Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11

Adaptive Finite Element Methods for Multiscale Partial Differential Equations

Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider elliptic homogenization problems discretized by the finite element heterogeneous multiscale method (FE-HMM). Unlike standard (single-scale) finite element methods, our multiscale discretization scheme relies on coupled macro and micro finite elements. The framework of the HMM allows to design an algorithm that follows the classical finite element structure on the macro level. The fine scales of the multiscale problems are taken into account by replacing the element-wise numerical integration over unknown macroscopic data by a numerical integration over suitably averaged micro solutions. These micro solutions are obtained from micro FE problems on sampling domains within the macro elements. This thesis is divided into two parts. In the first part, we discuss a short and versatile FE implementation of the multiscale algorithm. The implementation is flexible, easy to use and to modify and can handle simplicial or quadrilateral FE and various macro-micro coupling conditions for the constrained micro problems. The implementation of time-dependent problems is also discussed. Numerical examples including three dimensional problems are presented and demonstrate the efficiency and the versatility of the computational strategy. In the second part (the main part of this thesis), we present an a posteriori error analysis for the FE-HMM. The a posteriori analysis enables us to estimate the accuracy of a numerical solution (and therefore its reliability) and further it allows for the design of adaptive numerical methods, which are the most efficient. The crucial component for the design of an adaptive multiscale method is the introduction of appropriate error indicators. As the error indicators depend on macroscopic data (such as the macroscopic diffusion tensor) that are not readily available, we construct error indicators that only depend on the available macro and micro FE solutions, available from previous computations. We provide a posteriori estimates for the upper and lower bound in the energy norm. The corresponding macroscopic mesh refinement strategy is therefore both reliable and efficient. The microscopic mesh is refined simultaneously and – under appropriate assumptions – optimally with the macroscopic mesh. This means that the strategy reduces the macro and micro error at the same rate. In the case of a uniformly oscillating tensor and exact micro computations, the standard a posteriori error estimates for the FEM applied to the homogenized problem are recovered. Numerical experiments confirm the efficiency and reliability of the adaptive multiscale method and demonstrate the optimality of the chosen macro-micro coupling. We extend the adaptive FE-HMM to higher order FE. We further derive a posteriori estimates for the error in quantities of interest that are needed to make certain design decisions; the quantity of interest is represented by a linear functional. We derive and analyze a multiscale counterpart to the classical dual-weighted residual method and design a corresponding goal-oriented adaptive multiscale method. The efficiency of the method is shown in numerical experiments

Ricerche di Geomatica 2011

Questo volume raccoglie gli articoli che hanno partecipato al Premio AUTeC 2011. Il premio è stato istituito nel 2005. Viene conferito ogni anno ad una tesi di Dottorato giudicata particolarmente significativa sui temi di pertinenza del SSD ICAR/06 (Topografia e Cartografia) nei diversi Dottorati attivi in Italia

Segmentation of medical images under topological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 135-142).Major advances in the field of medical imaging over the past two decades have provided physicians with powerful, non-invasive techniques to probe the structure, function, and pathology of the human body. This increasingly vast and detailed amount of information constitutes a great challenge for the medical imaging community, and requires significant innovations in all aspect of image processing. To achieve accurate and topologically-correct delineations of anatomical structures from medical images is a critical step for many clinical and research applications. In this thesis, we extend the theoretical tools applicable to the segmentation of images under topological control, apply these new concepts to broaden the class of segmentation methodologies, and develop generally applicable and well-founded algorithms to achieve accurate segmentations of medical images under topological constraints. First, we introduce a digital concept that offers more flexibility in controlling the topology of digital segmentations. Second, we design a level set framework that offers a subtle control over the topology of the level set components. Our method constitutes a trade-off between traditional level sets and topology-preserving level sets.(cont.) Third, we develop an algorithm for the retrospective topology correction of 3D digital segmentations. Our method is nested in the theory of Bayesian parameter estimation, and integrates statistical information into the topology correction process. In addition, no assumption is made on the topology of the initial input images. Finally, we propose a genetic algorithm to accurately correct the spherical topology of cortical surfaces. Unlike existing approaches, our method is able to generate several potential topological corrections and to select the maximum-a-posteriori retessellation in a Bayesian framework. Our approach integrates statistical, geometrical, and shape information into the correction process, providing optimal solutions relatively to the MRI intensity profile and the expected curvature.by Florent Ségonne.Ph.D

When Cardiac Biophysics Meets Groupwise Statistics: Complementary Modelling Approaches for Patient-Specific Medicine

This habilitation manuscript contains research on biophysical and statistical modeling of the heart, as well as interactions between these two approaches

When Cardiac Biophysics Meets Groupwise Statistics: Complementary Modelling Approaches for Patient-Specific Medicine

This habilitation manuscript contains research on biophysical and statistical modeling of the heart, as well as interactions between these two approaches

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described