Informatica

A fast vectorized codes for assembly mixed finite element matrices for the generalized Navier–Stokes system in three space dimensions in the MATLAB language are proposed by the MINI element. Vectorization means that the loop over tetrahedra is avoided. Numerical experiments illustrate computational efficiency of the codes. An experimental superconvergence rate for the pressure component is established.

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 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.