The aim of this paper is to provide a general framework allowing to use exact observability of in... more The aim of this paper is to provide a general framework allowing to use exact observability of infinite dimensional systems to solve a class of inverse source problems. More precisely, we show that if a system is exactly observable, then we can identify a source term in this system by knowing the corresponding intensity and appropriate observations which often correspond to the measure of some boundary traces. This abstract theory is then applied to 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.
This volume presents a wide range of medical applications that can utilize mathematical computing... more This volume presents a wide range of medical applications that can utilize mathematical computing. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization.
Mathematics and Computers in Simulation, Jul 1, 2004
In this paper, we present results concerning the far field pattern generated by flat and almost f... more In this paper, we present results concerning the far field pattern generated by flat and almost flat cracks in 3D and the possibility of identifying these geometrical features from direct inspection of the far field pattern. We address the direct problem using a variational formulation of the boundary integral equation to avoid the hipersingularity in the double layer potential representation. Concerning the inverse problem, some estimates presenting a direct dependence on the far field behavior and the flatness of the crack are derived. From the knowledge of the plane that defines the main directions of the crack it is possible to get a first approximation that may be used as an initial guess for the Newton method. Numerical simulations validate the direct relation between a far field plane having almost null amplitude and the main directions of a plane that defines an almost flat crack.
Transient non-intrusive method for estimating spatial thermal contact conductance by means of the reciprocity functional approach and the method of fundamental solutions
Http Dx Doi Org 10 1080 17415977 2014 933830, Feb 6, 2015
Some of the most common scalar PDEs have fundamental solutions that have a radial feature. Theref... more Some of the most common scalar PDEs have fundamental solutions that have a radial feature. Therefore, the method of fundamental solutions (MFS) is usually associated to radial basis functions (RBF) as a particular case, when the basis functions have radial property. Here we will present a missing counterpart -some of the most common RBF approximation methods are just a particular case of the MFS boundary approximation when applied in a higher dimension. This idea was presented in . In this presentation we will consider the relation between MFS boundary interpolation in dimension d + 1 and RBF domain interpolation in dimension d, for the most commonly used RBF basis functions.
The reciprocity function approach applied to the non-intrusive estimation of spatially varying internal heat transfer coefficients in ducts: numerical and experimental results
It is known that the solution of an elastic scattering problem behaves asymptotically like a sum ... more It is known that the solution of an elastic scattering problem behaves asymptotically like a sum of a spherical P wave and a spherical S wave. In [7] Dassios proves an Atkinson-Wilcox expansion for this solution, allowing its reconstruction by means of two series, the terms of which can be calculated from the far field amplitudes of the asymptotic P and S waves. His proof, based on the integral representation formula, contains rather delicate calculations. We adopt here a different viewpoint, considering the scattered wave as a solution of the inhomogeneous Navier's equation with a distribution data, and obtain both simpler proofs for these results and more precise properties for the far field amplitudes, in particular the characterization of elastic far fields and a density result. 1 Introduction It is well-known that the scattered wave in a 3-D acoustic scattering problem has the following asymptotic behaviour : u(x) = e ikjxj jxj (F (x) +O( 1 jxj )) where x = x=jxj. The fun...
This paper presents a computationally fast methodology for the estimation of spatial and transien... more This paper presents a computationally fast methodology for the estimation of spatial and transient unknown thermal contact conductance between sandwiched materials, using non-intrusive measurements. The methodology is formulated in such a way that the spatial and temporal variations of the unknown function are obtained simply by solving a linear system, whose solution vector is composed of integrals containing measured temperatures and known heat fluxes applied at an external boundary. Good estimates are obtained, even for functions containing discontinuities in both time and space. Simulated measurements with and without errors are considered, showing very good results.
Numerical calculation of eigenfrequencies and eigenmodes of 3D simply connected domains using the Method of Fundamental Solutions
Numerical Methods for Partial Differential Equations
Summary In this work we apply the Method of Fundamental Solutions (MFS) to the numerical calculat... more Summary In this work we apply the Method of Fundamental Solutions (MFS) to the numerical calculation of eigenfrequencies and eigenmodes of 3D simply connected domains. This meshless method was considered for 2D shapes with simply geometry (cf. (8)) and ex- tended for a general 2D simply connected shape (cf. (1)). Here the application to 3D simply connected domains is analysed. We propose a choice of collocation and source points in 3D adapted from the algorithm presented in (1). Some numerical examples are considered to illustrate the convergence and the good approximations obtained with the proposed algorithm.
Density results using an infinite number of plane acoustic waves allow to de-rive meshless method... more Density results using an infinite number of plane acoustic waves allow to de-rive meshless methods for solving the homogeneous or the nonhomogeneous Helmholtz equation. In this work we consider the numerical simulation of acoustic source problems in a bounded domain using this method. We present several tests comparing with the method of fundamental solutions and a recent extension to nonhomogeneous problems.
Comparison between Meshfree and Boundary Element methods applied to BVPs in domains with corners
III European Conference on Computational Mechanics, 2006
A Dirichlet boundary value problem (BVP) for the Laplace equation will be considered in a bounded... more A Dirichlet boundary value problem (BVP) for the Laplace equation will be considered in a bounded domain with corners. Two distinct types of numerical methods will be applied for the solution of this problem. A modification of the Boundary Element Method (BEM), as presented in ...
The Method of Fundamental Solutions applied to a heat conduction inverse problem
III European Conference on Computational Mechanics, 2006
Page 1. The Method of Fundamental Solutions applied to a heat conduction inverse problem Carlos J... more Page 1. The Method of Fundamental Solutions applied to a heat conduction inverse problem Carlos JS Alves∗, Nuno FM Martins ∗Instituto Superior Técnico Avenida Rovisco Pais, 1096 Lisboa Codex, Portugal calves@math ...
On the Determination of a Robin Boundary Coefficient in an Elastic Cavity Using the MFS
Abstract In this work, we address a problem of recovering a boundary condi-tion on an elastic cav... more Abstract In this work, we address a problem of recovering a boundary condi-tion on an elastic cavity from a single boundary measurement on an external part of the boundary. The boundary condition is given by a Robin condition and we aim to identify its Robin coefficient ...
We consider the steady Stokes equations in a bounded domain Ω ⊂ R n , n = 2, 3 describing the mot... more We consider the steady Stokes equations in a bounded domain Ω ⊂ R n , n = 2, 3 describing the motion of an incompressible viscous fluid under the action of point-forces located inside Ω. The objective of this work is to solve the inverse problem of determining the number, location and strength of the these point-forces.
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Papers by C J S Alves