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Volumn 63, Issue 2, 2013, Pages 339-355

Review of inverse Laplace transform algorithms for Laplace-space numerical approaches

Author keywords

Boundary element method; Diffusion; Groundwater modeling; Helmholtz equation; Laplace space numerical methods; Numerical Laplace transform inversion

Indexed keywords


EID: 84878319621     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-012-9625-3     Document Type: Article
Times cited : (150)

References (36)
  • 1
    • 2942738939 scopus 로고    scopus 로고
    • Multi-precision Laplace transform inversion
    • doi:10.1002/nme.995
    • Abate, J., Valkó, P.: Multi-precision Laplace transform inversion. Int. J. Numer. Methods Eng. 60, 979-993 (2004). doi: 10. 1002/nme. 995.
    • (2004) Int. J. Numer. Methods Eng. , vol.60 , pp. 979-993
    • Abate, J.1    Valkó, P.2
  • 2
    • 0346454438 scopus 로고    scopus 로고
    • Inversion of the Laplace transform via Post-Widder formula
    • doi:10.1080/10652460108819314
    • Al-Shuaibi, A.: Inversion of the Laplace transform via Post-Widder formula. Integral Transforms Spec. Funct. 11(3), 225-232 (2001). doi: 10. 1080/10652460108819314.
    • (2001) Integral Transforms Spec. Funct. , vol.11 , Issue.3 , pp. 225-232
    • Al-Shuaibi, A.1
  • 5
    • 80052849879 scopus 로고    scopus 로고
    • Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation
    • doi:10.1016/j.advwatres.2011.02.008
    • Bakker, M., Kuhlman, K.: Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation. Adv. Water Resour. (2011). doi: 10. 1016/j. advwatres. 2011. 02. 008.
    • (2011) Adv. Water Resour.
    • Bakker, M.1    Kuhlman, K.2
  • 6
    • 84856020131 scopus 로고    scopus 로고
    • Automatic transport model data assimilation in Laplace space
    • doi:10.1029/2011WR010955, W01510
    • Barnhart, K. S., Illangasekare, T. H.: Automatic transport model data assimilation in Laplace space. Water Resour. Res. 48, W01510, 12 (2012). doi: 10. 1029/2011WR010955.
    • (2012) Water Resour. Res. , vol.48 , pp. 12
    • Barnhart, K.S.1    Illangasekare, T.H.2
  • 10
    • 33744806384 scopus 로고    scopus 로고
    • Parallel Laplace transform methods for boundary element solutions to diffusion-type problems
    • 2001
    • Davies, A., Crann, D.: Parallel Laplace transform methods for boundary element solutions to diffusion-type problems. J. Boundary Elements BETEQ 2001(1), 231-238 (2002).
    • (2002) J. Boundary Elements BETEQ , Issue.1 , pp. 231-238
    • Davies, A.1    Crann, D.2
  • 12
    • 0001987242 scopus 로고
    • Numerical inversion of the Laplace transform: A survey and comparison of methods
    • doi:10.1016/0021-9991(79)90025-1
    • Davies, B., Martin, B.: Numerical inversion of the Laplace transform: A survey and comparison of methods. J. Comput. Phys. 33, 1-32 (1979). doi: 10. 1016/0021-9991(79)90025-1.
    • (1979) J. Comput. Phys. , vol.33 , pp. 1-32
    • Davies, B.1    Martin, B.2
  • 13
    • 0001293615 scopus 로고
    • An improved method for numerical inversion of Laplace transforms
    • doi:10.1137/0903022
    • de Hoog, F., Knight, J., Stokes, A.: An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Statist. Comput. 3, 357-366 (1982). doi: 10. 1137/0903022.
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 357-366
    • de Hoog, F.1    Knight, J.2    Stokes, A.3
  • 14
    • 0027663475 scopus 로고
