Numerical Algorithms

, Volume 63, Issue 2, pp 339–355 | Cite as

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

  • Kristopher L. Kuhlman
Original Paper


A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time.


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


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Repository Performance DepartmentSandia National LaboratoriesCarlsbadUSA

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