Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches
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.
Keywords
Cite
@article{arxiv.1204.4754,
title = {Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches},
author = {Kristopher L. Kuhlman},
journal= {arXiv preprint arXiv:1204.4754},
year = {2016}
}