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Graduate Thesis of Carlos Reales

Reales, CarlosProgramPhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción
Enrollment Year2006
Senior Year2010
Thesis TitleNumerical modeling of electromagnetism problems in metallurgy

Thesis Summary:

The main objective of this thesis is to solve problems of axisimetric induced currents derived from the modeling of various metallurgical problems. In particular, the numerical simulation of an induction furnace and electromagnetic forming processes have motivated the models studied. Initially a formulation in terms of a vector potential for a problem of currents induced in harmonic regime in a bounded axisymmetric domain is studied. A mathematical analysis of this formulation is carried out in which it is shown that the corresponding variational formulation leads to a well presented problem whose solution has additional regularity. In addition, we show error estimates for standard finite element discretization. Later, two parabolic elliptic problems are discussed. One involves velocity terms that affect the ellipticity of one of the bilinear forms of the problem. The other involves a domain of the parabolic part that changes over time. For both, formulations are studied in magnetic potentials in bounded axisymmetric domains. Such formulations are degenerate, so different theories must be applied to the classic to prove existence and uniqueness of the solution. For the discretization, standard finite elements are used for the spatial variable and an implicit Euler method for the temporal variable. Error estimates are shown for semi-discrete and completely discrete problems. In each case, numerical tests are presented which prove the convergence of the proposed methods. As the problems addressed in this thesis come from metallurgy, applications of numerical methods are shown to this type problems.

Thesis Director(s) Alfredo Bermúdez, Rodolfo Rodríguez, Pilar Salgado
Thesis Project Approval Date2008, January 25
Thesis Defense Date2010, March 31
Professional MonitoringDepartamento de Matemáticas y Estadística, Universidad de Córdoba, Colombia, February 2004.
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ISI Publications from the Thesis

Alfredo BERMúDEZ, Carlos REALES, Rodolfo RODRíGUEZ, Pilar SALGADO: Numerical analysis of a finite element method for the axisymmetric eddy current model of an induction furnace. IMA Journal of Numerical Analysis, vol. 30, pp. 654-676, (2010)

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