 6
    • 0035505590 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for the heat equation on irregular domains
    • McCorquodale P., Colella P., and Johansen H. A Cartesian grid embedded boundary method for the heat equation on irregular domains. J. Comput. Phys. 173 (2001) 620-635
    • (2001) J. Comput. Phys. , vol.173 , pp. 620-635
    • McCorquodale, P.1    Colella, P.2    Johansen, H.3
  • 7
    • 0000084316 scopus 로고    scopus 로고
    • An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
    • Ye T., Mittal R., Udaykumar H.S., and Shyy W. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156 (1999) 209-240
    • (1999) J. Comput. Phys. , vol.156 , pp. 209-240
    • Ye, T.1    Mittal, R.2    Udaykumar, H.S.3    Shyy, W.4
  • 8
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • Leveque R.J., and Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1019-1044
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1019-1044
    • Leveque, R.J.1    Li, Z.2
  • 9
    • 0009853243 scopus 로고    scopus 로고
    • The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions
    • Wiegman A., and Bube K.P. 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
    • Wiegman, A.1    Bube, K.P.2
  • 10
    • 0010207466 scopus 로고    scopus 로고
    • Wavelet and finite element solutions for the Neumann problem using fictitious domains
    • Glowinski R., Pan Jr. T.-W., Wells R., and Zhou X. Wavelet and finite element solutions for the Neumann problem using fictitious domains. J. Comput. Phys. 126 1 (1996) 40-51
    • (1996) J. Comput. Phys. , vol.126 , Issue.1 , pp. 40-51
    • Glowinski, R.1    Pan Jr., T.-W.2    Wells, R.3    Zhou, X.4
  • 11
    • 0033477425 scopus 로고    scopus 로고
    • A penalization method to take into account obstacle in incompressible viscous flows
    • Angot Ph., Bruneau Ch.-H., and Fabrie P. A penalization method to take into account obstacle in incompressible viscous flows. Nümer. Math. 81 4 (1999) 497-520
    • (1999) Nümer. Math. , vol.81 , Issue.4 , pp. 497-520
    • Angot, Ph.1    Bruneau, Ch.-H.2    Fabrie, P.3
  • 13
    • 0026965615 scopus 로고
    • Least squares/domain imbedding methods for Neumann problems: application to fluid dynamics
    • Keyes D.E., Chan T.F., Meurant G., Scroggs J.S., and Voigt R.G. (Eds), SIAM, Philadelphia
    • Dean E.J., Dinh Q.V., Glowinski R., He J., Pan T.W., and Périaux J. Least squares/domain imbedding methods for Neumann problems: application to fluid dynamics. In: Keyes D.E., Chan T.F., Meurant G., Scroggs J.S., and Voigt R.G. (Eds). Domain Decomposition Methods for Partial Differential Equations (1992), SIAM, Philadelphia 451-475
    • (1992) Domain Decomposition Methods for Partial Differential Equations , pp. 451-475
    • Dean, E.J.1    Dinh, Q.V.2    Glowinski, R.3    He, J.4    Pan, T.W.5    Périaux, J.6
  • 14
    • 0028333573 scopus 로고
    • A fictitious domain method for Dirichlet problem and applications
    • Glowinski R., Pan T.-W., and Périaux J. A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 3-4 (1994) 283-303
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.111 , Issue.3-4 , pp. 283-303
    • Glowinski, R.1    Pan, T.-W.2    Périaux, J.3
  • 15
    • 0032324844 scopus 로고    scopus 로고
    • On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrange multiplier method
    • Glowinski R., and Kuznetsov Y. On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrange multiplier method. C.R. Acad. Sci. Paris t.327 Serie I (1998) 693-698
    • (1998) C.R. Acad. Sci. Paris , vol.t.327 , Issue.Serie I , pp. 693-698
    • Glowinski, R.1    Kuznetsov, Y.2
  • 16
    • 33751066517 scopus 로고    scopus 로고
    • J.-C. Latché, A fictitious degrees of freedom finite element method for free surface flows, Math. Modell. Numer. Anal., in press.
  • 17
    • 28444443377 scopus 로고    scopus 로고
    • A fictitious domain model for general embedded boundary conditions
    • Angot Ph. A fictitious domain model for general embedded boundary conditions. C.R. Acad. Sci. Paris Ser. Math. 341 11 (2005) 683-688
    • (2005) C.R. Acad. Sci. Paris Ser. Math. , vol.341 , Issue.11 , pp. 683-688
    • Angot, Ph.1
  • 18
    • 33751028365 scopus 로고    scopus 로고
    • Ph. Angot, H. Lomenède, I. Ramière, A general fictitious domain method with non-conforming structured mesh, Finite Volume for Complex Applications IV, Problems and Perspectives, in: F. Benkhaldoun, D. Ouazar, S. Raghay (Eds.), Hermes Science (2005), International Symposium on Finite Volumes IV (FVCA4), Marrakech, Marocco, 4-7 July 2005, pp. 261-272.
