메뉴 건너뛰기




Volumn 35, Issue 9, 2014, Pages 1189-1202

Efficient high-order immersed interface methods for heat equations with interfaces

Author keywords

alternative direction implicit (ADI) scheme; high order compact (HOC) scheme; immersed interface method (IIM); Richardson extrapolation method

Indexed keywords

EXTRAPOLATION;

EID: 84920256856     PISSN: 02534827     EISSN: 15732754     Source Type: Journal    
DOI: 10.1007/s10483-014-1851-6     Document Type: Article
Times cited : (8)

References (29)
  • 1
    • 49649145203 scopus 로고
    • Flow patterns around heart valves: a numerical method
    • Peskin, C. S. Flow patterns around heart valves: a numerical method. Journal of Computational Physics, 10, 252–271 (1972)
    • (1972) Journal of Computational Physics , vol.10 , pp. 252-271
    • Peskin, C.S.1
  • 3
    • 45149143078 scopus 로고
    • A three-dimensional computational method for blood flow in the heart, I: immersed elastic fibers in a viscous incompressible fluid
    • Peskin, C. S. and McQueen, D. M. A three-dimensional computational method for blood flow in the heart, I: immersed elastic fibers in a viscous incompressible fluid. Journal of Computational Physics, 81, 372–405 (1989)
    • (1989) Journal of Computational Physics , vol.81 , pp. 372-405
    • Peskin, C.S.1    McQueen, D.M.2
  • 4
    • 2342582725 scopus 로고    scopus 로고
    • Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics
    • Cortez, R., Fauci, L., Cowen, N., and Dillon, R. Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics. Computing in Science & Engineering, 6, 38–45 (2005)
    • (2005) Computing in Science & Engineering , vol.6 , pp. 38-45
    • Cortez, R.1    Fauci, L.2    Cowen, N.3    Dillon, R.4
  • 5
    • 0006006596 scopus 로고    scopus 로고
    • Computational methods for continuum models of platelet aggregation
    • Wang, N. T. and Fogelson, A. L. Computational methods for continuum models of platelet aggregation. Journal of Computational Physics, 151, 649–675 (1999)
    • (1999) Journal of Computational Physics , vol.151 , pp. 649-675
    • Wang, N.T.1    Fogelson, A.L.2
  • 6
    • 21444453996 scopus 로고    scopus 로고
    • An immersed boundary method with direct forcing for the simulation of particulate flows
    • Uhlmann, M. An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics, 209, 448–476 (2005)
    • (2005) Journal of Computational Physics , vol.209 , pp. 448-476
    • Uhlmann, M.1
  • 7
    • 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. Journal on Numerical Analysis, 31, 1019–1044 (1994)
    • (1994) Journal on Numerical Analysis , vol.31 , pp. 1019-1044
    • Leveque, R.J.1    Li, Z.2
  • 8
    • 0003050917 scopus 로고    scopus 로고
    • A note on immersed interface method for three-dimensional elliptic equations
    • Li, Z. A note on immersed interface method for three-dimensional elliptic equations. Computers & Mathematics with Applications, 31, 9–17 (1996)
    • (1996) Computers & Mathematics with Applications , vol.31 , pp. 9-17
    • Li, Z.1
  • 9
    • 0036208213 scopus 로고    scopus 로고
    • Maximum principle preserving schemes for interface problems
    • Li, Z. and Ito, K. Maximum principle preserving schemes for interface problems. Journal of Scientific Computing, 23, 339–361 (2001)
    • (2001) Journal of Scientific Computing , vol.23 , pp. 339-361
    • Li, Z.1    Ito, K.2
  • 10
    • 0037246341 scopus 로고    scopus 로고
    • The immersed interface/multigrid methods for interface problems
    • Adams, L. and Li, Z. The immersed interface/multigrid methods for interface problems. Journal on Scientific Computing, 24, 463–479 (2003)
    • (2003) Journal on Scientific Computing , vol.24 , pp. 463-479
    • Adams, L.1    Li, Z.2
  • 11
    • 0009853243 scopus 로고    scopus 로고
    • The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions
    • Wiegmann, A. and Bube, K. P. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. Journal on Numerical Analysis, 37, 827–862 (2000)
    • (2000) Journal on Numerical Analysis , vol.37 , pp. 827-862
    • Wiegmann, A.1    Bube, K.P.2
  • 12
    • 2942565816 scopus 로고    scopus 로고
    • A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions
    • Berthelsen, P. A. A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. Journal of Computational Physics, 197, 364–386 (2004)
    • (2004) Journal of Computational Physics , vol.197 , pp. 364-386
    • Berthelsen, P.A.1
  • 13
    • 0000641836 scopus 로고    scopus 로고
    • A fast iterative algorithm for elliptic interface problems
    • Li, Z. A fast iterative algorithm for elliptic interface problems. Journal on Numerical Analysis, 35, 230–254 (1998)
    • (1998) Journal on Numerical Analysis , vol.35 , pp. 230-254
    • Li, Z.1
  • 14
    • 77954141981 scopus 로고    scopus 로고
    • A second order virtual node method for elliptic problems with interfaces and irregular domains
    • Bedrossian, J., von Brecht, J. H., Zhu, S., Sifakis, E., and Teran, J. M. A second order virtual node method for elliptic problems with interfaces and irregular domains. Journal of Computational Physics, 229, 6405–6426 (2010)
    • (2010) Journal of Computational Physics , vol.229 , pp. 6405-6426
