Search results for "Numerical Analysis"
showing 10 items of 883 documents
Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models
2018
Estimating the vehicle crashworthiness parameters experimentally is expensive and time consuming. For these reasons different modelling approaches are utilized to predict the vehicle behaviour and reduce the need for full-scale crash testing. The earlier numerical methods used for vehicle crashworthiness analysis were based on the use of lumped parameters models (LPM), a combination of masses and nonlinear springs interconnected in various configurations. Nowadays, the explicit nonlinear finite element analysis (FEA) is probably the most widely recognized modelling technique. Although informative, finite element models (FEM) of vehicle crash are expensive both in terms of man-hours put into…
Interrogating witnesses for geometric constraint solving
2012
International audience; Classically, geometric constraint solvers use graph-based methods to decompose systems of geometric constraints. These methods have intrinsic limitations, which the witness method overcomes; a witness is a solution of a variant of the system. This paper details the computation of a basis of the vector space of free infinitesimal motions of a typical witness, and explains how to use this basis to interrogate the witness for dependence detection. The paper shows that the witness method detects all kinds of dependences: structural dependences already detectable by graph-based methods, but also non-structural dependences, due to known or unknown geometric theorems, which…
Darboux integrable system with a triple point and pseudo-abelian integrals
2016
We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.
Numerical Treatment of the Filament-Based Lamellipodium Model (FBLM)
2017
We describe in this work the numerical treatment of the Filament-Based Lamellipodium Model (FBLM). This model is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel F-actin filaments. It includes, among others, the bending stiffness of the filaments, adhesion to the substrate, and the cross-links connecting the two families. The numerical method proposed is a Finite Element Method (FEM) developed specifically for the needs of this problem. It is comprised of composite Lagrange–Hermite two-dimensional elements defined over a two-dimensional space. We present some elements of the FEM and emphasize in the numerical treatment of t…
A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: The urokinase model
2016
In the present work we investigate a model that describes the chemotactically and proteolytically driven tissue invasion by cancer cells. The model is a system of advection-reaction-diffusion equations that takes into account the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of such a system constitutes a challenge due to the merging, emerging, and traveling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate very fine discretization grids to resolve these dynamics in an accurate way. To reduce the computational cost without sacrificing the accuracy of the solution, we apply adaptive…
A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients
2017
We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…
Better numerical approximation by Durrmeyer type operators
2018
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.
Estimates for the differences of positive linear operators and their derivatives
2019
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.
Better approximation of functions by genuine Bernstein-Durrmeyer type operators
2018
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.
Tracking of blood vessels motion from 4D-flow MRI data
2022
This paper presents a novel approach to track objects from 4D Flow MRI data. A salient feature of the proposed method is that it fully exploits the geometrical and dynamical nature of the information provided by this imaging modality. The underlying idea consists in formulating the tracking problem as a data assimilation problem, in which both position and velocity observations are extracted from the 4D Flow MRI data series. Optimal estate estimation is then performed in a sequential fashion via Kalman filtering. The capabilities of the method are extensively assessed in a numerical study involving synthetic and clinical data.