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Jais, Mathias. "Parameter identification for Maxwell's equations." Thesis, Cardiff University, 2006. http://orca.cf.ac.uk/54581/.
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In this work we present a variational algorithm to determine the parameters iir(x) and er(x) in the Maxwell system VxE + k xTH = 0, V x H - kerE = 0 in a body Q from boundary measurements of electromagnetic pairs (n x En dci,n x Hn dn), n= 1,2,…, where n is the outer unit normal. We show that this inverse problem can be solved by minimizing a positive functional C7(m,c) and using a conjugate gradient scheme. Apart from implementations with global boundary, we also consider the case of partial boundary, where we have only data available on a subset T C dQ. Further do we develop uniqueness results, to show that the given data (n x En dn, n x Hn dn), n = 1,2,…, is a sufficient basis to solve the inverse problem. We investigate the uniqueness properties of the inverse problem in the case of global boundary data as well as in the case of partial boundary data. To show the effectivness and the stability of our approach we present various numerical results with noisy data. Finally we outline an alternative method, where one is only interested in recovering the support of the functions fi l 1 and er 1.
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Rihani, Mahran. "Maxwell's equations in presence of metamaterials." Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. https://theses.hal.science/tel-03670420.
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Le sujet principal de cette thèse est l’étude de la propagation des ondes électromagnétiques, en régime harmonique, dans un milieu hétérogène composé d’un diélectrique et d’un matériau négatif (c’est-à-dire avec une permittivité diélectrique négative ε et/ou une perméabilité magnétique négative μ) qui sont séparés par une interface avec une pointe conique. En raison du changement de signe de ε et/ou μ, les équations de Maxwell peuvent être mal posées dans les cadres classiques (basés sur l’espace L2). D’autre part, nous savons que lorsque les deux problèmes scalaires associés, impliquant respectivement ε et μ, sont bien posés dans H1, les équations de Maxwell sont bien posées. En combinant la méthode de la T-coercivité avec l’analyse de Mellin dans les espaces de Sobolev à poids, nous présentons, dans la première partie de ce travail, une étude détaillée de ces problèmes scalaires. Nous prouvons que pour chacun d’entre eux, le caractère bien posé dans H1 est perdu si et seulement si le contraste associé appartient à un ensemble critique appelé intervalle critique. Ces intervalles correspondent aux ensembles de contrastes négatifs pour lesquels des singularités propagatives, aussi appelées ondes de trou noir, apparaissent à l’extrémité de la pointe. Contrairement au cas d’un coin 2D, pour une pointe 3D, plusieurs ondes de trou noir peuvent exister. Des expressions explicites de ces intervalles critiques sont obtenues pour le cas particulier des pointes coniques circulaires. Pour les contrastes critiques, en utilisant le principe de radiation de Mandelstam, nous construisons des cadres fonctionnels dans lesquels le caractère bien posé des problèmes scalaires est restauré. Le cadre physiquement pertinent est sélectionné par un principe d’absorption limite. En outre, nous présentons, dans la deuxième partie de ce travail, une nouvelle méthode numérique pour les problèmes scalaires dans le cas des contrastes non-critiques. Cette approche, contrairement aux techniques existantes, ne nécessite pas d’hypothèses supplémentaires sur le maillage au voisinage de l’interface. La troisième partie de la thèse concerne l’étude des équations de Maxwell avec un ou deux coefficients critiques. En utilisant de nouveaux résultats de potentiels vecteurs dans des espaces de Sobolev à poids, nous expliquons comment construire de nouveaux cadres fonctionnels pour les problèmes électrique et magnétique, qui sont directement liés à ceux obtenus pour les deux problèmes scalaires associés. Si l’on utilise le cadre qui respecte le principe d’absorption limite pour les problèmes scalaires, alors les cadres fournis pour les problèmes électrique et magnétique sont également cohérents avec le principe d’absorption limite. Enfin, la dernière partie porte sur des résultats d’homogénéisation des équations de Maxwell harmoniques et des problèmes scalaires associés dans un domaine 3D qui contient une distribution périodique d’inclusions faites de matériau négatif. En utilisant l’approche de la T-coercivité, nous obtenons des conditions sur les contrastes telles que le processus d’homogénéisation est possible pour les problèmes scalaires et vectoriels. De façon peu intuitive, nous montrons que les matrices homogénéisées associées auxproblèmes limites sont soit définies positives, soit définies négativesThe main subject of this thesis is the study of time-harmonic electromagnetic waves in a heterogeneous medium composed of a dielectric and a negative material (i.e. with a negative dielectric permittivity ε and/or a negative magnetic permeability μ) which are separated by an interface with a conical tip. Because of the sign-change in ε and/or μ, the Maxwell’s equations can be ill-posed in the classical L2 −frameworks. On the other hand, we know that when the two associated scalar problems, involving respectively ε and μ, are well-posed in H1, the Maxwell’s equations are well-posed. By combining the T-coercivity approach with the Mellin analysis in weighted Sobolev spaces, we present, in the first part of this work, a detailed study of these scalar problems. We prove that for each of them, the well-posedeness in H1 is lost iff the associated contrast belong to some critical set called the critical interval. These intervals correspond to the sets of negative contrasts for which propagating singularities, also known as black hole waves, appear at the tip. Contrary to the case of a 2D corner, for a 3D tip, several black hole waves can exist. Explicit expressions of these critical intervals are obtained for the particular case of circular conical tips. For critical contrasts, using the Mandelstam radiation principle, we construct functional frameworks in which well-posedness of the scalar problems is restored. The physically relevant framework is selected by a limiting absorption principle. In the process, we present a new numerical strategy for 2D/3D scalar problems in the non-critical case. This approach, presented in the second part of this work, contrary to existing ones, does not require additional assumptions on the mesh near the interface. The third part of the thesis concerns Maxwell’s equations with one or two critical coefficients. By using new results of vector potentials in weighted Sobolev spaces, we explain how to construct new functional frameworks for the electric and magnetic problems, directly related to the ones obtained for the two associated scalar problems. If one uses the setting that respects the limiting absorption principle for the scalar problems, then the settings provided for the electric and magnetic problems are also coherent with the limiting absorption principle. Finally, the last part is devoted to the homogenization process for time-harmonic Maxwell’s equations and associated scalar problems in a 3D domain that contains a periodic distribution of inclusions made of negative material. Using the T-coercivity approach, we obtain conditions on the contrasts such that the homogenization results is possible for both the scalar and the vector problems. Interestingly, we show that the homogenized matrices associated with the limit problems are either positive definite or negative definite
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Strohm, Christian. "Circuit Simulation Including Full-Wave Maxwell's Equations." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22544.
