Search results for " numerical analysis."

Annihilation Operators for Exponential Spaces in Subdivision

2022

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

2021

<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…

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.

A new incremental method of computing the limit load in deformation plasticity models

2015

The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter $\zeta\in[0,\zeta_{lim})$, where $\zeta_{lim}$ is generally unknown. In the new method, the incremental procedure is operated in terms of an inverse mapping and the respective parameter $\alpha$ is changing in the interval $(0,+\infty)$. Theoretically, in each step of this algorithm, we obtain a guaranteed lower bound of $\zeta_{lim}$. Reduction of the problem to a finite element subspace associated with a mesh $\mathcal T_h$ generates computable bound $\zeta_{lim,h…

Wave Propagation in a 3-D Optical Waveguide

2003

In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.\cite{MS} The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavio…

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…

Torus computed tomography

2020

We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…

Laminar flow through fractal porous materials: the fractional-order transport equation

2015

Abstract The anomalous transport of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force–flux relation for the motion in a porous solid, then a generalized version of the Hagen–Poiseuille equation has been obtained with the aid of Riemann–Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.

On the thermo-mechanical behaviour of the IFMIF target assembly under steady state and transient operative scenarios

Multivariate morphometric analysis of the Stipa turkestanica group (Poaceae: Stipa sect. Stipa)

2015

Based on numerical analyses of macromorphological characters (cluster analysis, principal coordinate analysis and principal component analysis), scanning electron microscopy observation of lemma and lamina micromorphology, as well as field observations, five taxa belonging to the Stipa turkestanica group have been recognized in the mountain area of Central Asia. They are S. turkestanica subsp. turkestanica, S. turkestanica subsp. trichoides, S. macroglossa subsp. macroglossa, S. macroglossa subsp. kazachstanica and S. kirghisorum. As a result of this study, we propose one new combination, S. macroglossa var. pubescens, and designate lectotypes for S. turkestanica subsp. trichoides and S. ma…