Modelamiento de problemas de radiación/dispersión electromagnética mediante el método de elementos finitos

dc.contributor.advisorOsorio Lema, Mauricio Andrésspa
dc.contributor.advisorCamargo Mazuera, Liliana Marcelaspa
dc.contributor.authorRíos Casas, Julián Andrésspa
dc.date.accessioned2020-09-07T15:11:25Zspa
dc.date.available2020-09-07T15:11:25Zspa
dc.date.issued2020-06-30spa
dc.description.abstractEn el presente trabajo se estudia el problema de radiación en una cavidad con condiciones de frontera de conductor perfecto e impedancia. Partimos de la ecuaciones de Maxwell en régimen armónico para construir una ecuación diferencial de segundo orden que, junto a las condiciones de frontera mencionadas conforman el problema fuerte. Basados en éste, construimos una formulación variacional cuyo análisis de existencia y unicidad de la solución se lleva a cabo vía alternativa de Fredholm. Posteriormente se deriva una formulación discreta usando los elementos finitos de Nédélec de primer orden, en donde la convergencia de la solución se estudia usando la teoría de operadores colectivamente compactos y finalmente, describimos con detalle la implementación de la formulación discreta usando Matlab, llevando a cabo análisis de error en las normas L^2, H(curl) y estudiamos el orden de convergencia.spa
dc.description.abstractIn this document, the cavity radiation problem under perfect conductor and impedance boundary conditions is studied. We start from time-harmonic Maxwell's equations to construct a second order differential equation that, with the afore menctioned boundary conditions, constitutes the strong problem. Based on this, we construct a variational formulation whose existence and uniqueness analysis of the solution is done via Fredholm's alternative. Later, a discrete formulation is built using the Nédélec's first order finite element, where the convergence of the solution is studied using the collectively compact operators theory and finally, we describe a detailed implementation of the discrete formulation using Matlab, analyzing the error estimates in the norms L^2, H(curl;) and studying the convergence rate.spa
dc.description.degreelevelMaestríaspa
dc.format.extent122spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/78407
dc.language.isospaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.departmentEscuela de matemáticasspa
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemática Aplicadaspa
dc.relation.referencesN. Matthew and O. Sadiku, “Elementos de electromagnetismo,” España, Crítica, 2003.spa
dc.relation.referencesW. Cai, “Numerical methods for Maxwell’s equations in inhomogeneous media with material interfaces,” Journal of Computational Mathematics, pp. 156–167, 2004.spa
dc.relation.referencesK. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on antennas and propagation, vol. 14, no. 3, pp. 302–307, 1966spa
dc.relation.referencesJ. C. Nédélec, “A new family of mixed finite elements in Rˆ3,” Numerische Mat- hematik, vol. 50, no. 1, pp. 57–81, 1986.spa
dc.relation.referencesM. Olm, S. Badia, and A. Martín, “On a general implementation of h- and p-adaptive curl-conforming finite elements,” Advances in Engineering Software, vol. 132, pp. 74–91, 06 2019.spa
dc.relation.referencesP. Monk et al., Finite element methods for Maxwell’s equations. Oxford University Press, 2003.spa
dc.relation.referencesG. Gatica, Introducción al análisis funcional: teoría y aplicaciones. Reverté.spa
dc.relation.referencesR. Kress, Linear integral equations. Applied Mathematical Sciences 82, Springer New York, 2 ed., 1999.spa
dc.relation.referencesW. McLean, Strongly elliptic systems and boundary integral equations. Cambridge University Press, 1 ed., 2000.spa
dc.relation.referencesV. Girault and P. A. Raviart, Finite element methods for Navier - Stokes equations: theory and algorithms. Springer Series in Computational Mathematics, Springer - Verlag, 1986.spa
dc.relation.referencesJ. Necas, “Les méthodes directes en théorie des équations elliptiques,” 1967.spa
dc.relation.referencesS. Brenner and R. Scott, The mathematical theory of finite element methods, vol. 3. Springer Science & Business Media, 1994.spa
dc.relation.referencesP. G. Ciarlet, The finite element method for elliptic problems, vol. 4. North - Holland, 1978.spa
dc.relation.referencesL. Chen, “Finite element methods for Maxwell equations,” Lecture Notes, 2016.spa
