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 multiple-input multiple-output (MIMO) wireless systems, the receiver must extract each transmitted signal from received signals. Iterative signal detection with belief propagation (BP) can improve the error rate performance, by increasing the number of detection and decoding iterations in MIMO systems. This number of iterations is, however, limited in actual systems because each additional iteration increases latency, receiver size, and so on. This paper proposes a convergence acceleration technique that can achieve better error rate performance with fewer iterations than the conventional iterative signal detection. Since the Log-Likelihood Ratio (LLR) of one bit propagates to all other bits with BP, improving some LLRs improves overall decoder performance. In our proposal, all the coded bits are divided into groups and only one group is detected in each iterative signal detection whereas in the conventional approach, each iterative signal detection run processes all coded bits, simultaneously. Our proposal increases the frequency of initial LLR update by increasing the number of iterative signal detections and decreasing the number of coded bits that the receiver detects in one iterative signal detection. Computer simulations show that our proposal achieves better error rate performance with fewer detection and decoding iterations than the conventional approach.

An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.