    • Bedrossian, J.1    von Brecht, J.H.2    Zhu, S.3    Sifakis, E.4    Teran, J.M.5
  • 15
    • 31744448526 scopus 로고    scopus 로고
    • High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
    • Zhou, Y. C., Zhao, S., Feig, M., and Wei, G. W. High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources. Journal of Computational Physics, 213, 1–30 (2006)
    • (2006) Journal of Computational Physics , vol.213 , pp. 1-30
    • Zhou, Y.C.1    Zhao, S.2    Feig, M.3    Wei, G.W.4
  • 16
    • 77649188716 scopus 로고    scopus 로고
    • An interpolation matched interface and boundary method for elliptic interface problems
    • Pan, K., Tan, Y., and Hu, H. An interpolation matched interface and boundary method for elliptic interface problems. Journal of Computational and Applied Mathematics, 234, 73–94 (2010)
    • (2010) Journal of Computational and Applied Mathematics , vol.234 , pp. 73-94
    • Pan, K.1    Tan, Y.2    Hu, H.3
  • 17
    • 45849096468 scopus 로고    scopus 로고
    • Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
    • Chen, T. and Strain, J. Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems. Journal of Computational Physics, 227, 7503–7542 (2008)
    • (2008) Journal of Computational Physics , vol.227 , pp. 7503-7542
    • Chen, T.1    Strain, J.2
  • 18
    • 83655201150 scopus 로고    scopus 로고
    • Mathematical model and computer simulation of three dimensional thin film elliptic interface problems
    • Joshi, P. and Kumar, M. Mathematical model and computer simulation of three dimensional thin film elliptic interface problems. Computers & Mathematics with Applications, 63, 25–35 (2011)
    • (2011) Computers & Mathematics with Applications , vol.63 , pp. 25-35
    • Joshi, P.1    Kumar, M.2
  • 19
    • 0033239108 scopus 로고    scopus 로고
    • Convergence analysis of the immersed interface method
    • Huang, H. and Li, Z. Convergence analysis of the immersed interface method. Journal of Numerical Analysis, 19, 583–608 (1999)
    • (1999) Journal of Numerical Analysis , vol.19 , pp. 583-608
    • Huang, H.1    Li, Z.2
  • 22
    • 0000687740 scopus 로고
    • ADI methods for heat equations with discontinuities along an arbitrary interface
    • Li, Z. and Mayo, A. ADI methods for heat equations with discontinuities along an arbitrary interface. American Mathematical Society, 48, 311–315 (1994)
    • (1994) American Mathematical Society , vol.48 , pp. 311-315
    • Li, Z.1    Mayo, A.2
  • 23
    • 0032635767 scopus 로고    scopus 로고
    • Fast and accurate numerical approaches for Stefan problems and crystal growth
    • Li, Z. and Soni, B. Fast and accurate numerical approaches for Stefan problems and crystal growth. Numerical Heat Transfer, Part B: Fundamentals, 35, 461–484 (1999)
    • (1999) Numerical Heat Transfer, Part B: Fundamentals , vol.35 , pp. 461-484
    • Li, Z.1    Soni, B.2
  • 24
    • 34147165720 scopus 로고    scopus 로고
    • The immersed interface method for two-dimensional heatdiffusion equations with singular own sources
    • Kandilarov, J. D. and Vulkov, L. G. The immersed interface method for two-dimensional heatdiffusion equations with singular own sources. Applied Numerical Mathematics, 57, 486–497 (2007)
    • (2007) Applied Numerical Mathematics , vol.57 , pp. 486-497
    • Kandilarov, J.D.1    Vulkov, L.G.2
  • 25
    • 0032069387 scopus 로고    scopus 로고
    • Theoretical and numerical analysis on a thermo-elastic system with discontinuities
    • Li, Z., Wang, D., and Zou, J. Theoretical and numerical analysis on a thermo-elastic system with discontinuities. Journal of Computational and Applied Mathematics, 92, 37–58 (1998)
    • (1998) Journal of Computational and Applied Mathematics , vol.92 , pp. 37-58
    • Li, Z.1    Wang, D.2    Zou, J.3
  • 26
    • 35848943928 scopus 로고    scopus 로고
    • The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains
    • Li, Z. and Ito, K. The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains. Society for Industrial and Applied Mathematics, 33, 119–167 (2006)
    • (2006) Society for Industrial and Applied Mathematics , vol.33 , pp. 119-167
    • Li, Z.1    Ito, K.2
  • 27
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
    • Osher, S. and Sethian, J. A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79, 12–49 (1988)
    • (1988) Journal of Computational Physics , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 28
    • 0001439074 scopus 로고    scopus 로고
    • The immersed interface method for the Navier-Stokes equations with singular forces
    • Li, Z. and Lai, M. C. The immersed interface method for the Navier-Stokes equations with singular forces. Journal of Computational Physics, 171, 822–842 (2001)
    • (2001) Journal of Computational Physics , vol.171 , pp. 822-842
    • Li, Z.1    Lai, M.C.2
  • 29
    • 3042771625 scopus 로고    scopus 로고
    • High order ADI method for solving unsteady convection-diffusion problems
    • Karaa, S. and Zhang, J. High order ADI method for solving unsteady convection-diffusion problems. Journal of Computational Physics, 198, 1–9 (2004)
    • (2004) Journal of Computational Physics , vol.198 , pp. 1-9
    • Karaa, S.1    Zhang, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.