Multiscale hybrid-mixed methods for heterogeneous elastic models

• Ano de defesa: 2019
• Autor(a) principal: Pereira, Weslley da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Laboratório Nacional de Computação Científica; Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA); Brasil; LNCC; Programa de Pós-Graduação em Modelagem Computacional
• Palavras-chave em Português: Elasticidade; Análise de sistemas; Computação de alto desempenho; Método dos elementos finitos; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL
• Link de acesso: https://tede.lncc.br/handle/tede/300

This thesis aims the development, analysis, and implementation of new Multiscale Hybrid- Mixed methods (MHM, for short) for solving problems modeled by linear elastostatic and elastodynamic equations. The MHM methods allow polytopal partitions and make low-order approximation spaces, based on discontinuous Lagrange multipliers, inf-sup stable. Obtained as a byproduct of a new infinite-dimensional mathematical scope, which is equivalent to the classical weak formulation, the MHM methods are superconvergent under local regularity assumptions and preserve physical properties such as local force balance, local compressibility constraints, and total energy. Also, the MHM methods are robust in the quasi-incompressible material case by adopting a stabilized finite element method as a second-level solver. For all those cases, we prove existence and uniqueness of solutions, as well as error analysis by considering two-levels of discretizations. Numerical results validate theoretical results, and heterogeneous media test-cases highlight the quality of the MHM approximations in coarse partitions, which capture fine-scale features via multiscale base functions. From the computational viewpoint, scalability tests confirm the high degree of intrinsic parallelism of MHM methods and indicate parameter choices. We conclude that new MHM methods induce accurate and computationally efficient algorithms on large parallel machines for solving elasticity and elastodynamic problems in highly heterogeneous domains.