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Diese Arbeit widmet sich der Simulation von elektrischen/elektronischen Schaltungen welche um elektromagnetische Bauelemente erweitert werden. Im Fokus stehen unterschiedliche Kopplungen der Schaltungsgleichungen, modelliert mit der modifizierten Knotenanalyse, und den elektromagnetischen Bauelementen mit deren verfeinerten Modell basierend auf den vollen Maxwell-Gleichungen in der Lorenz-geeichten A-V Formulierung welche durch Finite-Integrations-Technik räumlich diskretisiert werden. Eine numerische Analyse erweitert die topologischen Kriterien für den Index der resultierenden differential-algebraischen Gleichungen, wie sie bereits in anderen Arbeiten mit ähnlichen Feld/Schaltkreis-Kopplungen hergeleitet wurden. Für die Simulation werden sowohl ein monolithischer Ansatz als auch Waveform-Relaxationsmethoden untersucht. Im Mittelpunkt stehen dabei Zeitintegration, Skalierungsmethoden, strukturelle Eigenschaften und ein hybride Ansatz zur Lösung der zugrundeliegenden linearen Gleichungssysteme welcher den Einsatz spezialisierter Löser für die jeweiligen Teilsysteme erlaubt. Da die vollen Maxwell-Gleichungen zusätzliche Ableitungen in der Kopplungsstruktur verursachen, sind bisher existierende Konvergenzaussagen für die Waveform-Relaxation von gekoppelten differential-algebraischen Gleichungen nicht anwendbar und motivieren eine neue Konvergenzanalyse. Auf dieser Analyse aufbauend werden hinreichende topologische Kriterien entwickelt, welche eine Konvergenz von Gauß-Seidel- und Jacobi-artigen Waveform-Relaxationen für die gekoppelten Systeme garantieren. Schließlich werden numerische Benchmarks zur Verfügung gestellt, um die eingeführten Methoden und Theoreme dieser Abhandlung zu unterstützen.This work is devoted to the simulation of electrical/electronic circuits incorporating electromagnetic devices. The focus is on different couplings of the circuit equations, modeled with the modified nodal analysis, and the electromagnetic devices with their refined model based on full-wave Maxwell's equations in Lorenz gauged A-V formulation which are spatially discretized by the finite integration technique. A numerical analysis extends the topological criteria for the index of the resulting differential-algebraic equations, as already derived in other works with similar field/circuit couplings. For the simulation, both a monolithic approach and waveform relaxation methods are investigated. The focus is on time integration, scaling methods, structural properties and a hybrid approach to solve the underlying linear systems of equations with the use of specialized solvers for the respective subsystems. Since the full-Maxwell approach causes additional derivatives in the coupling structure, previously existing convergence statements for the waveform relaxation of coupled differential-algebraic equations are not applicable and motivate a new convergence analysis. Based on this analysis, sufficient topological criteria are developed which guarantee convergence of Gauss-Seidel and Jacobi type waveform relaxation schemes for introduced coupled systems. Finally, numerical benchmarks are provided to support the introduced methods and theorems of this treatise.
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Wang, Jenn-Nan. "Inverse backscattering for acoustic and Maxwell's equations /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5794.
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Nilsson, Martin. "Iterative solution of Maxwell's equations in frequency domain." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86390.
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We have developed an iterative solver for the Moment Method. It computes a matrix–vector product with the multilevel Fast Multipole Method, which makes the method scale with the number of unknowns. The iterative solver is of Block Quasi-Minimum Residual type and can handle several right-hand sides at once. The linear system is preconditioned with a Sparse Approximate Inverse, which is modified to handle dense matrices. The solver is parallelized on shared memory machines using OpenMP. To verify the method some tests are conducted on varying geometries. We use simple geometries to show that the method works. We show that the method scales on several processors of a shared memory machine. To prove that the method works for real life problems, we do some tests on large scale aircrafts. The largest test is a one million unknown simulation on a full scale model of a fighter aircraft.
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Savage, Joe Scott. "Vector finite elements for the solution of Maxwell's equations." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/13901.
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Strohm, Christian [Verfasser]. "Circuit Simulation Including Full-Wave Maxwell's Equations / Christian Strohm." Berlin : Humboldt-Universität zu Berlin, 2021. http://d-nb.info/1229435077/34.
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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Chilton, Sven. "A fourth-order adaptive mesh refinement solver for Maxwell's Equations." Thesis, University of California, Berkeley, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3616542.
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We present a fourth-order accurate, multilevel Maxwell solver, discretized in space with a finite volume approach and advanced in time with the classical fourth-order Runge Kutta method (RK4). Electric fields are decomposed into divergence-free and curl-free parts; we solve for the divergence-free parts of Faraday's Law and the Ampère-Maxwell Law while imposing Gauss' Laws as initial conditions. We employ a damping scheme inspired by the Advanced Weather Research and Forecasting Model to eliminate non-physical waves reflected off of coarse-fine grid boundaries, and Kreiss-Oliger artificial dissipation to remove standing wave instabilities. Surprisingly, artificial dissipation appears to damp the spuriously reflected waves at least as effectively as the atmospheric community's damping scheme.
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McCauley, Alexander P. (Alexander Patrick). "Novel applications of Maxwell's equations to quantum and thermal phenomena." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/77488.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 229-244).