    • On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications
    • doi:10.1145/155743.155788
    • Duffy, D. G.: On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications. ACM Trans. Math. Softw. 19(3), 333-359 (1993). doi: 10. 1145/155743. 155788.
    • (1993) ACM Trans. Math. Softw. , vol.19 , Issue.3 , pp. 333-359
    • Duffy, D.G.1
  • 16
    • 0001383683 scopus 로고
    • Modification of the theory of leaky aquifers
    • doi:10.1029/JZ065i011p03713
    • Hantush, M.: Modification of the theory of leaky aquifers. J. Geophys. Res. 65(11), 3713-3725 (1960). doi: 10. 1029/JZ065i011p03713.
    • (1960) J. Geophys. Res. , vol.65 , Issue.11 , pp. 3713-3725
    • Hantush, M.1
  • 18
    • 41249092819 scopus 로고    scopus 로고
    • Application of the Weeks method for the numerical inversion of the Laplace transform to the matrix exponential
    • Kano, P. O., Brio, M., Moloney, J. V.: Application of the Weeks method for the numerical inversion of the Laplace transform to the matrix exponential. Communications in Mathematical Sciences 3(3), 335-372 (2005).
    • (2005) Communications in Mathematical Sciences , vol.3 , Issue.3 , pp. 335-372
    • Kano, P.O.1    Brio, M.2    Moloney, J.V.3
  • 19
    • 67349139124 scopus 로고    scopus 로고
    • Laplace-transform analytic-element method for transient porous-media flow
    • doi:10.1007/s10665-008-9251-1
    • Kuhlman, K. L., Neuman, S. P.: Laplace-transform analytic-element method for transient porous-media flow. J. Eng. Math. 64(2), 113-130 (2009). doi: 10. 1007/s10665-008-9251-1.
    • (2009) J. Eng. Math. , vol.64 , Issue.2 , pp. 113-130
    • Kuhlman, K.L.1    Neuman, S.P.2
  • 23
    • 84966209497 scopus 로고
    • A modification of the Weeks method for numerical inversion of the Laplace transform
    • doi:10.2307/2008097
    • Lyness, J., Giunta, G.: A modification of the Weeks method for numerical inversion of the Laplace transform. Math. Comput. 47(175), 313-322 (1986). doi: 10. 2307/2008097.
    • (1986) Math. Comput. , vol.47 , Issue.175 , pp. 313-322
    • Lyness, J.1    Giunta, G.2
  • 24
    • 70350580475 scopus 로고    scopus 로고
    • Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers
    • doi:10.1111/j.1365-246X.2009.04336.x
    • Malama, B., Kuhlman, K., Revil, A.: Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers. Geophys. J. Int. 179(2), 990-1003 (2009). doi: 10. 1111/j. 1365-246X. 2009. 04336. x.
    • (2009) Geophys. J. Int. , vol.179 , Issue.2 , pp. 990-1003
    • Malama, B.1    Kuhlman, K.2    Revil, A.3
  • 25
    • 85121847429 scopus 로고    scopus 로고
    • Improved forward and inverse analyses of saturated-unsaturated flow toward a well in a compressible unconfined aquifer
    • doi:10.1029/2009WR008899, W07508
    • Mishra, P. K., Neuman, S. P.: Improved forward and inverse analyses of saturated-unsaturated flow toward a well in a compressible unconfined aquifer. Water Resour. Res. 46(7), W07508, 16 (2010). doi: 10. 1029/2009WR008899.
    • (2010) Water Resour. Res. , vol.46 , Issue.7 , pp. 16
    • Mishra, P.K.1    Neuman, S.P.2
  • 26
    • 67650983044 scopus 로고    scopus 로고
    • Laplace-transform finite element solution of nonlocal and localized stochastic moment equations of transport
    • Morales-Casique, E., Neuman, S. P.: Laplace-transform finite element solution of nonlocal and localized stochastic moment equations of transport. Commun. Comput. Phys. 6(1), 131-161 (2009).
