Search results for " numerical analysis."

An order-adaptive compact approximation Taylor method for systems of conservation laws

2021

Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…

ANALISI DEL PROCESSO DI ROTTURA PER SOLLEVAMENTO DEL FONDO DI SCAVI CONTROVENTATI

2012

Nella presente nota si riportano i principali risultati di un’analisi sui meccanismi di rottura per sollevamento del fondo di scavi sostenuti da diaframmi. È stata studiata l’influenza su tali meccanismi di fattori quali: lo stato tensionale iniziale; il rapporto tra larghezza e altezza dello scavo; la profondità d’infissione dei diaframmi al di sotto del fondo dello scavo; la dissipazione delle sovrappressioni interstiziali. I risultati ottenuti indicano che i metodi correntemente utilizzati per la valutazione delle condizioni di stabilità del fondo scavo, basati sull’analisi in termini di tensioni totali e sull’impiego della resistenza non drenata su possono portare a sopravvalutare le co…

Experimental and numerical analysis of flexural behaviour of GFRP pultruded material

2014

Case Study of the Structural Behavior of a Catalan Bricks Masonry Vault

2015

Catalan vaults are a peculiar type of low thickness vaulted brick masonry structure. Knowledge of load-deflection response and load bearing capacity are important aspects to consider with the aim of preserving these structural members as part of the cultural heritage. In order to investigate these aspects, complete knowledge of the constituent materials and geometry (dimension, thickness, constructive section) is necessary in such a way as to predict the load-deflection response and the effective load-carrying capacity; the latter can be determined utilizing simplified models (limit analysis) or by means of a numerical analysis (finite element method). With this aim, the structural behaviou…

A mesh less approch based upon Radial basis function Hermite collocation method for predicting the cooling and the freezing times of foods

2005

This work presents a meshless numerical scheme for the solution of time dependent non linear heat transfer problems in terms of a radial basis function Hermite collocation approach. The proposed scheme is applied to foodstuff's samples during freezing process; evaluation of the time evolution of the temperature profile along the sample, as well as at the core, is carried out. The moving phase-change zone is identified in the domain and plotted at several timesteps. The robustness of the proposed scheme is tested by a comparison of the obtained numerical results with those found using a Finite Volume Method and with experimental results.

Polynomial mapped bases: theory and applications

2022

Abstract In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.

Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves

2018

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrodinger equation in the semiclassical limit.

Iterative Reconstruction of Signals on Graph

2020

We propose an iterative algorithm to interpolate graph signals from only a partial set of samples. Our method is derived from the well known Papoulis-Gerchberg algorithm by considering the optimal value of a constant involved in the iteration step. Compared with existing graph signal reconstruction algorithms, the proposed method achieves similar or better performance both in terms of convergence rate and computational efficiency.

Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing

2020

In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Y\'a\~nez, A new WENO-2r algorithm with progressive order of accuracy close to discontinuities, submitted to SIAM J. Numer. Anal.. This new strategy tries to improve the results of WENO-($2r-1$) algorithm close to the singularities, resulting in an optimal order of accuracy at these zones. The main idea is to modify the optimal weights so that they have a nonlinear expression that depends on the position of the discontinuities. In this paper we study the application of the new algorithm to signal processing using Harten's multiresolution. Se…

Multidomain spectral method for the Gauss hypergeometric function

2018

International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…