Orientador: Alagacone Sri Ranga / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:37:15Z (GMT). No. of bitstreams: 1 Felix_HeronMartins_D.pdf: 783541 bytes, checksum: cea4459f391a5da7e61d9cff02244ec0 (MD5) Previous issue date: 2015 / Resumo: O objetivo do presente trabalho se divide em duas partes: na primeira, estudaremos uma regra de quadratura interpolatória sobre os zeros de polinômios núcleo obtidos a partir de uma sequência de polinômios L-ortogonais, oferecendo técnicas numéricas para a obtenção dos nós e pesos dessa regra de quadratura. Na segunda parte, forneceremos uma caracterização dos polinômios de Szegö em termos de duas sequências reais, dentre as quais uma é sequência encadeada. Tal caracterização afeta a relação entre os polinômios núcleo e os polinômios ortogonais no círculo unitário aos quais estes estão associados / Abstract: The main goal of the present work falls under two parts: firstly, we'll study a quadrature rule over the zeros of the kernel polynomials obtained from a sequence of L-orthogonal polynomials, offering numerical techniques for evaluating the nodes and weights of such quadrature rule. Secondly, we'll give a characterization for Szegö polynomials in terms of two real sequences, in which one is a chained sequence. Such characterization influences the connection between the kernel polynomials and the related orthogonal polynomials over the unit circle / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Please read the abstract in the section 00front of this document / Thesis (PhD (Applied Mathematics))--University of Pretoria, 2000. / Mathematics and Applied Mathematics / unrestricted

Smoothed Particle Hydrodynamics (SPH) is a meshless numerical method which has long been put into practice for scientific and engineering applications. It arises as a numerical discretization of convolution-like integral operators that approximate local differential operators. There have been many studies on the SPH with an emphasis on its role as a numerical scheme for partial differential equations while little attention is paid to the underlying continuum nonlocal models that lie intermediate between the two. The main goal of this thesis is to provide mathematical understanding of the SPH-like meshless methods by means of ongoing developments in studies of nonlocal models with a finite range of nonlocal interactions. It is timely for such a work to be initiated with growing interests in the nonlocal models. The thesis touches on numerical, theoretical and modeling aspects of the nonlocal integro-differential equations pertaining to the SPH-like schemes. As illustrative examples of each aspect it presents robust SPH-like schemes for advection-convection equations, discusses the stabilities of nonsymmetric nonlocal gradient operators, and proposes a new formulation of nonlocal Dirichlet-like type boundary conditions.

京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13010号 / 論工博第4135号 / 新制||工||1649(附属図書館) / 32938 / 京都大学大学院工学研究科都市環境工学専攻 / (主査)教授 髙橋 大弐, 教授 鉾井 修一, 教授 竹脇 出 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20323号 / 工博第4260号 / 新制||工||1660(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 間瀬 肇, 教授 平石 哲也, 准教授 森 信人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20324号 / 工博第4261号 / 新制||工||1660(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 木村 亮, 教授 三村 衛, 准教授 木元 小百合 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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