    • (2009) Commun. Comput. Phys. , vol.6 , Issue.1 , pp. 131-161
    • Morales-Casique, E.1    Neuman, S.P.2
  • 27
    • 34247500374 scopus 로고    scopus 로고
    • Python for scientific computing
    • doi:10.1109/MCSE.2007.58
    • Oliphant, T. E.: Python for scientific computing. Comput. Sci. Eng. 9(3), 10-20 (2007). doi: 10. 1109/MCSE. 2007. 58.
    • (2007) Comput. Sci. Eng. , vol.9 , Issue.3 , pp. 10-20
    • Oliphant, T.E.1
  • 28
    • 77958410085 scopus 로고
    • A new numerical method for the inversion of the Laplace transform
    • doi:10.1093/imamat/10.2.185
    • Piessens, R.: A new numerical method for the inversion of the Laplace transform. J. Inst. Math. Appl. 10, 185-192 (1972). doi: 10. 1093/imamat/10. 2. 185.
    • (1972) J. Inst. Math. Appl. , vol.10 , pp. 185-192
    • Piessens, R.1
  • 30
    • 84976835846 scopus 로고
    • Algorithm 368: numerical inversion of Laplace transforms
    • doi:10.1145/361953.361969
    • Stehfest, H.: Algorithm 368: numerical inversion of Laplace transforms. Commun. ACM 13(1), 47-49 (1970). doi: 10. 1145/361953. 361969.
    • (1970) Commun. ACM , vol.13 , Issue.1 , pp. 47-49
    • Stehfest, H.1
  • 31
    • 84981755249 scopus 로고
    • Flow to wells in the presence of radial discontinuities
    • doi:10.1111/j.1745-6584.1969.tb01666.x
    • Sternberg, Y.: Flow to wells in the presence of radial discontinuities. Ground Water 7(6), 17-20 (1969). doi: 10. 1111/j. 1745-6584. 1969. tb01666. x.
    • (1969) Ground Water , vol.7 , Issue.6 , pp. 17-20
    • Sternberg, Y.1
  • 32
    • 0026471304 scopus 로고
    • The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations
    • doi:10.1029/91WR02560
    • Sudicky, E., McLaren, R.: The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations. Water Resour. Res. 28(2), 499-514 (1992). doi: 10. 1029/91WR02560.
    • (1992) Water Resour. Res. , vol.28 , Issue.2 , pp. 499-514
    • Sudicky, E.1    McLaren, R.2
  • 33
    • 0002152334 scopus 로고
    • The accurate numerical inversion of Laplace transforms
    • doi:10.1093/imamat/23.1.97
    • Talbot, A.: The accurate numerical inversion of Laplace transforms. IMA J. Appl. Math. 23(1), 97 (1979). doi: 10. 1093/imamat/23. 1. 97.
    • (1979) IMA J. Appl. Math. , vol.23 , Issue.1 , pp. 97
    • Talbot, A.1
  • 34
    • 0001665007 scopus 로고
    • Numerical inversion of Laplace transforms using Laguerre functions
    • doi:10.1145/321341.321351
    • Weeks, W.: Numerical inversion of Laplace transforms using Laguerre functions. J. ACM 13(3), 419-429 (1966). doi: 10. 1145/321341. 321351.
    • (1966) J. ACM , vol.13 , Issue.3 , pp. 419-429
    • Weeks, W.1
  • 35
    • 0033296255 scopus 로고    scopus 로고
    • Algorithms for parameter selection in the Weeks method for inverting the Laplace transform
    • doi:10.1137/S1064827596312432
    • Weideman, J.: Algorithms for parameter selection in the Weeks method for inverting the Laplace transform. SIAM J. Sci. Comput. 21(1), 111-128 (1999). doi: 10. 1137/S1064827596312432.
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.1 , pp. 111-128
    • Weideman, J.1
  • 36
    • 0004201980 scopus 로고
    • Princeton, NJ: Princeton University Press
    • Widder, D.: The Laplace Transform. Princeton University Press, Princeton, NJ (1941).
    • (1941) The Laplace Transform
    • Widder, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.