This thesis is concerned with the extension of Maxwell's equations to situations far removed from standard electromagnetism, in order to discover novel phenomena. We discuss our contributions to the efforts to describe quantum fluctuations, known as Casimir forces, in terms of classical electromagnetism. We prove that chirality in metamaterials can have no appreciable effect on the Casimir force, and design an alternative metamaterial in which the structure can have a strong effect on the Casimir force. We present a geometry that exhibits a repulsive Casimir force between metallic objects in vacuum, and describe our efforts to enhance this repulsive force using the numerical techniques that we and others developed. We then show how our techniques can be extended to study the physics of near-field radiative heat transfer, computing for the first time the exact heat transfer and power flux profiles between a plate and non-spherical objects. We find in particular that the heat flux profile is non-monotonic in separation from the cone tip. Finally, we demonstrate how techniques to compute photonic bandstructures in periodic systems can be extended to certain types of quasi-periodic structures, termed photonic-quasicrystals (PQCs).
by Alexander P. McCauley.
Ph.D.
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Kaus, Cynthia Christine 1965. "Topological and geometrical considerations for Maxwell's equations on unstructured meshes." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282472.
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A discrete differential form approach to solving Maxwell's equations numerically on unstructured meshes is presented. A differential form representation of Maxwell's equations provides a natural and coordinate-free means of studying these equations and their solutions in the presence of curved objects. We begin by reviewing basic properties of differential forms and the operators associated with them for their use in describing electromagnetic fields and sources. Because we are interested in numerically solving Maxwell's equations on unstructured meshes, we introduce discrete representations of these differential forms and the underlying manifolds. This allows a discrete representation of Maxwell's equations in terms of chains and cochains on an arbitrary polyhedral cell complex. The discrete boundary operator, coboundary operator and star operator on cochains are constructed and shown to maintain divergence-free regions. The constructions of the dual of a polyhedral cell complex and the star operator, which give a one-to-one correspondence between the primary and the dual cell complexes, are introduced. This star operation gives the relationship between the magnetic field 1-cochain on the dual cell complex and the magnetic flux 2-cochain on the primary cell complex, and the relationship between the electric field 1-cochain on the primary cell and the electric flux 2-cochain on the dual cell complex. With the construction of these operators, the dual cell complex, and the associated cochains, we have determined the corresponding numerical update equations for the electromagnetic fields on unstructured meshes. The numerical update equations provided by the discrete differential form approach are determined explicitly for cubical, parallelepiped, tetrahedral, and trapezoid cell complexes. For the special cases of an orthogonal complex and a parallelepiped complex, these discrete differential form update equations recover those provided by both Yee's algorithm and the discrete surface integral (DSI) algorithm. It is demonstrated that the discrete differential form update equations differ from those obtained with the DSI approach on the more irregular trapezoid cell complex and, hence, may overcome the known late-time instabilities associated with the DSI approach applied to such highly unstructured meshes.
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Krigman, Steven Slava. "Boundary controllability of Maxwell's equations with nonzero conductivity and an application to an inverse source problem." Thesis, Boston University, 2004. https://hdl.handle.net/2144/30678.
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Thesis (Ph.D.)--Boston UniversityPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.
This thesis studies the question of control of Maxwell's equations in a medium with positive conductivity by means of boundary surface currents. Two types of domains and media are considered in connection with this question. First is a bounded simply connected star-shaped domain in R^3 which is made up of a heterogeneous medium with small conductivity, with controls being applied over the entire boundary. Using the Hilbert Uniqueness Method of Lions, the exact boundary controllability over a sufficiently long time period is established for this case, provided the conductivity is small enough to satisfy a certain technical inequality. It is also found that the requirement for the conductivity term to be very small remains in place even if the medium considered is homogenous. In order to remove this constraint, a special domain type is considered next - a cube - made up of a homogenous medium where the conductivity is allowed to take on any non-negative value. An additional restriction imposed here in order to make this problem more suitable for practical implementations is that the controls are applied over only one face of the cube. Employing the Method of Moments the spectral controllability is established for this case. It is also established that the exact controllability fails for this geometry regardless of the size of the conductivity term. This thesis will also consider the question of reconstructing the source of electromagnetic radiation, which is related to the controllability problem.
2031-01-02
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Schwarzbach, Christoph. "Stability of finite element solutions to Maxwell's equations in frequency domain." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:bsz:105-24780.
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Eine Standardformulierung der Randwertaufgabe für die Beschreibung zeitharmonischer elektromagnetischer Phänomene hat die Vektor-Helmholtzgleichung für das elektrische Feld zur Grundlage. Bei niedrigen Frequenzen führt der große Nullraum des Rotationsoperators zu einem instabilen Lösungsverhalten. Wird die Randwertaufgabe zum Beispiel mit Hilfe der Methode der Finiten Elemente in ein lineares Gleichungssystem überführt, äußert sich die Instabilität in einer schlechten Konditionszahl ihrer Koeffizientenmatrix. Eine stabilere Formulierung wird durch die explizite Berücksichtigung der Kontinuitätsgleichung erreicht. Zur numerischen Lösung der Randwertaufgaben wurde eine Finite-Elemente-Software erstellt. Sie berücksichtigt unter anderem unstrukturierte Gitter, räumlich variable, anisotrope Materialparameter sowie die Erweiterung der Maxwell-Gleichungen durch Perfectly Matched Layers. Die Software wurde anhand von Anwendungen in der marinen Geophysik erfolgreich getestet. Insbesondere demonstriert die Einbeziehung von Seebodentopographie in Form einer stetigen Oberflächentriangulierung die geometrische Flexibilität der SoftwareThe physics of time-harmonic electromagnetic phenomena can be mathematically described by boundary value problems. A standard approach is based on the vector Helmholtz equation in terms of the electric field. The curl operator involved has a large, non-trivial kernel which leads to an instable solution behaviour at low frequencies. If the boundary value problem is solved approximately using, e. g., the finite element method, the instability expresses itself by a badly conditioned coefficient matrix of the ensuing system of linear equations. A stable formulation is obtained by taking the continuity equation explicitly into account. In order to solve the boundary value problem numerically a finite element software package has been implemented. Its features comprise, amongst others, the treatment of unstructured meshes and piecewise polynomial, anisotropic constitutive parameters as well as the extension of Maxwell’s equations to the Perfectly Matched Layer. Successful application of the software is demonstrated with examples from marine geophysics. In particular, the incorporation of seafloor topography by a continuous surface triangulation illustrates the geometric flexibility of the software
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Verfürth, Barbara [Verfasser]. "Numerical multiscale methods for Maxwell's equations in heterogeneous media / Barbara Verfürth." Augsburg : Universität Augsburg, 2018. http://d-nb.info/1202246702/34.
