Análise direta e inversa de um modelo de difusão anômala bi-fluxo com termos fonte com variação espacial e temporal

• Autor(a) principal: Marinho, Gisele Moraes
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13632
• topic: Anomalous diffusion; Generalized integral transform technique; Finite volume method; Bayesian inference; Difusão anômala; Técnica da transformada integral generalizada; Método de volumes finitos; Inferência bayesiana; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

This thesis addresses the problem of bi-flux anomalous diffusion from the perspective of direct and inverse problems. The Finite Volume Method and the Generalized Integral Transform Technique are employed in the one-dimensional and two-dimensional bi-flux model solution. Both approaches are systematically developed and critically verified for cases involving the different types of boundary conditions that appear in the model. The Generalized Integral Transform Technique provides numerical-analytical hybrid solutions that can be employed as benchmark results for validating other numerical model solutions. An inverse problem of reconstructing space and time-wise source terms is introduced and solved by a bayesian approach using the Markov Chain Monte Carlo Method. Aspects regarding the use of Markovian Random fields as priori information and the use of an adaptative Metropolis-Hastings algorithm are discussed. Simulated measurements are employed, and the estimates provide good approximations to the exact sources term, demonstrating that the presented methodology is efficient for the reconstruction of source terms in the bi-flux diffusion equation.