dc.relation.referencesJ. C. Nédélec, “Mixed finite elements in rˆ3,” Numerische Mathematik, vol. 35, no. 3, pp. 315–341, 1980.spa
dc.relation.referencesC. Amrouche, C. Bernardi, M. Dauge, and V. Girault, “Vector potentials in three- dimensional non-smooth domains,” Mathematical Methods in the Applied Sciences, vol. 21, no. 9, pp. 823–864, 1998.spa
dc.relation.referencesZ. Chen, Q. Du, and J. Zou, “Finite element methods with matching and nonmat- ching meshes for Maxwell equations with discontinuous coefficients,” SIAM Journal on Numerical Analysis, vol. 37, no. 5, pp. 1542–1570, 2000.spa
dc.relation.referencesP. Jacobsson, “Nédélec elements for computational electromagnetics,” 2007.spa
dc.relation.referencesJ. H. Bramble, J. E. Pasciak, and J. Xu, “The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms,” Mathematics of Computation, vol. 56, no. 193, pp. 1–34, 1991.spa
dc.relation.referencesA. Kirsch and P. Monk, “A finite element/spectral method for approximating the time-harmonic Maxwell system in Rˆ3,” SIAM Journal on Applied Mathematics, vol. 55, no. 5, pp. 1324–1344, 1995.spa
dc.relation.referencesS. Caorsi, P. Fernandes, and M. Raffetto, “On the convergence of Galerkin fini- te element approximations of electromagnetic eigenproblems,” SIAM Journal on Numerical Analysis, vol. 38, no. 2, pp. 580–607, 2000.spa
dc.relation.referencesD. Colton and R. Kress, “Inverse acoustic and electromagnetic scattering theory,”spa
dc.relation.referencesR. Leis, “Initial boundary value problems in mathematical physics,” Tubner, 1986.spa
dc.relation.referencesG. Hsiao, P. Monk, and N. Nigam, “Error analysis of a finite element - Integral equation scheme for approximating the time - harmonic Maxwell system,” SIAM journal on numerical analysis, vol. 40, no. 1, pp. 198–219, 2002.spa
dc.relation.referencesB. López Rodríguez and M. Osorio, “Seminario sobre elementos finitos,” Lecture Notes, 2018.spa
dc.relation.referencesC. Bahriawati and C. Carstensen, “Three MATLAB implementations of the lowest- order Raviart - Thomas MFEM with a posteriori error control,” Computational Methods in Applied Mathematics Comput. Methods Appl. Math., vol. 5, no. 4, pp. 333–361, 2005.spa
dc.relation.referencesO. C. Zienkiewicz and R. L. Taylor, The finite element method: solid mechanics, vol. 2. Butterworth - Heinemann, 2000.spa
dc.relation.referencesS. Nicaise, “Edge elements on anisotropic meshes and approximation of the Maxwell equations,” SIAM Journal on Numerical Analysis, vol. 39, no. 3, pp. 784–816, 2001.spa
dc.relation.referencesL. Camargo, B. López-Rodrıguez, M. Osorio, and M. Solano, “An HDG method for Maxwell’s equations in heterogeneous media,”spa
dc.relation.referencesD. Boffi, “A note on the de-Rham complex and a discrete compactness property,” Applied mathematics letters, vol. 14, no. 1, pp. 33–38, 2001.spa
dc.relation.referencesD. Boffi, F. Brezzi, and L. Gastaldi, “On the convergence of eigenvalues for mixed formulations,” Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, vol. 25, no. 1-2, pp. 131–154, 1997.spa
dc.relation.referencesD. Boffi, F. Brezzi, and L. Gastaldi, “On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form,” Mathematics of compu- tation, vol. 69, no. 229, pp. 121–140, 2000.spa
dc.rightsDerechos reservados - Universidad Nacional de Colombiaspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-SinDerivadas 4.0 Internacionalspa
dc.rights.spaAcceso abiertospa
dc.rights.urihttp://creativecommons.org/licenses/by-nd/4.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.proposalEcuaciones de Maxwellspa
dc.subject.proposalTheory of electromagnetismeng
dc.subject.proposalTeoria de electromagnetismospa
dc.subject.proposalDiscreet spaceseng
dc.subject.proposalEspacios discretosspa
dc.subject.proposalAbstract finite elementseng
dc.subject.proposalElementos finitos abstractosspa
dc.subject.proposalVariational formulationeng
dc.subject.proposalAlgebraic analysiseng
dc.subject.proposalFormulación variacionalspa
dc.subject.proposalAnálisis algebraicospa
dc.subject.proposalMaxwell equationseng
dc.titleModelamiento de problemas de radiación/dispersión electromagnética mediante el método de elementos finitosspa
dc.title.alternativeModeling of electromagnetic radiation/scattering problems using the finite element methodspa
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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