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Meagher, Timothy P. "A New Finite Difference Time Domain Method to Solve Maxwell's Equations." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4389.
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We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, Er(x,y), of the electric field and the normal component, Dn(x,y), of the electric displacement are continuous. Meanwhile, the magnetic field, H(x,y), stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.
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Ward, Andrew John. "Transfer matrices photonic bands and related quantities." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244070.
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Schütte, Maria [Verfasser]. "On shape sensitivity analysis for 3D time-dependent Maxwell's equations / Maria Schütte." Paderborn : Universitätsbibliothek, 2017. http://d-nb.info/1127109979/34.
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Brookes, P. J. "Time domain methods for the solution of Maxwell's equations on unstructured grids." Thesis, Swansea University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636158.
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Designers of aerospace vehicle have recently highlighted computational simulations of electromagnetic systems as a key phase of the design process. Problems of interest involve the simulation of electromagnetic waves, over a wide frequency range, interacting with complex geometries of varying electrical length. This thesis represents the investigation and development of efficient numerical techniques for the simulation of time dependent electromagnetic phenomena. Unstructured grid based algorithms, which have already been successfully employed in the simulation of steady inviscid fluid flows, are applied to the solution of Maxwell's linear curl equations. Finite element time domain solution procedures employing element and edge based data structures are investigated and developed, with a view to extending the range of wave frequencies involved in scattering problems. A two-step Taylor-Galerkin procedure is modified to incorporate a capability to model the wave scattering effects of thin wires. In addition, a hybridisation of the Yee finite difference time domain algorithm and a finite volume time domain procedure is shown to alleviate the restriction of employing Cartesian grids to approximate complex geometries, whilst maintaining an attractively low operation court. Current high performance computing resources are exploited through an efficient parallel implementation of an existing edge based solution algorithm. The extended solution capabilities are demonstrated by the simulation of the scattering effects of a complete aircraft.
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Dean, Andrew John. "Non structured mesh for the finite integral method of solving Maxwell's equations." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339203.
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Kim, Joonshik. "Finite Element Time Domain Techniques for Maxwell's Equations Based on Differential Forms." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1293588301.
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Sturm, Andreas [Verfasser], and M. [Akademischer Betreuer] Hochbruck. "Locally Implicit Time Integration for Linear Maxwell's Equations / Andreas Sturm ; Betreuer: M. Hochbruck." Karlsruhe : KIT-Bibliothek, 2017. http://d-nb.info/1132997453/34.
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Dosopoulos, Stylianos. "Interior Penalty Discontinuous Galerkin Finite Element Method for the Time-Domain Maxwell's Equations." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337787922.
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Dubcová, Lenka. "Novel self-adaptive higher-order finite elements methods for Maxwell's equations of electromagnetics." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2008. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Wood, Jeffrey C. "An analysis of mixed finite element methods for Maxwell's equations on non-uniform meshes." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282161.
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Müller, Dominik [Verfasser], and R. [Akademischer Betreuer] Schnaubelt. "Well-posedness for a general class of quasilinear evolution equations - with applications to Maxwell's equations / Dominik Müller. Betreuer: R. Schnaubelt." Karlsruhe : KIT-Bibliothek, 2014. http://d-nb.info/1054989370/34.
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Zschiedrich, Lin [Verfasser]. "Transparent boundary conditions for Maxwell's equations : Numerical concepts beyond the PML method / Lin Werner Zschiedrich." Berlin : Freie Universität Berlin, 2009. http://d-nb.info/1023784203/34.
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Findeisen, Stefan Matthias [Verfasser], and C. [Akademischer Betreuer] Wieners. "A Parallel and Adaptive Space-Time Method for Maxwell's Equations / Stefan Matthias Findeisen. Betreuer: C. Wieners." Karlsruhe : KIT-Bibliothek, 2016. http://d-nb.info/1108452647/34.
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Niegemann, Jens [Verfasser], and K. [Akademischer Betreuer] Busch. "Higher-Order Methods for Solving Maxwell's Equations in the Time-Domain / Jens Niegemann. Betreuer: K. Busch." Karlsruhe : KIT-Bibliothek, 2009. http://d-nb.info/1014099129/34.
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Freese, Jan Philip [Verfasser], and C. [Akademischer Betreuer] Wieners. "Numerical homogenization of time-dependent Maxwell's equations with dispersion effects / Jan Philip Freese ; Betreuer: C. Wieners." Karlsruhe : KIT-Bibliothek, 2021. http://d-nb.info/1227451113/34.
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Edelvik, Fredrik. "Hybrid Solvers for the Maxwell Equations in Time-Domain." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2156.
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The most commonly used method for the time-domain Maxwell equations is the Finite-Difference Time-Domain method (FDTD). This is an explicit, second-order accurate method, which is used on a staggered Cartesian grid. The main drawback with the FDTD method is its inability to accurately model curved objects and small geometrical features. This is due to the Cartesian grid, which leads to a staircase approximation of the geometry and small details are not resolved at all. This thesis presents different ways to circumvent this drawback, but still take advantage of the benefits of the FDTD method. An approach to avoid staircasing errors but still retain the efficiency of the FDTD method is to use a hybrid grid. A few layers of unstructured cells are used close to curved objects and a Cartesian grid is used for the rest of the domain. For the choice of solver on the unstructured grid two different alternatives are compared: an explicit Finite-Volume Time-Domain (FVTD) solver and an implicit Finite-Element Time-Domain (FETD) solver. The hybrid solvers calculate the scattering from complex objects much more efficiently compared to using FDTD on highly resolved Cartesian grids. For the same accuracy in the solution roughly a factor of 10 in memory requirements and a factor of 20 in execution time are gained. The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this thesis a technique to generalize a well-known subcell model for thin wires, in order to take arbitrarily oriented wires in FETD and FDTD into account, is proposed. The method gives considerable modeling flexibility compared to earlier methods and is proven stable. The results show excellent consistency and very good accuracy on different antenna configurations. The recursive convolution method is often used to model frequency dispersive materials in FDTD. This method is used to enable modeling of such materials in the unstructured FVTD and FETD solvers. The stability of both solvers is analyzed and their accuracy is demonstrated by computing the radar cross section for homogeneous as well as layered spheres with frequency dependent permittivity.
