메뉴 건너뛰기




Volumn 228, Issue 2, 2009, Pages 312-335

Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential

Author keywords

Artificial boundary condition; Exterior potential; Numerical simulations; Schr dinger equation; Unconditionally stable discretization schemes

Indexed keywords

INITIAL VALUE PROBLEMS; NUMERICAL MODELS;

EID: 56749091936     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.09.013     Document Type: Article
Times cited : (65)

References (29)
  • 1
    • 85189838217 scopus 로고    scopus 로고
    • M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th Printing, Volume 55 of National Bureau of Standards Applied Mathematics Series, For Sale by the Superintendent of Documents, US Government Printing Office, Washington, DC, 1964.
    • M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th Printing, Volume 55 of National Bureau of Standards Applied Mathematics Series, For Sale by the Superintendent of Documents, US Government Printing Office, Washington, DC, 1964.
  • 2
    • 51149087560 scopus 로고    scopus 로고
    • A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations
    • Antoine X., Arnold A., Besse C., Ehrhardt M., and Schädle A. A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Commun. Comput. Phys. 4 4 (2008) 729-796
    • (2008) Commun. Comput. Phys. , vol.4 , Issue.4 , pp. 729-796
    • Antoine, X.1    Arnold, A.2    Besse, C.3    Ehrhardt, M.4    Schädle, A.5
  • 3
    • 0035593089 scopus 로고    scopus 로고
    • Construction structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation
    • Antoine X., and Besse C. Construction structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation. J. Math. Pures Appl. (9) 80 7 (2001) 701-738
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.7 , pp. 701-738
    • Antoine, X.1    Besse, C.2
  • 4
    • 0038684989 scopus 로고    scopus 로고
    • Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation
    • Antoine X., and Besse C. Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. J. Comput. Phys. 188 1 (2003) 157-175
    • (2003) J. Comput. Phys. , vol.188 , Issue.1 , pp. 157-175
    • Antoine, X.1    Besse, C.2
  • 5
    • 33750189006 scopus 로고    scopus 로고
    • Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
    • (Electronic)
    • Antoine X., Besse C., and Descombes S. Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations. SIAM J. Numer. Anal. 43 6 (2006) 2272-2293 (Electronic)
    • (2006) SIAM J. Numer. Anal. , vol.43 , Issue.6 , pp. 2272-2293
    • Antoine, X.1    Besse, C.2    Descombes, S.3
  • 6
    • 5644226324 scopus 로고    scopus 로고
    • Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
    • (Electronic)
    • Antoine X., Besse C., and Mouysset V. Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. Math. Comput. 73 248 (2004) 1779-1799 (Electronic)
    • (2004) Math. Comput. , vol.73 , Issue.248 , pp. 1779-1799
    • Antoine, X.1    Besse, C.2    Mouysset, V.3
  • 7
    • 0031632570 scopus 로고    scopus 로고
    • Numerically absorbing boundary conditions for quantum evolution equations
    • Arnold A. Numerically absorbing boundary conditions for quantum evolution equations. VLSI Design 6 1-4 (1998) 313-319
    • (1998) VLSI Design , vol.6 , Issue.1-4 , pp. 313-319
    • Arnold, A.1
  • 8
    • 17244364206 scopus 로고    scopus 로고
    • Scattering theory for the Schrödinger equation with repulsive potential
    • Bony J., Carles R., Häfner D., and Michel L. Scattering theory for the Schrödinger equation with repulsive potential. J. Math. Pures Appl. 84 5 (2005) 509-579
    • (2005) J. Math. Pures Appl. , vol.84 , Issue.5 , pp. 509-579
    • Bony, J.1    Carles, R.2    Häfner, D.3    Michel, L.4
  • 9
    • 24144475004 scopus 로고    scopus 로고
    • Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential
    • Carles R. Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential. Commun. Contemp. Math. 7 4 (2005) 483-508
    • (2005) Commun. Contemp. Math. , vol.7 , Issue.4 , pp. 483-508
    • Carles, R.1
  • 11
    • 85189837350 scopus 로고    scopus 로고
    • G. Doetsch, Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, vol. 3. Auflage. R. Oldenburg Verlag Munchen, Wien, 1967.
    • G. Doetsch, Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, vol. 3. Auflage. R. Oldenburg Verlag Munchen, Wien, 1967.
  • 12
    • 4444373625 scopus 로고    scopus 로고
    • Solutions to the discrete Airy equation: Application to parabolic equation calculations
    • Ehrhardt M., and Mickens R. Solutions to the discrete Airy equation: Application to parabolic equation calculations. J. Comput. Appl. Math. 172 (2004) 183-206
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 183-206
    • Ehrhardt, M.1    Mickens, R.2
  • 13
    • 44649170905 scopus 로고    scopus 로고
    • Exact artificial boundary conditions for problems with periodic structures
    • Ehrhardt M., and Zheng C. Exact artificial boundary conditions for problems with periodic structures. J. Comput. Phys. 227 (2008) 6877-6898
    • (2008) J. Comput. Phys. , vol.227 , pp. 6877-6898
    • Ehrhardt, M.1    Zheng, C.2
  • 14
    • 27344459965 scopus 로고    scopus 로고
    • Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains
    • Ehrhardt M., and Zisowsky A. Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains. J. Comput. Appl. Math. 187 (2006) 1-28
    • (2006) J. Comput. Appl. Math. , vol.187 , pp. 1-28
