A Comparative Analysis of Numerical Inverse Laplace Transform Methods for Electromagnetic Transient Analysis

Nowadays, transient analysis of electromagnetic systems is widely adopted as a virtual prototyping tool in the design of electrical and electronic devices. Time domain (TD) methods for the solutions of Maxwell's equations represent the most obvious approach to tackling this type of problem. Frequency domain (FD) analysis techniques are also commonly used to return the TD response through the inverse Fourier transform. This approach suffers from the need to compute the frequency response over a wide frequency range that has to be finely sampled to avoid aberrations in the inverse transform. A valuable alternative is represented by the numerical inversion of the Laplace transform (NILT) that conjugates the capability to return the TD responses with the possibility to adopt complex frequency models that are free of most of the issues of TD techniques. The aim of this work is to perform a comparative analysis of two of the most popular methods for the computation of the numerical inverse Laplace transform, known as the NILT, and fast inversion of the Laplace transform (FILT), clarifying the issues and limitations behind these methods and pointing out possible solutions.