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Aghabarati, Ali. "Multilevel and algebraic multigrid methods for the higher order finite element analysis of time harmonic Maxwell's equations." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=121485.
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The Finite Element Method (FEM) applied to wave scattering and quasi-static vector field problems in the frequency domain leads to sparse, complex-symmetric, linear systems of equations. For large problems with complicated geometries, most of the computer time and memory used by FEM goes to solving the matrix equation. Krylov subspace methods are widely used iterative methods for solving large sparse systems. They depend heavily on preconditioning to accelerate convergence. However, application of conventional preconditioners to the "curl-curl" operator which arises in vector electromagnetics does not result in a satisfactory performance and specialized preconditioning techniques are required. This thesis presents effective Multilevel and Algebraic Multigrid (AMG) preconditioning techniques for p-adaptive FEM analysis. In p-adaption, finite elements of different polynomial orders are present in the mesh and the system matrix can be structured into blocks corresponding to the orders of the basis functions. The new preconditioners are based on a p-type multilevel Schwarz (pMUS) approximate inversion of the block structured system. A V-cycle multilevel correction starts by applying Gauss-Seidel to the highest block level, then the next level down, and so on. On the other side of the V, Gauss-Seidel iterations are applied in the reverse order. At the bottom of the cycle is the lowest order system, which is usually solved exactly with a direct solver. The proposed alternative is to use Auxiliary Space Preconditioning (ASP) at the lowest level and continue the V-cycle downwards, first into a set of auxiliary, node-based spaces, then through a series of progressively smaller matrices generated by an Algebraic Multigrid (AMG). The algebraic coarsening approach is especially useful for problems with fine geometric details, requiring a very large mesh in which the bulk of the elements remain at low order. In addition, for wave problems, a "shifted Laplace" technique is applied, in which part of the ASP/AMG algorithm uses a perturbed, complex frequency. A significant convergence acceleration is achieved. The performance of Krylov algorithms is further enhanced during p-adaption by incorporation of a deflation technique. This projects out from the preconditioned system the eigenvectors corresponding to the smallest eigenvalues. The construction of the deflation subspace is based on efficient estimation of the eigenvectors from information obtained when solving the first problem in a p-adaptive sequence. Extensive numerical experiments have been performed and results are presented for both wave and quasi-static problems. The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners. Deflated Krylov methods preconditioned with the current Multilevel/ASP/AMG approach are always considerably faster than the reference methods and speedups of up to 10 are achieved for some test problems.La méthode des éléments finis (FEM) appliquée à la dispersion des ondes et aux problèmes de champ de vecteurs quasi-statique dans le domaine fréquentiel mène à des systèmes d'équations linéaires rares, symétriques-complexes. Pour de grands problèmes ayant des géométries complexes, la plupart du temps et de la mémoire d'ordinateur utilisé par FEM va à la résolution de l'équation de la matrice. Les méthodes itératives de Krylov sont celles largement utilisées dans la résolution de grands systèmes creux. Elles dépendent fortement des préconditionnement qui accélèrent la convergence. Toutefois, l'application de préconditionnements conventionnels à l'opérateur "rot-rot" qui surgit en électromagnétisme vectoriel n'aboutit pas à des résultats satisfaisants et des techniques de préconditionnement spécialisés sont exigées.Cette thèse présente des techniques de préconditionnement efficaces multiniveau et multigrilles algébrique (AMG) pour l'analyse p-adaptative FEM. Dans la p-adaptation, des éléments finis de différents ordres polynomiaux sont présents dans le maillage et la matrice du système peut être structurée en blocs correspondant aux ordres des fonctions de base. Les nouveaux préconditionneurs sont basés sur un type d'inversion approximative à multiniveau p Schwarz (pMUS) du système structuré de bloc. Une correction à niveaux multiples en cycle V débute par l'application de Gauss-Seidel au niveau du bloc le plus élevé, suivi par le niveau inférieur, et ainsi de suite. De l'autre côté du V, des itérations de Gauss-Seidel sont appliquées en ordre inverse. Au bas du cycle se trouve le système d'ordre le plus bas, qui est habituellement résolu exactement avec un solveur direct. L'alternative proposée est d'utiliser l'espace auxiliaire de préconditionnement (ASP) au niveau le plus bas et de poursuivre le cycle en V vers le bas, d'abord en un ensemble d'auxiliaires, basé sur les espacements de nœuds, à travers une série de plus en plus petites de matrices générées par un multigrille algébrique (AMG). L'approche de grossissement algébrique est particulièrement utile aux problèmes ayant de fins détails géométriques, nécessitant une très grande maille dans laquelle la majeure partie des éléments restent à un niveau plus bas.En outre, pour des problèmes d'onde, la technique "décalé Laplace" est appliquée, dans laquelle une partie de l'algorithme ASP/AMG utilise une fréquence complexe perturbée. Une accélération de la convergence significative est atteinte. La performance des algorithmes de Krylov est davantage renforcée au cours du p-adaptation par l'incorporation d'une technique de déflation. Cette saillie fait dépasser hors du système préconditionné, les vecteurs propres correspondants aux plus petites valeurs propres. La construction du sous-espace de déflation est basée sur une estimation efficace des vecteurs propres à partir d'informations obtenues lors de la résolution du premier problème dans une séquence p-adaptatif. Des expériences numériques approfondies ont été effectuées et les résultats sont présentés à la fois aux problèmes d'onde et quasi-statiques. Les cas de test sont considérés comme compliqués à résoudre et les résultats numériques montrent la robustesse et l'efficacité des nouveaux préconditionnements. Les méthodes de Krylov de déflation préconditionnés par l'approche multiniveaux/ASP/AMG actuelle sont toujours considérablement plus rapides que les méthodes de référence et des accélérations allant jusqu'à 10 sont atteintes pour certains problèmes de test.
