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

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Abstract

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.

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  1. Repository Performance Department, Sandia National Laboratories, 4100 National Parks Highway, Carlsbad, New Mexico, USA

    Kristopher L. Kuhlman

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Kuhlman, K.L. Review of inverse Laplace transform algorithms for Laplace-space numerical approaches. Numer Algor 63, 339–355 (2013). https://doi.org/10.1007/s11075-012-9625-3

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  • DOI: https://doi.org/10.1007/s11075-012-9625-3

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