Numerical inverse Laplace transform (NILT) methods are potential methods for time domain simulations, for instance the analysis of the transient phenomena in systems with lumped and/or distributed parameters. This paper proposes a numerical inverse Laplace transform method based originally on hyperbolic relations. The method is further enhanced by properly adapting several convergence acceleration techniques, namely, the epsilon algorithm of Wynn, the quotient-difference algorithm of Rutishauser and the Euler transform. The resulting accelerated models are compared as for their accuracy and computational efficiency. Moreover, an expansion to two dimensions is presented for the first time in the context of the accelerated hyperbolic NILT method, followed by the error analysis. The expansion is done by repeated application of one-dimensional partial numerical inverse Laplace transforms. A detailed static error analysis of the resulting 2D NILT is performed to prove the effectivness of the method. The work is followed by a practical application of the 2D NILT method to simulate voltage/current distributions along a transmission line. The method and application are programmed using the Matlab language.

In the paper, a technique of the numerical inversion of multidimensional Laplace transforms (nD NILT), based on a complex Fourier series approximation is elaborated in light of a possible ralative error achievable. The detailed error analysis shows a relationship between the numerical integration of a multifold Bromwich integral and a complex Fourier series approximation, and leads to a novel formula relating the limiting relative error to the nD NILT technique parameters.

We studied transient fields on a perfectly conducting sphere excited by a half sine pulse wave and examined the Poynting vectors, the energy densities and the energy velocities of the creeping waves. We used FILT (Fast Inversion of Laplace Transform) method for transient analysis. We compared the amplitudes of the creeping wave with that of steady state high frequency approximation obtained by the Watson transformation. The main results are: (1) We confirmed in the transient response that the pulse propagates clockwise and counterclockwise along the geodesic circumference. (2) In the transient electromagnetic field observed in the E-plane we can recognize creeping waves clearly. (3) The existence of creeping waves is not clear in the H-plane. (4) The pulse wave propagation on the sphere is seen more clearly from the Poynting vectors and the energy densities than the field components. (5) The energy velocity of the wave front is equal to the light velocity as should be. The energy velocity of the wave body becomes smaller with the passage of time. (6) The amplitude of the creeping wave for a beat pulse and the amplitude obtained by the Watson transform for mono spectrum agree in the order of relative error below 25%.