Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

Details Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

2012-04-20

arxiv.org/abs/1204.4754v1

Mathematics

Numerical Analysis

Scientific paper

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, focusing on requirements of Laplace-space numerical approaches in general. 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 possible. We find Fourier series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for image function evaluation re-use across at least a log cycle of time.

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