Search results for " Operator"

Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation

2011

We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…

Regularization and finite element approximation of the wave equation with Dirichlet boundary data

1990

Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators

2017

In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…

Shaping communities of local optima by perturbation strength

2017

Recent work discovered that fitness landscapes induced by Iterated Local Search (ILS) may consist of multiple clusters, denoted as funnels or communities of local optima. Such studies exist only for perturbation operators (kicks) with low strength. We examine how different strengths of the ILS perturbation operator affect the number and size of clusters. We present an empirical study based on local optima networks from NK fitness landscapes. Our results show that a properly selected perturbation strength can help overcome the effect of ILS getting trapped in clusters of local optima. This has implications for designing effective ILS approaches in practice, where traditionally only small per…

A new approach for critical resources allocation

2009

This paper presents a solution based on Artificial Intelligence using Multi-objective Genetic Algorithms to optimize the allocation of teachers and classrooms. The implementation was created in order to optimize the process in both cases, allowing them to compete so as to establish a balance and arrive at a feasible solution quickly and efficiently.

An operatorial description of desertification

2016

We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional…

On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants

2004

In the present paper, we analyze computational properties of the functional type a posteriori error estimates that have been derived for elliptic type boundary-value problems by duality theory in calculus of variations. We are concerned with the ability of this type of a posteriori estimates to provide accurate upper bounds of global errors and properly indicate the distribution of local ones. These questions were analyzed on a series of boundary-value problems for linear elliptic operators of 2nd and 4th order. The theoretical results are confirmed by numerical tests in which the duality error majorant for the classical diffusion problem is compared with the standard error indicator used i…

Mathematical Morphology Based on Fuzzy Operators

1993

A vision procedure may be considered as the repeated application of image operators until the vision goal is reached. The type of these operators and the spaces on which they are defined and act depends on the specific problem and on what we are searching on the image. Morphological operations, as filtering, edge detection, skeletonizing, and so on, are mainly required at low and medium levels of the vision procedure, where local and global knowledge is used to enhance the image information content, before a final decision about the image is taken.

A choice of bilevel linear programming solving parameters: factoraggregation approach

2013

Our paper deals with the problem of choosing correct parameters for the bilevel linear program- ming solving algorithm proposed by M. Sakawa and I. Nishizaki. We suggest an approach based on fac- toraggregation, which is a specially designed general aggregation operator. The idea of factoraggregation arises from factorization by the equivalence relation generated by the upper level objective function. We prove several important properties of the factorag- gregation result regarding the analysis of param- eters in order to find an optimal solution for the problem. We illustrate the proposed method with some numerical and graphical examples, in particu- lar we consider a modification of the m…

Numerical Approximation of Elliptic Variational Problems

2003

This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.