JNAIAM
Subject: Mathematics
Date: 01/08/2006
Published by: Promacon
Frequency: 4
ISSN: 1790-8140 ...
ISSN Electronic: 1790-8159
Copyrights: ESCMSE

Mathematical Reviews (MathSciNet) Zentralblatt MATH Database

European Societies of Computational Methods in Science and Engineering
ESCMSE

Editorial Board


Editor-in-Chief and Founder : T.E. Simos, Greece

Assistant Editor-in-Chief : G. Psihoyios, UK

Editorial Assistant : E. Ralli-Simou

Editors :

P. E. Bjørstad, Norway

S. C. Brenner, USA

J. Cash, UK

Mario Collotta, Italy

R. Cools, Belgium

A. Cuyt, Belgium

R. W. Freund, USA

I. Gladwell, USA

A. Klar, Germany

W. F. Mitchell, USA

G. Vanden Berghe, Belgium

G. Alistair Watson, UK

D.P. Laurie, South Africa

Martin Berzins

Luigi Brugnano

J.C. Butcher

Daniel W. Lozier

Brynjulf Owren

International Conference of Computational Methods in Science and Enginnering

ICCMSE 2008

International Conference of Numerical Analysis and Applied Mathematics

ICNAAM 2008

International e-Conference on Computer Science

IeCCS 2008

William F. Mitchell

Applied and Computational Mathematics Division National Institute of Standards and Technology Gaithersburg, MD, USA 20899-8910

Abstract: One aspect of adaptive mesh refinement in the finite element method for solving partial differential equations is the method by which elements are refined. In the early 1980’s the dominant method for refining triangles was the red-green algorithm of Bankand Sherman. The red refinements are the desired refinements, but will result in an incompatible mesh when used alone. The green refinements are used to recover compatibility for stability of the finite element discretization, and are removed before the next adaptive step. Prof. Bob Skeel raised the question as to whether it is possible to perform adaptive refinement of triangles without this complicated patching/unpatching process. As a result, a new triangle refinement method, called newest vertex bisection, was devised as an alternative to red-green refinement in the mid 1980’s. The new approach is simpler and maintains compatibility of the mesh at all times, avoiding the patching/unpatching of the green refinement. In this historical paper we review the development of the newest vertex bisection method for adaptive refinement, and subsequent extensions of the method.

Keywords: finite elements; adaptive mesh refinement; newest vertex bisection
Mathematics Subject Classification: 65-03, 65N30, 65N50
PACS: 02.60.Lj, 02.70.Dh

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Gaussian Scale Mixtures Miguel Martins Felgueiras ^{1 *}, João Paulo Martins^**, Rui Filipe Santos^**

^* CEAUL Lisbon and ESTG, CIGS, Polytechnic Institute of Leiria, Portugal
^** CEAUL Lisbon and ESTG, Polytechnic Institute of Leiria, Portugal

Abstract: In this paper we present a parsimonious approximation of a Gaussian mixture when its components share a common mean value, i.e. a scale mixture. We show that a shifted and scaled Student’s t-distribution can be approximated to this type of mixture, and use the result to develop a hypothesis test for the equality of the components mean value. A simulation study to check the quality of the approximation is also provided, together with an application to logarithmic daily returns.

Keywords: Gaussian scale mixture, Student’s t-distribution, log-returns, simulation.
Mathematics Subject Classification: 60E05; 62P20.

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Eva Volna and Martin Kotyrba¹

Faculty of Science Department of Informatics and Computers, University of Ostrava, 30 dubna 22, 70103 Ostrava, Czech Republic

¹Corresponding author. E-mail: martin.kotyrba@osu.cz

Abstract: The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing an optimal set of routes for a fleet of vehicles in order to serve a given set of customers. Vehicle routing problem forms an integral part of the supply chain management, which plays a significant role in productivity improvement in organizations through an efficient and effective delivery of goods/services to customers. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems, it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper, we have performed an experimental study that indicates a suitable use of genetic algorithms for the vehicle routing problem. We tested instances from Capacitated Vehicle Routing Problem Library (CVRPLIB) series A, B, E, M and X. The obtained experimental outputs were compared with the following heuristics: the Clarke and Wright heuristic, sweep algorithm, and Taillard's algorithm.

Keywords VRP - Vehicle Routing Problem, combinatorics, Clarke and Wright heuristic, Sweep algorithm,Taillard's algorithm, Genetic algorithm.
Mathematics Subject Classification: 97K20, 90C59

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S. Iqbal^a, A. R. Ansari^b1, A. Javed^c and A. M. Siddiqui^d

^aDepartment of Computer Science, COMSATS Institute of Information Technology, Sahiwal Campus, Pakistan.
^bCentre for Advance Studies in Engineering (CASE), 19-Attaturk Avenue, G-5/1, Islamabad, Pakistan.
^cDepartment of Mathematics & Natural Sciences, Gulf University for Science & Technology, P.O. Box 7207, Hawally 32093, Kuwait
^dDepartment of Mathematics, York Campus, Pennsylvania State University, York,PA 17403, USA

Abstract: A weighted-residual based a posteriori error estimation formulation in Galerkin's finite element fashion using quadratic Lagrange polynomials has been formulated to find numerical solutions of obstacle, unilateral and contact second-order boundary-value problems. The approach having piecewise quadratic shape functions has been utilized for checking ">the approximate solutions for spatially adaptive finite element grids. The local element balance based on the residual has been considered as an error assessment criterion. Numerical testing indicates that local errors are large at the interface regions where the gradients are large. A comparison of an adaptive refined grid with that of a uniform mesh for second order obstacle boundary value problems, confirms the superiority of the adaptive scheme without increasing the number of unknown coefficients.

Keywords: Adaptive grid renement scheme, Quadratic Lagrange polynomials, Galerkin's method, Finite element method, Boundary-value problems
Mathematics Subject Classication: 65M60

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