EVENTO
The Multiscale Hybrid-Hybrid-Mixed method
Tipo de evento: Defesa de Dissertação de Mestrado
Many problems of practical interest in science and engineering are of multiscale type, and many of those are described by partial differential equations (PDEs) with oscillatory coefficients. The corresponding numerical solutions using classical methods are extremely expensive in terms of memory and CPU.Multiscale schemes such as the MsFEM and MHM methods have been developed to solve such problems, based on two-level ideas.This work proposes a new numerical method, the Multiscale Hybrid-Hybrid-Mixed method (MHHM). Thestarting point is a hybrid formulation of three fields: the solution in each element interior, its trace and flux on the mesh skeleton. Continuity of traces and fluxes are weakly imposed. Multiscale effects areincorporated into basis functions through localized Neuman problems. A series of static condensationstransforms the saddle point problem into an elliptic one, posed at the interfaces. At the discrete level, this reduces drastically the size of the global system. The matrix of the associated linear system is symmetric and positive definite, and can be solved by classical iterative schemes. We prove the well-posedness of the method and establish error estimates. We also perform numerical tests to confirm the theoretical predictions and compare the method with the FEM, MsFEM and MHM schemes.Para assistir acesse: https://us02web.zoom.us/j/89313864686?pwd=dXRyQ2ZVWU52UzVlUnJTWEUwWnRoZz09
Data Início: 29/03/2022 Hora: 15:00 Data Fim: 29/03/2022 Hora: 18:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Webinar
Aluno: Franklin da Conceição de Barros - - LNCC
Orientador: Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Frédéric Gerard Christian Valentin - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Henrique Versieux - Instituto de Matemática Pura e Aplicada - IMPA Marcio Arab Murad - Laboratório Nacional de Computação Científica - LNCC Marcus Vinicius Sarkis Martins - - WPI/EUA
Suplente Banca Examinadora: Sandra Mara Cardoso Malta - Laboratório Nacional de Computação Científica - LNCC
