A multiscale finite element framework for additive manufacturing process modeling
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Journal Title
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Volume Title
Insinööritieteiden korkeakoulu |
Master's thesis
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Authors
Date
2018-04-16
Department
Major/Subject
Mathematics
Mcode
SCI3076
Degree programme
Master's Programme in Mechanical Engineering (MEC)
Language
en
Pages
56+0
Series
Abstract
This thesis describes a finite element framework for solving partial differential equations with highly varying spatial coefficients. The goal is to model the heat transfer in a heterogeneous powder medium of the selective laser melting process. An operator based framework is developed and the implementation details are discussed. The main idea of the work is based on the two level domain decomposition and construction of special operators to transfer the system between the coarse and fine levels. The system of equations is solved on a coarse level and the solution is transferred to the fine level. The operators are computed using Localized Orthogonal Decomposition (LOD) method. The method is applied to several numerical experiments and an optimal convergence rates in the H1 and L2 norms are observed. The computational efficiency of LOD is studied and its limitations are discussed.Description
Supervisor
Hannukainen, AnttiThesis advisor
Laukkanen, AnssiKeywords
multiscale method, localized orthogonal decomposition, heat equation, finite element method