Informatica

We propose a fast MATLAB implementation of the mini-element (i.e. $P1$-Bubble/$P1$) for the finite element approximation of the generalized Stokes equation in 2D and 3D. We use cell arrays to derive vectorized assembling functions. We also propose a Uzawa conjugate gradient method as an iterative solver for the global Stokes system. Numerical experiments show that our implementation has an (almost) optimal time-scaling. For 3D problems, the proposed Uzawa conjugate gradient algorithm outperforms MATLAB built-in linear solvers.

The current increment in energy consumption has renewed the interest in the development of alternatives to fossil fuels. In this regard, the interest in solving the different control problems existing in nuclear fusion reactors like Tokamaks has been intensified. The aim of this manuscript is to show how the ASTRA code, which is used to simulate the performance of Tokamaks, can be integrated into the Matlab-Simulink tool in order to make easier the development of suitable controllers for Tokamaks. As a demonstrative case study to show the feasibility and the goodness of the proposed integration, a modified anti-windup PID-based controller coupled with an optimization algorithm for the loop voltage has been implemented. This integration represents an original and innovative work in the Tokamak control area and it provides new possibilities for the development and application of advanced control schemes to the standardized ASTRA code.

The goal of this work is to describe the underlying theoretical and algorithmic basis of a MATLAB-based software developed by the authors. The software is intended for investigation of time series (signals) which can be modeled as the sum of real-valued quasipolynomials plus white noise. With the help of the software described, one can compute the expressions of the Cramér-Rao lower bound on the covariance matrix of the estimation error of unbiased estimates of damping factors and frequencies of quasipolynomials and to obtain estimates of these parameters using three versions of Prony method. Using this software, one can generate various models of quasipolynomials, obtain plots of their poles with respect to the unit circle, compute and plot 2σ-bounds (where σ is given by the CRB formula) around each pole, and also pole estimates obtained in each realization. Results of numerical experiments are presented.