Carlos J. S. Alves

An empirical analysis of productivity growth in a Portuguese retail chain using Malmquist productivity index

Abstract This paper estimates total productivity change and decomposes it into technically efficient change and technological change for a Portuguese retail store chain with data envelopment analysis. The benchmarking procedure implemented is an internal benchmarking, where the stores in the chain are compared against each other. The aim of this procedure is to seek out those best practices that will lead to improved performance throughout the whole chain. We rank the stores according to their total productivity change for the period 1999–2000, concluding that some stores experienced productivity growth while others experienced productivity decrease. Managerial implications arising from the study are considered.

A new method of fundamental solutions applied to nonhomogeneous elliptic problems

Abstract The classical method of fundamental solutions (MFS) has only been used to approximate the solution of homogeneous PDE problems. Coupled with other numerical schemes such as domain integration, dual reciprocity method (with polynomial or radial basis functions interpolation), the MFS can be extended to solve the nonhomogeneous problems. This paper presents an extension of the MFS for the direct approximation of Poisson and nonhomogeneous Helmholtz problems. This can be done by using the fundamental solutions of the associated eigenvalue equations as a basis to approximate the nonhomogeneous term. The particular solution of the PDE can then be evaluated. An advantage of this mesh-free method is that the resolution of both homogeneous and nonhomogeneous equations can be combined in a unified way and it can be used for multiscale problems. Numerical simulations are presented and show the quality of the approximations for several test examples.

BOUNDARY INTEGRAL FORMULAE FOR THE RECONSTRUCTION OF IMPERFECTIONS OF SMALL DIAMETER IN AN ELASTIC MEDIUM

We consider an isotropic Lame system for an elastic medium consisting of finitely many imperfections of small diameter, embedded in a homogeneous reference medium. The Lame coefficients of the imperfections are different from those of the background medium. First, we establish an asymptotic formula for the displacement vector in terms of the reference Lame coefficients, the location of the imperfections, and their geometry. Second, we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure.

On inverse scattering by screens

A generalization of Isakovs theorem to admissible shapes that include screens with a Robin boundary condition (in which the impedance is also an unknown) is presented. We also establish a characterization that enables us to distinguish the far field of plane screens from others. Numerical results using a quasi-Newton method are presented.

Recovering the source term in a linear diffusion problem by the method of fundamental solutions

This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed.

Solving Inverse Source Problems Using Observability. Applications to the Euler-Bernoulli Plate Equation

The aim of this paper is to provide a general framework for solving a class of inverse source problems by using exact observability of infinite dimensional systems. More precisely, we show that if a system is exactly observable, then a source term in this system can be identified by knowing its intensity and appropriate observations which often correspond to measurements of some boundary traces. This abstract theory is then applied to obtain new identifiability results for a system governed by the Euler-Bernoulli plate equation. Using a different methodology, we show that exact observability can be used to identify both the locations and the intensities of combinations of point sources in the plate equation.

The direct method of fundamental solutions and the inverse Kirsch- Kress method for the reconstruction of elastic inclusions or cavities

In this work we consider the inverse problem of detecting inclusions or cavities in an elastic body, using a single boundary measurement on an external boundary. We discuss the identifiability questions on shape reconstruction, presenting counterexamples for Robin boundary conditions or with additional unknown Lame parameters. Using the method of fundamental solutions (MFS) we adapt a method introduced twenty years ago by Andreas Kirsch and Rainer Kress [17] (in the context of an exterior problem in acoustic scattering) to this inverse problem in a bounded domain. We prove density results that justify the reconstruction of the solution from the Cauchy data using the MFS. We also establish some connections between this linear part of the KirschKress method and the direct MFS, through matrices of boundary layer integrals. Several numerical examples are presented, showing that with noisy data we were able to retrieve a fairly good reconstruction of the shape (or of its convex hull) with this MFS version of the Kirsch-Kress method.

Advances in meshfree techniques

Preface A Global-Local Approach for the Construction of Enrichment Functions for the Generalized HIM and Its Application to Three-Dimensional Cracks, by C. Armando Duarte, Dae-Jin Kim and Ivo Babusca Study of Some Optimal XFEM Type Methods, by Elie Chahine, Patrick Laborde, Julien Pommier Yves Renard and Michel Salaun, by Generalized Finite Element Method in Mixed Variational Formulation: A Study of Convergence and Solvability, by W. Gois and S.P.B. Proenca Stability in Lagrangian and Semi-Lagrangian Reproducing Kernel Discretizations Using Nodal Integration in Nonlinear Solid Mechanics, by Jiun-Shyan Chen and Youcai Wu Simulation of Forming Processes by the cr-Shapes-Based Natural Element Method, by I. Alfaro, E. Cueto, F Chinesta and M. Doblare New Advances in Meshless Methods: Coupling Natural Element and Moving Least Squares Techniques, by F Chinesta, J. Yvonnet, P. Villon, P Breitkopf P Joyot, I. Alfaro and E. Cueto Eliminating Shear-Locking in Meshless Methods: A Critical Overview and a New Framework for Structural Theories, by Carlos Tiago and Vitor MA. Leitao FEMJSPH Coupling Techniques for High Velocity Impact Simulations, by Levent Aktay and Alastair F Johnson On the Construction of Mass Conservative and Meshless Adaptive Particle Advection Methods, by Armin Iske Spectral-Like Accuracy in Space of a Meshless Vortex Method, by LA. Barba A Hybrid Meshless/Spectral-Element Method for the Shallow Water Equations on the Sphere, by Christopher D. Blakely Iterated Approximate Moving Least Squares Approximation,by Gregory E. Fasshauer and Jack G. Zhang A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs, by Carlos J.S. Alves and Svilen S. Valtchev From Global to Local Radial Basis Function Collocation Method for Transport Phenomena, by Bozidar Sarler Computation of Static Deformations and Natural Frequencies of Shear Deformable Plates by an RBF-Pseudospectral Method with an Optimal Shape Parameter, by A.J.M. Ferreira andG.E. Fasshauer Author Index Subject Index.

Inverse scattering for elastic plane cracks

It is known that hard planar acoustic screens generate null far-field amplitude on the directions defined by the plane that encloses them. We proved in an earlier paper that this property actually characterizes plane screens among scatterers of any shape, and we generalized it to other boundary conditions. Furthermore it was proved that a single incident wave is sufficient to distinguish screens that lie in the same plane. Generalizations of these results are carried out in this paper to the elastic case.

Iterative and range test methods for an inverse source problem for acoustic waves

We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples.