Mathematical foundations of adaptive isogeometric analysis

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA)

Etude de la diffusion de particules lourdes sur des systèmes atomiques et nucléaires

In this thesis quantum mechanical non-relativistic few-body problem is discussed. Basing on fundamentals ideas of Faddeev and Yakubovski three and four body equations are formulated and solved for fermionic atomic and nuclear systems. Former equations are modified to include long range interactions. Original results for nuclear and molecular physics were obtained : - Positively charged particle scattering on Hydrogen atoms was considered. Predictions for $\pi^(+)$-H, $\mu^(+)$-H and p$^(+)$-H scattering lengths were given. Existence of an unknown, very weakly bound H$^(+)_(2)$ bound state was predicted. - Motivated by the possible observation of bound four neutron structure at GANIL we have studied compatibility of such an existence within the current nuclear interaction models. - 4 nucleon scattering at low energies was investigated. Obtained results for n-3H, p-3H and p-3He systems were compared with the experimental data. Validity of realistic nucleon-nucleon interaction models is questioned.Cette thèse est consacrée à l'étude numérique de systèmes quantiques non-relativistes à trois et quatre particules. Les équations de Faddeev-Yakubovski ont été modifiées pour pouvoir inclure les interactions à longue portée et ont été appliquées à l'étude des nombreux systèmes physiques. Des résultats originaux ont été obtenus pour les systèmes nucléaires et moléculaires : - Dans le cadre de la physique moléculaire, la diffusion des particules chargées sur les atomes d'hydrogène a été étudiée. Les longueurs de diffusion pour les systèmes $[pi^(+)$-H, $\mu^(+)$-H et p$^+$-H ont été prédites. L'existence d'un nouvel état, très faiblement lié de l'ion moléculaire H$^(+)_(2)$ a été prédit. - Suite à l'annonce d'une possible mise en évidence expérimentale du tetraneutron (état lié à 4 neutrons) au GANIL, nous avons étudié la compatibilité d'une telle existence avec nos connaissances des forces neutron-neutron. - La diffusion des systèmes à 4 nucléons (n-3H, p-3H et p-3He) à basse énergie a été examinée. Les résultats sont comparés aux résultats expérimentaux. La validité des potentiels nucléon- nucléon a ainsi été remise en cause. MOTS-CLES: Few-body, quatre corps, diffusion, diffusion Coulombienne, états liés, états de resonance, tetraneutron, ion moléculaire d'hydrogèn

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield

ICASE semiannual report, April 1 - September 30, 1989

The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings