dc.contributorNós, Rudimar Luiz
dc.contributorNós, Rudimar Luiz
dc.contributorBobko, Nara
dc.contributorSampaio, Júlio César Santos
dc.creatorMicheletti, João Pedro Santos Brito
dc.date.accessioned2022-07-06T12:30:26Z
dc.date.accessioned2022-12-06T15:08:11Z
dc.date.available2022-07-06T12:30:26Z
dc.date.available2022-12-06T15:08:11Z
dc.date.created2022-07-06T12:30:26Z
dc.date.issued2021-08-23
dc.identifierMICHELETTI, João Pedro Santos Brito. Solução numérica da equação de Poisson em malhas estruturadas bidimensionais e tridimensionais. 2021. Trabalho de Conclusão de Curso (Licenciatura em Matemática) - Universidade Tecnológica Federal do Paraná, Curitiba, 2021.
dc.identifierhttp://repositorio.utfpr.edu.br/jspui/handle/1/29011
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/5261322
dc.description.abstractIn this work, we numerically solve second-order elliptic partial differential equations such as the Laplace and Poisson equations, using the finite difference method in two-dimensional and threedimensional structured meshes. To solve the system of linear equations arising from the finite difference discretization, we use the iterative methods of Gauss-Seidel and SOR. Furthermore, we build manufactured solutions for some Poisson equations and compare the exact and numerical solutions, and test optimal values for the relaxation parameter in the SOR method. We also apply the theory studied in the numerical solution of stationary or equilibrium problems and employ Matlab and Tecplot 360 to visualize the numerical solution. We conclude that the convergence of the SOR method is slow in problems with Neumann boundary conditions and in problems with singularities.
dc.publisherUniversidade Tecnológica Federal do Paraná
dc.publisherCuritiba
dc.publisherBrasil
dc.publisherLicenciatura em Matemática
dc.publisherUTFPR
dc.rightsopenAccess
dc.subjectFunções harmônicas
dc.subjectDiferenças finitas
dc.subjectMATLAB (Programa de computador)
dc.subjectSimulação (Computadores)
dc.subjectHarmonic functions
dc.subjectFinite differences
dc.subjectMATLAB (Computer program)
dc.subjectComputer simulation
dc.titleSolução numérica da equação de Poisson em malhas estruturadas bidimensionais e tridimensionais
dc.typebachelorThesis


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