    • Ehrhardt, M.1    Zisowsky, A.2
  • 15
    • 84966208271 scopus 로고
    • Absorbing boundary conditions for numerical simulation of waves
    • Engquist B., and Majda A. Absorbing boundary conditions for numerical simulation of waves. Math. Comp. 31 (1977) 629-651
    • (1977) Math. Comp. , vol.31 , pp. 629-651
    • Engquist, B.1    Majda, A.2
  • 17
    • 0001776327 scopus 로고
    • Propagation des singularités des solutions d'équations pseudo-différentielles quasi-homogènes
    • Lascar R. Propagation des singularités des solutions d'équations pseudo-différentielles quasi-homogènes. Ann. Inst. Fourier (Grenoble) 27 2 (1977) 79-123
    • (1977) Ann. Inst. Fourier (Grenoble) , vol.27 , Issue.2 , pp. 79-123
    • Lascar, R.1
  • 18
    • 85189838175 scopus 로고    scopus 로고
    • M. Levy, Parabolic equation methods for electromagnetic wave propagation, Volume 45 of IEE Electromagnetic Waves Series, Institution of Electrical Engineers (IEE), London, 2000.
    • M. Levy, Parabolic equation methods for electromagnetic wave propagation, Volume 45 of IEE Electromagnetic Waves Series, Institution of Electrical Engineers (IEE), London, 2000.
  • 19
    • 0002807367 scopus 로고
    • Free-space boundary conditions for the time dependent wave equation
    • Lindmann E. Free-space boundary conditions for the time dependent wave equation. J. Comput. Phys. 18 (1985) 16-78
    • (1985) J. Comput. Phys. , vol.18 , pp. 16-78
    • Lindmann, E.1
  • 20
    • 35649027372 scopus 로고    scopus 로고
    • Numerical Maxwell-Schrödinger model for laser-molecule interaction and propagation
    • Lorin E., Bandrauk A., and Chelkowski S. Numerical Maxwell-Schrödinger model for laser-molecule interaction and propagation. Comput. Phys. Commun. 177 12 (2007) 908-932
    • (2007) Comput. Phys. Commun. , vol.177 , Issue.12 , pp. 908-932
    • Lorin, E.1    Bandrauk, A.2    Chelkowski, S.3
  • 21
    • 85189837621 scopus 로고    scopus 로고
    • E. Lorin, S. Chelkowski, A.D. Bandrauk, Mathematical modeling of boundary conditions for laser-molecule time dependent Schrödinger equations and some aspects of their numerical computation - one-dimensional case, Numer. Meth. for P.D.E., in press.
    • E. Lorin, S. Chelkowski, A.D. Bandrauk, Mathematical modeling of boundary conditions for laser-molecule time dependent Schrödinger equations and some aspects of their numerical computation - one-dimensional case, Numer. Meth. for P.D.E., in press.
  • 22
    • 0031058871 scopus 로고    scopus 로고
    • Rational square-root approximations for parabolic equation algorithms
    • Milinazzo F., Zala C., and Brooke G. Rational square-root approximations for parabolic equation algorithms. J. Acoust. Soc. Am. 101 2 (1997) 760-766
    • (1997) J. Acoust. Soc. Am. , vol.101 , Issue.2 , pp. 760-766
    • Milinazzo, F.1    Zala, C.2    Brooke, G.3
  • 24
    • 85189837206 scopus 로고    scopus 로고
    • L. Nirenberg, Pseudodifferential operators and some applications, Volume 17 of Regional Conference Series in Mathematics AMS 17, Lectures on Linear Partial Differential Equations, AMS, 1973.
    • L. Nirenberg, Pseudodifferential operators and some applications, Volume 17 of Regional Conference Series in Mathematics AMS 17, Lectures on Linear Partial Differential Equations, AMS, 1973.
  • 25
    • 37149019632 scopus 로고    scopus 로고
    • Approximation, stability and fast evaluation of exact artificial boundary condition for the one-dimensional heat equation
    • Zheng C. Approximation, stability and fast evaluation of exact artificial boundary condition for the one-dimensional heat equation. J. Comput. Math. 25 6 (2007) 730-745
    • (2007) J. Comput. Math. , vol.25 , Issue.6 , pp. 730-745
    • Zheng, C.1
  • 26
    • 35348884878 scopus 로고    scopus 로고
    • A perfectly matched layer approach to the nonlinear Schrödinger wave equations
    • Zheng C. A perfectly matched layer approach to the nonlinear Schrödinger wave equations. J. Comput. Phys. 227 (2007) 537-556
    • (2007) J. Comput. Phys. , vol.227 , pp. 537-556
    • Zheng, C.1
  • 27
    • 41849137270 scopus 로고    scopus 로고
    • An exact absorbing boundary condition for the Schrödinger equation with sinusoidal potentials at infinity
    • Zheng C. An exact absorbing boundary condition for the Schrödinger equation with sinusoidal potentials at infinity. Commun. Comput. Phys. 3 3 (2008) 641-658
    • (2008) Commun. Comput. Phys. , vol.3 , Issue.3 , pp. 641-658
    • Zheng, C.1
  • 28
    • 85189837060 scopus 로고    scopus 로고
    • A. Zisowsky, Discrete transparent boundary conditions for systems of evolution equations, Ph.D. Thesis, TU Berlin, 2003.
    • A. Zisowsky, Discrete transparent boundary conditions for systems of evolution equations, Ph.D. Thesis, TU Berlin, 2003.
  • 29
    • 27744450526 scopus 로고    scopus 로고
    • Discrete transparent boundary conditions for transient kp-Schrödinger equations with application to quantum-heterostructures
    • Zisowsky A., Arnold A., Ehrhardt M., and Koprucki T. Discrete transparent boundary conditions for transient kp-Schrödinger equations with application to quantum-heterostructures. J. Appl. Math. Mech. (ZAMM) 85 (2005) 793-805
    • (2005) J. Appl. Math. Mech. (ZAMM) , vol.85 , pp. 793-805
    • Zisowsky, A.1    Arnold, A.2    Ehrhardt, M.3    Koprucki, T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.