  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.
