Search results for "Analisi numerica"

Fixed point iterative schemes for variational inequality problems

2018

In a wide class of evolutionary processes, the problem of computing the solutions of an initial value problem is encountered. Here, we consider projected dynamical systems in the sense of \cite{Daniele} and references therein. Precisely, a projected dynamical system is an operator which solves the initial value problem: \begin{equation}\label{PDS}\frac{dx(t)}{dt}= \Pi_{\mathbb{K}}\left(x(t),-F(x(t))\right), \quad x(0)=x_0 \in \mathbb{K}, \, t \in [0,+\infty[,\tag{P}\end{equation} where $\mathbb{K}$ is a convex polyhedral set in $\mathbb{R}^n$, $F: \mathbb{K} \to \mathbb{R}^n$ and $\Pi_{\mathbb{K}}: \mathbb{R} \times \mathbb{K} \to \mathbb{R}^n$ is given as follows $\Pi_{\mathbb{K}}(x,-F(x))…

The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG

2015

The estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution pro- cess requires an accurate and fast forward solver. In this paper the method of fundamental solutions is, for the first time, proposed as a meshfree, boundary-type, and easy-to-implement alternative to the boundary element method (BEM) for solving the M/EEG forward problem. The solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three-dimensional Laplace equation. Numerical accuracy, convergence, and computational load are investigated. The proposed met…

Un modello numerico particellare per la magnetoencefalografia

2011

A Meshless Approach for Electromagnetic Simulation of Metallic Carbon Nanotubes

2009

In this paper, a study on the electromagnetic behaviour of a single wall carbon nanotube model is described. The electrons available for conduction are treated as a thin cylindrical layer fluid and their motion is described by means of classical hydrodynamics equations in linearized form. These equations are solved in time domain using the Smoothed Particle Hydrodynamics method. The method suitably handled runs on GRID environment.

SOIL IONIZATION DUE TO HIGH PULSE TRANSIENT CURRENTS LEAKED BY EARTH ELECTRODES

2009

This paper proposes a numerical model of the soil ionization phenomena that can occur when earth electrodes are injected by high pulse transient currents, as the one associated with a direct lightning stroke. Based on finite difference time domain numerical scheme, this model ascribes the electrical breakdown in the soil to the process of discharge in the air. In fact, as soon as the local electric field overcomes the electrical strength, the air in the voids trapped among soil particles is ionized, and the current is conducted by ionized plasma paths locally grown. The dimension of these ionized air channels is strictly dependent upon the local temperature. Thus, a local heat balance is en…

G1 rational blend interpolatory schemes: a comparative study

2012

Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bezier patches. As it is well known, any method aiming at constructing a parametric, tangent plane (G^1) continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patc…

A numerical method for imaging of biological microstructures by VHF waves

2014

Imaging techniques give a fundamental support to medical diagnostics during the pathology discovery as well as for the characterization of bio-medical structures. The imaging methods involve electromagnetic waves in a frequency range that spans from some Hz to GHz and over. Most of these methods involve ionizing waves and scanning of a large human body area even if only a focused inspection is needed. In this paper, a numerical method to evaluate the shape of microstructures for application in the medical field, with a very low invasiveness for the human body, is proposed. In particular, the tooth’s root canal is considered. In fact, this is one of the hot topics in the endodontic procedure…

On the use of a meshless solver for PDEs governing electromagnetic transients

2009

In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.

A Meshfree Boundary Method for M/EEG Forward Computations

2014

Electric scalar potential estimations for non-invasive brain activity detection through multinode Shepard method

2022

Electric scalar potential estimation is a key step for non-invasive investigations of brain activity with high time resolutions. The neural sources can be reconstructed by solving a typical inverse problem based on a forward problem formulated as a set of boundary value problems coupled by interface conditions. In this paper, we propose a Shepard multinode method to numerically estimate electric scalar potentials via collocation. The method is based on a special kind of inverse distance weighting partition of unity method to increase polynomial precision, approximation order, and accuracy of the classical Shepard approximation. The barycentric form, through the use of cardinal basis functio…