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In the paper, an efficient and reliable algorithm for solving the circuit nonlinear algebraic-differential equations based on a sophisticated arrangement of Newton interpolation polynomial is characterized first. After that, a novel method is introduced for improving the convergence with four suggested criteria that are being compared. Unlike the similar algorithms focused on an operating point analysis only, the proposed method also works in a transient analysis. For enhancing the efficiency of repeated solutions of linear systems necessary in the Newton-Raphson method, a novel modification of the Markowitz criterion is suggested, which is compatible with the fast modes of the LU factorization. The modified criterion consists in an estimation of probabilities of the fill-in enlargement. The probabilities are determined for all columns of the system matrix before the LU factorization, where the column probability is calculated as the average value of the probabilities for all the column elements. Finally, the columns are reordered so that first and last should be those with the minimum and maximum probabilities, respectively. As a verification of this fundamental proposal of the paper, a comprehensive set of numerical tests has been carried out.

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GPU cards have been used for scientific calculations for many years. Despite their ever-increasing performance, there are cases where they may still have problems. This article addresses possible performance and memory issues and their solutions that may occur during GPU calculations of iterative algorithms. Specifically, the article focuses on the optimization of transient simulation of extra-large highly nonlinear time-dependent circuits in SPICE-like electronic circuit simulator core enhanced with NVIDIA/CUDA (Compute Unified Device Architecture) interface and iterative Krylov Subspace methods with emphasis on improved accuracy. The article presents procedures for solving problems that may occur during this integration and negatively affect either the simulation speed or the accuracy of the calculation. Finally, a comparison of the implementation of an iterative calculation procedure with the use of GPU cards, calculation by the direct method and calculation on the CPU only is presented.

Although practically all function blocks of the satellite navigation receivers are realized using the CMOS digital integrated circuits, it is appropriate to create a separate low noise antenna preamplifier based on a low noise pHEMT. Such an RF front end can be strongly optimized to attain a suitable tradeoff between the noise figure and transducer power gain. Further, as all the four principal navigation systems (GPS, GLONASS, Galileo, and COMPASS) work in similar frequency bands (roughly from 1.1 to 1.7 GHz), it is reasonable to create the low noise preamplifier for all of them. In the paper, a sophisticated method of the amplifier design is suggested based on multiobjective optimization. A substantial improvement of a standard optimization method is also outlined to satisfy a uniform coverage of Pareto front. Moreover, for enhancing efficiency of many times repeated solutions of large linear systems during the optimization, a new modification of the Markowitz criterion is suggested compatible with fast modes of the LU factorization. Extraordinary attention was also given to the accuracy of modeling. First, an extraction of pHEMT model parameters was performed including its noise part, and several models were compared. The extraction was carried out by an original identification procedure based on a combination of metaheuristic and direct methods. Second, the equations of the passive elements (including transmission lines and T-splitters) were carefully defined using frequency dispersion of their parameters as Q, ESR, etc. Third, an optimal selection of the operating point and essential passive elements was performed using the improved optimization method. Finally, the s-parameters and noise figure of the amplifier were measured, and stability and third-order intermodulation products were also checked.