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Chanaud, Mathieu. "Conception d’un solveur haute performance de systèmes linéaires creux couplant des méthodes multigrilles et directes pour la résolution des équations de Maxwell 3D en régime harmonique discrétisées par éléments finis." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14324/document.
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Cette thèse présente une méthode parallèle de résolution de systèmes linéaires creux basée sur un algorithme multigrille géométrique. Les estimations de la solution sont calculées par méthode directe sur le niveau grossier ou par méthode itérative de type splitting sur les maillages raffinés; des opérateurs inter-grilles sont définis pour interpoler les solutions approximatives entre les différents niveaux de raffinements. Ce solveur est utilisé dans le cadre de simulations électromagnétiques en 3D (équations de Maxwell en régime harmonique discrétisées par éléments finis de Nédélec de premier ordre) en tant que méthode stationnaire ou comme préconditionneur d’une méthode de Krylov (GMRES)Multigrid algorithm. The system is solved thanks to a direct method on the coarse mesh anditerative splitting method on refined meshes; inter-grid operators are defined to interpolate theapproximate solutions on the different refinement levels. Applied to 3D electromagnetic simulations(Nédélec first order finite element approximation of time harmonic Maxwell equations) thissolver is used either as a stationary method or as a preconditioner for a Krylov subspace method(GMRES)
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Pa¸ur, Tomislav [Verfasser], and M. [Akademischer Betreuer] Hochbruck. "Error analysis of implicit and exponential time integration of linear Maxwell's equations / Tomislav Pa¸ur. Betreuer: M. Hochbruck." Karlsruhe : KIT-Bibliothek, 2013. http://d-nb.info/1047839822/34.
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Klimek, Mariusz [Verfasser], Sebastian [Akademischer Betreuer] Schöps, and Stefan [Akademischer Betreuer] Kurz. "Space-Time Discretization of Maxwell's Equations in the Setting of Geometric Algebra / Mariusz Klimek ; Sebastian Schöps, Stefan Kurz." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2018. http://d-nb.info/1152384236/34.
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Boat, Matthew. "The time-domain numerical solution of Maxwell's electromagnetic equations, via the fourth order Runge-Kutta discontinuous Galerkin method." Thesis, Swansea University, 2008. https://cronfa.swan.ac.uk/Record/cronfa42532.
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This thesis presents a high-order numerical method for the Time-Domain solution of Maxwell's Electromagnetic equations in both one- and two-dimensional space. The thesis discuses the validity of high-order representation and improved boundary representation. The majority of the theory is concerned with the formulation of a high-order scheme which is capable of providing a numerical solution for specific two-dimensional scattering problems. Specifics of the theory involve the selection of a suitable numerical flux, the choice of appropriate boundary conditions, mapping between coordinate systems and basis functions. The effectiveness of the method is then demonstrated through a series of examples.
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Kung, Christopher W. "Development of a time domain hybrid finite difference/finite element method for solutions to Maxwell's equations in anisotropic media." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1238024768.
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Blank, Elisabeth [Verfasser], and W. [Akademischer Betreuer] Dörfler. "The Discontinuous Galerkin Method for Maxwell's Equations: Application to Bodies of Revolution and Kerr-Nonlinearities / Elisabeth Blank. Betreuer: W. Dörfler." Karlsruhe : KIT-Bibliothek, 2013. http://d-nb.info/1032243287/34.
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Crouch, Matthew. "Luminosity performance limitations due to the beam-beam interaction in the Large Hadron Collider." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/luminosity-performance-limitations-due-to-the-beambeam-interaction-in-the-large-hadron-collider(287b2265-a67d-406a-8c94-0fc193e2401b).html.
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In the Large Hadron Collider (LHC), particle physics events are created by colliding high energy proton beams at a number of interaction points around the ring. One of the main performance indicating parameters of the LHC is the luminosity. The luminosity is limited by, amongst other things, the strength of the beam-beam interaction. In this thesis, the effect of the beam-beam interaction on the luminosity performance of the LHC and the proposed High Luminosity Large Hadron Collider (HL-LHC) is investigated. Results from a number of dedicated, long-range beam-beam machine studies are presented and analysed. In these studies, the minimum beam-beam separation for two different beta star optics are identified. This separation defines the minimum operational crossing angle in the LHC. The data from these studies are then compared to simulation of the dynamic aperture and the results are discussed. In addition to studies of the LHC, an analytical approach is derived in order to describe the hourglass effect, which may become a contributing factor in limiting the luminosity performance of the HL-LHC.
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Peillon, Etienne. "Simulation and analysis of sign-changing Maxwell’s equations in cold plasma." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAE004.