  • 19
    • 33751069127 scopus 로고
    • A remark on the method of fictive domains
    • (in Russian)
    • Rukhovets L.A. A remark on the method of fictive domains. Differential Equations 3 4 (1967) (in Russian)
    • (1967) Differential Equations , vol.3 , Issue.4
    • Rukhovets, L.A.1
  • 20
    • 49649145203 scopus 로고
    • Flow patterns around heart valves: a numerical method
    • Peskin C.S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 2 (1972) 252-271
    • (1972) J. Comput. Phys. , vol.10 , Issue.2 , pp. 252-271
    • Peskin, C.S.1
  • 21
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • Peskin C.S. The immersed boundary method. Acta Numer. 11 (2002) 479-517
    • (2002) Acta Numer. , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 22
    • 7544246268 scopus 로고    scopus 로고
    • A fat boundary method for the Poisson problem in a domain with holes
    • Maury B. A fat boundary method for the Poisson problem in a domain with holes. SIAM J. Sci. Comput. 16 3 (2001) 319-339
    • (2001) SIAM J. Sci. Comput. , vol.16 , Issue.3 , pp. 319-339
    • Maury, B.1
  • 23
    • 33751052117 scopus 로고    scopus 로고
    • M. Ismail, The fat boundary method for the numerical resolution of elliptic problems in perforated domains, Application to 3D fluid flows, Ph.D. thesis, University Pierre and Marie Curie, Paris VI, France, 2004.
  • 24
    • 33751028643 scopus 로고    scopus 로고
    • L. Tomas, Shape optimization and fictitious domains: analysis of new formulations and algorithm aspects, Ph.D. thesis, Ecole Centrale de Lyon, France, 1997.
  • 25
    • 4243910610 scopus 로고
    • A method of fictitious domains for the second and third value problems
    • (in Russian)
    • Kopčenov V.D. A method of fictitious domains for the second and third value problems. Trudy Mat. Inst. Steklov 131 (1974) 119-127 (in Russian)
    • (1974) Trudy Mat. Inst. Steklov , vol.131 , pp. 119-127
    • Kopčenov, V.D.1
  • 28
    • 33751065497 scopus 로고    scopus 로고
    • I. Ramière, M. Belliard, Ph. Angot, On the simulation of nuclear power plant components using a fictitious domain approach, in: Proceedings of the 11th International Topical Meeting on Nuclear Thermal-Hydraulics (NURETH-11), Avignon (France) 2-6 October 2005, Paper 193.
  • 29
    • 33751042769 scopus 로고    scopus 로고
    • Ph. Angot, Contribution à l'étude des transferts thermiques dans des systèmes complexes: application aux composants électroniques, Thèse de doctorat (Mécanique), Université de Bordeaux I, 1989.
  • 30
    • 0033228345 scopus 로고    scopus 로고
    • Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows
    • 2AS Math. Meth. Appl. Sci. 22 16 (1999) 1395-1412
    • (1999) 2AS Math. Meth. Appl. Sci. , vol.22 , Issue.16 , pp. 1395-1412
    • Angot, Ph.1
  • 31
    • 33751026060 scopus 로고    scopus 로고
    • Eléments d'analyse pour l'étude de quelques modéles d'écoulements de fluides visqueux incompressibles
    • Boyer F., and Fabrie P. Eléments d'analyse pour l'étude de quelques modéles d'écoulements de fluides visqueux incompressibles. Mathématiques et Applications 52 (2006)
    • (2006) Mathématiques et Applications , vol.52
    • Boyer, F.1    Fabrie, P.2
  • 33
    • 85088754619 scopus 로고    scopus 로고
    • I. Ramière, Ph. Angot, M. Belliard, Fictitious domain methods to solve convection-diffusion problems with general boundary conditions, AIAA 2005-4709, 17th Computational Fluid Dynamics Conference - AIAA, Toronto, Canada, 6-9 June 2005.
  • 35
    • 33751046444 scopus 로고
    • Springer Verlag, Wien pp. 89-113
    • Hackbusch W. Local Defect Correction Method and Domain Decomposition Techniques. Computing Suppl. vol. 5 (1984), Springer Verlag, Wien pp. 89-113
    • (1984) Computing Suppl. , vol.5
    • Hackbusch, W.1
  • 36
    • 0002365321 scopus 로고    scopus 로고
    • Calculs des écoulements diphasiques dans les échangeurs par une méthode aux éléments finis
    • Grandotto M., and Obry P. Calculs des écoulements diphasiques dans les échangeurs par une méthode aux éléments finis. Revue européenne des éléments finis 5 1 (1996) 53-74
    • (1996) Revue européenne des éléments finis , vol.5 , Issue.1 , pp. 53-74
    • Grandotto, M.1    Obry, P.2
  • 37
    • 33751041308 scopus 로고    scopus 로고
    • M. Grandotto, M. Bernard, J.P. Gaillard, J.L. Cheissoux, E. De Langre, A 3d finite element analysis for solving two phase flow problems in pwr steam generators, in: 7th International Conference on Finite Element Methods in Flow Problems, Huntsville, Alabama, USA, April 1989.
  • 38
    • 33751044757 scopus 로고    scopus 로고
    • D. Bestion, M. Boucker, P. Boudier, Ph. Fillion, M. Grandotto, A. Guelfi, J.M. Hérard, E. Hervieu, P. Péturaud, A new multi-scale platform for advanced nuclear Thermal-hydraulics, in: Proceedings of the 11th International Topical Meeting on Nuclear Thermal-Hydraulics (NURETH-11), Avignon (France) 2-6 October 2005, Paper 31.
  • 41
    • 0002716979 scopus 로고
    • CGS: A fast Lanczos-type solver for nonsymmetric linear system
    • Sonneveld P. CGS: A fast Lanczos-type solver for nonsymmetric linear system. SIAM J. Sci. Statist. Comput. 10 (1989) 36-52
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 36-52
    • Sonneveld, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.