Fabio Marcuzzi

The Best-Approximation Weighted-Residuals method for the steady convection-diffusion-reaction problem

Abstract: In this paper we present an analytical, parameter-free, Petrov-Galerkin method that gives stable solutions of convection dominated boundary-value problems. We call it the Best Approximation Weighted Residuals (BAWR) method since it gives the best approximation in the norm induced by the inner-product used to build the weighted-residuals approximation. The method computes the optimal weighting functions by solving suitable adjoint problems. Moreover, through a localization technique it becomes computationally efficient without loosing accuracy. The analysis is confirmed by numerical results.

EFFICIENT RECONSTRUCTION OF CORROSION PROFILES BY INFRARED THERMOGRAPHY

In this paper, we propose a novel algorithm to solve the hidden corrosion estimation problem from experimental data produced by infrared thermography. This is therefore a thermal inverse problem. The algorithm is put in a predictor-corrector form and uses an Adaptive Finite Element model as the reference model. The adaptation is done in the (linear) predictor step, while the parameter estimation is done in the (nonlinear) corrector step. An ad-hoc regularization strategy has been developed. Experiments with real data have confirmed the effectiveness of the method. Considerable computational savings have been achieved compared to a standard algorithm formulation.

An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

In this paper, an algorithm based on unstructured triangular meshes using standard refinement patterns for anisotropic adaptive meshes is presented. It consists of three main actions: anisotropic refinement, solution-weighted smoothing and patch unrefinement. Moreover, a hierarchical mesh formulation is used. The main idea is to use the error and error gradient on each mesh element to locally control the anisotropy of the mesh. The proposed algorithm is tested on interpolation and boundary-value problems with a discontinuous solution.

Adaptivity in space and time for shallow water equations

In this paper, adaptive algorithms for time and space discretizations are added to an existing solution method previously applied to the Venice Lagoon Tidal Circulation problem. An analysis of the interactions between space and time discretizations adaptation algorithms is presented. In particular, it turns out that both error estimations in space and time must be present for maintaining the adaptation efficiency. Several advantages, for adaptivity and for time decoupling of the equations, offered by the operator-splitting adopted for shallow water equations solution are presented. Copyright

Numerical algorithms for an inverse problem of corrosion detection

This paper describes a numerical strategy for the detection of hidden corrosion in an internal, unobservable surface of a material object, whose geometry and material properties are known. Since the corrosion is not directly measurable, it is estimated using a nondestructive infrared thermographic inspection. The a priori knowledge about the material object allows us to use a physical-mathematical model to support the estimate. Given a suitable parametrization of the depth of the real corroded profile, the numerical algorithm performs a nonlinear estimate of the corroded model domain parameters, adopting a predictor-corrector scheme.

A parallel solver for adaptive finite element discretizations

A parallel solver for the adaptive finite element analysis is presented. The primary aim of this work has been to establish an efficient parallel computational procedure which requires only local computations to update the solution of the system of equations arising from the finite element discretization after a local mesh-adaptation step. For this reason a set of algorithms has been developed (two-level domain decomposition, recursive hierarchical mesh-refinement, selective solution-update of linear systems of equations) which operate upon general and easily available partitioning, meshing and linear systems solving algorithms.

A parabolic inverse convection-diffusion-reaction problem solved using space-time localization and adaptivity

This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a Projected Damped Gauss Newton (PDGN), in the second one it is ill-posed and an adaptive parametrization with space-time localization will be adopted to regularize it.

An approximate waves-bordering algorithm for adaptive finite elements analysis

In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equations that updates recursively and stops when the norm of the residual has gone under a user-defined threshold.

Linear estimation of physical parameters with subsampled and delayed data

Abstract An improved algorithm for the estimation of physical parameters with sub-sampled and delayed data is here presented. It shows a much better accuracy than the state-of-the-art when the sampling time of data acquisition T s is much higher than the discretization step T s c that should be used to get a highly accurate discrete model, i.e. T s ≫ T s c , which is a common situation in multi-body and finite-element modelling applications. Moreover, the method proposed is capable of compensating delays between different acquisition channels. For the numerical experiments we focus on a mainstream class of models in applied mechanics, i.e. linear elasto-dynamics.

Analytic heuristics for a fast DSC-MRI

Hemodynamics of the human brain may be studied with Dynamic Susceptibility Contrast MRI (DSC-MRI) imaging. The sequence of volumes obtained exhibits a strong spatiotemporal correlation, that can be exploited to predict which measurements will bring mostly the new information contained in the next frames. In general, the sampling speed is an important issue in many applications of the MRI, so that the focus of many current researches is to study methods to reduce the number of measurement samples needed for each frame without degrading the image quality. For the DSC-MRI, the frequency under-sampling of single frame can be exploited to make more frequent space or time acquisitions, thus increasing the time resolution and allowing the analysis of fast dynamics not yet observed. Generally (and also for MRI), the recovery of sparse signals has been achieved by Compressed Sensing (CS) techniques, which are based on statistical properties rather than deterministic ones.. By studying analytically the compound Fourier+Wavelet transform, involved in the processes of reconstruction and sparsification of MR images, we propose a deterministic technique for a rapid-MRI, exploiting the relations between the wavelet sparse representation of the recovered and the frequency samples. We give results on real images and on artificial phantoms with added noise, showing the superiority of the methods both with respect to classical Iterative Hard Thresholding (IHT) and to Location Constraint Approximate Message Passing (LCAMP) reconstruction algorithms.