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De nos jours, les plasmas sont principalement utilisés à des fins industrielles. L'un des exemples les plus fréquemment cités d'utilisation industrielle est la production d'énergie électrique via des réacteurs nucléaires à fusion. Pour contenir le plasma correctement à l'intérieur du réacteur, un champ magnétique est imposé en arrière-plan, et la densité et la température du plasma doivent être précisément contrôlées. Cela est effectué en envoyant des ondes électromagnétiques à des fréquences et dans des directions spécifiques en fonction des caractéristiques du plasma.La première partie de cette thèse de doctorat est consacrée à l'étude du modèle du plasma avec un fort champ magnétique en arrière-plan, ce qui correspond à un métamatériau hyperbolique. L'objectif est d'étendre les résultats existant en 2D au cas 3D et de dériver une condition de radiation. Nous introduisons une séparation des champs électriques et magnétiques ressemblant à la décomposition TE et TM habituelle, puis nous présentons quelques résultats sur les deux problèmes résultants. Les résultats sont dans un état très partiel et constituent un brouillon approximatif sur le sujet.La deuxième partie étudie l'EDP dégénérée associée aux ondes résonantes « lower-hybrid » dans le plasma. Le problème aux limites associé est bien posé dans un cadre variationnel « naturel ». Cependant, ce cadre n'inclut pas le comportement singulier présenté par les solutions physiques obtenues via le principe d'absorption limite. Ce comportement singulier est important du point de vue physique car il induit le chauffage du plasma mentionné précédemment. Un des résultats clés de cette deuxième partie est la définition d'une notion de saut à travers l'interface à l'intérieur du domaine, ce qui permet de caractériser la décomposition de la solution d'absorption limite en parties régulière et singulièreNowadays, plasmas are mainly used for industrial purpose. One of the most frequently cited examples of industrial use is electric energy production via fusion nuclear reactors. Then, in order to contain plasma properly inside the reactor, a background magnetic field is imposed, and the density and temperature of the plasma must be precisely controlled. This is done by sending electromagnetic waves at specific frequencies and directions depending on the characteristics of the plasma.The first part of this PhD thesis consists in the study of the model of plasma in a strong background magnetic field, which corresponds to a hyperbolic metamaterial. The objective is to extend the existing results in 2D to the 3D-case and to derive a radiation condition. We introduce a splitting of the electric and magnetic fields resembling the usual TE and TM decomposition, then, it gives some results on the two resulting problems. The results are in a very partial state, and constitute a rough draft on the subject.The second part consists in the study of the degenerate PDE associated to the lower-hybrid resonant waves in plasma. The associated boundary-value problem is well-posed within a ``natural'' variational framework. However, this framework does not include the singular behavior presented by the physical solutions obtained via the limiting absorption principle. Notice that this singular behavior is important from the physical point of view since it induces the plasma heating mentioned before. One of the key results of this second part is the definition of a notion of weak jump through the interface inside the domain, which allows to characterize the decomposition of the limiting absorption solution into a regular and a singular parts
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Zhao, Huawei. "Computational models and numerical techniques for solving Maxwell's equations : a study of the heating of lossy dielectric materials inside arbitary shaped cavities." Thesis, Queensland University of Technology, 1997.
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Obiozor, Clarence Nwabunwanne. "Finite element analysis of a defective induction motor." Ohio University / OhioLINK, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1171672609.
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Sakly, Hamdi. "Opérateur intégral volumique en théorie de diffraction électromagnétique." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S028.
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Le problème de diffraction électromagnétique gouverné par les équations de Maxwell admet une formulation équivalente par une équation intégrale volumique fortement singulière. Cette thèse a pour but d'examiner l'opérateur intégral qui décrit cette équation. La première partie de ce manuscrit porte sur l'étude de son spectre essentiel. Cette analyse est intéressante en vue d'obtenir les conditions nécessaires et suffisantes pour avoir l'unicité de solutions du problème surtout quand il s'agirait de la diffraction des ondes par des matériaux négatifs où les techniques classiques perdent leurs utilité. Après avoir justifié le bon choix du cadre fonctionnel, nous étudions tout d'abord le cas où les paramètres caractéristiques du milieu à savoir la permittivité électrique et la perméabilité magnétique sont constants par morceaux avec discontinuité au travers du bord de la cible. Dans ce cadre, nous donnons une réponse complète à la question pour les domaines réguliers et Lipschitziens. Ensuite, et à l'aide d'une technique de localisation, nous donnons une extension de ces résultats dans le cas des paramètres réguliers par morceaux pour deux opérateurs intégraux, l'un qui correspond à la version diélectrique du problème et l'autre pour sa version magnétique. Nous terminons cette thèse par l'étude de la dérivée de forme des opérateurs diélectrique et magnétique et nous en déduisons une nouvelle caractérisation de la dérivée de forme des solutions des deux problèmes de diffractionThe electromagnetic diffraction problem which is governed by the Maxwell equations admits an equivalent formulation in terms of a strongly singular volume integral equation. This thesis aims to examine the integral operator that describes this equation. The first part of this document focuses on the study of its essential spectrum. This analysis is interesting to get the necessary and sufficient conditions of solution uniqueness of the problem especially when we consider the diffraction of waves by negative materials where classic tools lose their usefulness. After justifying the adequate choice of the functional framework, we first study the case where the characteristics parameters of the medium like the electric permittivity and magnetic permeability are piecewise constant with discontinuity across the boundary of the target. In this context, we give a full answer to the question for smooth and Lipschitz domains. Then, by using a localization technique, we give an extension of those results in the case of piecewise regular parameters for two integrals operators, one which corresponds to the dielectric version of the problem and the other for its magnetic version. We end this thesis by the study of the shape derivative of the dielectric and magnetic operators and we derive a new characterization of the shape derivative of the two diffraction problems solution
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Schwarzbach, Christoph [Verfasser], Klaus [Akademischer Betreuer] Spitzer, Klaus [Gutachter] Spitzer, Peter [Gutachter] Weidelt, and Eldad [Gutachter] Haber. "Stability of finite element solutions to Maxwell's equations in frequency domain / Christoph Schwarzbach ; Gutachter: Klaus Spitzer, Peter Weidelt, Eldad Haber ; Betreuer: Klaus Spitzer." Freiberg : TU Bergakademie Freiberg, 2009. http://d-nb.info/1220836885/34.
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Dolean, Victorita. "Algorithmes par decomposition de domaine et méthodes de discrétisation d'ordre elevé pour la résolution des systèmes d'équations aux dérivées partielles. Application aux problèmes issus de la mécanique des fluides et de l'électromagnétisme." Habilitation à diriger des recherches, Université de Nice Sophia-Antipolis, 2009. http://tel.archives-ouvertes.fr/tel-00413574.
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My main research topic is about developing new domain decomposition algorithms for the solution of systems of partial differential equations. This was mainly applied to fluid dynamics problems (as compressible Euler or Stokes equations) and electromagnetics (time-harmonic and time-domain first order system of Maxwell's equations). Since the solution of large linear systems is strongly related to the application of a discretization method, I was also interested in developing and analyzing the application of high order methods (such as Discontinuos Galerkin methods) to Maxwell's equations (sometimes in conjuction with time-discretization schemes in the case of time-domain problems). As an active member of NACHOS pro ject (besides my main afiliation as an assistant professor at University of Nice), I had the opportunity to develop certain directions in my research, by interacting with permanent et non-permanent members (Post-doctoral researchers) or participating to supervision of PhD Students. This is strongly refflected in a part of my scientific contributions so far. This memoir is composed of three parts: the first is about the application of Schwarz methods to fluid dynamics problems; the second about the high order methods for the Maxwell's equations and the last about the domain decomposition algorithms for wave propagation problems.
