Search results for " Numerical analysis"
showing 10 items of 106 documents
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme
2017
This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which leads to an efficient computation with a small number of degrees of freedom especially in three space dimensions. In this paper, Part II, we apply a semi-implicit time discretization which yields the linear scheme. We concentrate on the diffusive viscoelastic model, i.e. in the constitutive equation for time evolution of the conformation tensor a diffusive effect is included. Under mild stability condi…
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.
Monotone cubic spline interpolation for functions with a strong gradient
2021
Abstract Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can appear due to the Gibbs phenomenon. Also, preservation of data monotonicity is a requirement in some applications, and that property is not automatically verified by the interpolator. Hence, some additional techniques have to be incorporated so as to ensure monotonicity. The final interpolator is not actually a spline as C 2 regularity and monotonicity are not ensured at the same time. In this paper, we study sufficient conditions to obtain monot…
Numerical Modelling for Assessing the Structural Efficiency of CAM® Reinforcement System for Masonry Walls
2022
A large portion of the Italian building heritage is made of masonry construc-tions, which were erected in the first decades of the last century and were conceived to support gravitational loads only. Many research activities have been carried out in order to propose retrofitting techniques aimed at improving seismic behaviour of existing ma-sonry buildings. The present paper focuses on the CAM® reinforcing system. Such a retrofitting technique, which is widely used in Italy, consists in the application of pre-tensioned stainless steel ribbons on existing masonry walls, conferring to them addi-tional strength, ductility and beneficial confinement effects. The preliminary outcomes of a common…
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…
Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
2019
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…
Numerical Analysis of Bearing Capacity of a Ring Footing on Geogrid Reinforced Sand
2021
A ring footing is found to be of practical importance in supporting symmetrical constructions for example silos, oil storage container etc. In the present paper, numerical analysis was carried out with explicit code FLAC3D 7.0 to investigate bearing capacity of a ring footing on geogrid reinforced sand. Effects of the ratio n of its inner/outer diameter (Di/D) of a ring footing, an optimum depth to lay the geogrid layer were examined. It was found that an intersection zone was developed in soil under inner-side (aisle) of ring footing, contributing to its bearing capacity. Substantial increase of bearing capacities could be realized if ratio n of a ring footing was around 0.6. Numerical res…
On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method
2017
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.