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Bažantová, Lucie. "Modelování ohřevu tkání v KV diatermii." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219736.
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This thesis deals with the basic theory of the electromagnetic field in the first part and the field interactions with biological tissues. Than describes shortwave diathermy as a technique used for purposes of medical treatment. The aim is to built a model of tissue heating in shortwave diathermy in COMSOL Multiphysics environment, so there is included a description of the programming environment, including the mathematical method that COMSOL uses for calculations. The output of the whole work is a model of the lower limb in the knee part and display the results after his diathermy heating.
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Riaz, Azba. "Une nouvelle formulation Galerkin discontinue pour équations de Maxwell en temps, a priori et a posteriori erreur estimation." Thesis, Cergy-Pontoise, 2016. http://www.theses.fr/2016CERG0790/document.
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Dans la première partie de cette thèse, nous avons considéré les équations de Maxwell en temps et construit une formulation discontinue de Galerkin (DG). On a montré que cette formulation est bien posée et ensuite on a établi des estimateurs a priori pour cette formulation. On a obtenu des résultats numériques pour valider les estimateurs a priori obtenus théoriquement. Dans la deuxième partie de cette thèse, des estimateurs d'erreur a posteriori de cette formulation sont établis, pour le cas semi-discret et pour le système complètement discrétisé. Dans la troisième partie de cette thèse, on considére les équations de Maxwell en régime harmonique. On a développé une formulation discontinue de Galerkin mixte. On a établi des estimations d'erreur a posteriori pour cette formulationIn the first part of this thesis, we have considered the time-dependent Maxwell's equations in second-order form and constructed discontinuous Galerkin (DG) formulation. We have established a priori error estimates for this formulation and carried out the numerical analysis to confirm our theoretical results. In the second part of this thesis, we have established a posteriori error estimates of this formulation for both semi discrete and fully discrete case. In the third part of the thesis we have considered the time-harmonic Maxwell's equations and we have developed mixed discontinuous Galerkin formulation. We showed the well posedness of this formulation and have established a posteriori error estimates
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Tomezyk, Jérôme. "Résolution numérique de quelques problèmes du type Helmholtz avec conditions au bord d'impédance ou des couches absorbantes (PML)." Thesis, Valenciennes, 2019. http://www.theses.fr/2019VALE0017/document.
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Dans cette thèse, nous étudions la convergence de méthode de type éléments finis pour les équations de Maxwell en régime harmonique avec condition au bord d'impédance et l'équation de Helmholtz avec une couche parfaitement absorbante(PML). On étudie en premier, la formulation régularisée de l'équation de Maxwell en régime harmonique avec condition au bord d'impédance (qui consiste à ajouter le term ∇ div à l'équation originale pour avoir un problème elliptique) et on garde la condition d'impédance comme une condition au bord essentielle. Pour des domaines à bord régulier, le caractère bien posé de cette formulation est bien connu mais cela n'est pas le cas pour des domaines polyédraux convexes. On commence alors le premier chapitre par la preuve du caractère bien posé dans le cas du polyèdre convexe, qui est basé sur le fait que l'espace variationnel est inclus dans H¹. Dans le but d'avoir des estimations explicites en le nombre d'onde k de ce problème, il est obligatoire d'avoir des résultats de stabilité explicites en ce nombre d'onde. C'est aussi proposé, pour quelques situations particulières, dans ce chapitre. Dans le second chapitre on décrit les singularités d'arêtes et de coins pour notre problème. On peut alors déduire la régularité de la solution du problème original, ainsi que de son adjoint. On a tous les ingrédients pour proposer une analyse de convergence explicite en k pour une méthode d'éléments finis avec éléments de Lagrange. Dans le troisième chapitre, on considère une méthode d'éléments finis hp non conforme pour un domaine à bord régulier. Pour obtenir des estimations explicites en k, on introduit un résultat de décomposition, qui sépare la solution du problème original (ou de son adjoint) en une partie régulière mais fortement oscillante et une partie moins régulière mais peu oscillante. Ce résultat permet de montrer des estimations explicites en k. Le dernier chapitre est dédié à l'équation de Helmholtz avec une PML. L'équation de Helmholtz dans l'espace entier est souvent utilisée pour modéliser la diffraction d'onde acoustique (en régime harmonique), avec la condition de radiation à l'infini de Sommerfeld. L'ajout d'une PML est une façon pour passer d'un domaine infini à un domaine fini, elle correspond à l'ajout d'une couche autour du domaine de calcul qui absorbe très vite toutes les ondes sortantes. On propose en premier un résultat de stabilité explicite en k. On propose alors deux schémas numériques, une méthode d'éléments finis hp et une méthode multi- échelle basée sur un sous-espace local de correction. Le résultat de stabilité est utilisé pour mettre en relation de choix des paramètres des méthodes numériques considérées avec k. Nous montrons aussi des estimations d'erreur a priori. A la fin de ces chapitres, des tests numériques sont proposés pour confirmer nos résultats théoriquesIn this thesis, we propose wavenumber explicit convergence analyses of some finite element methods for time-harmonic Maxwell's equations with impedance boundary condition and for the Helmholtz equation with Perfectly Matched Layer (PML). We first study the regularized formulation of time-harmonic Maxwell's equations with impedance boundary conditions (where we add a ∇ div-term to the original equation to have an elliptic problem) and keep the impedance boundary condition as an essential boundary condition. For a smooth domain, the wellposedness of this formulation is well-known. But the well-posedness for convex polyhedral domain has been not yet investigated. Hence, we start the first chapter with the proof of the well-posedness in this case, which is based on the fact that the variational space is embedded in H¹. In order to perform a wavenumber explicit error analysis of our problem, a wavenumber explicit stability estimate is mandatory. We then prove such an estimate for some particular configurations. In the second chapter, we describe the corner and edge singularities for such problem. Then we deduce the regularity of the solution of the original and the adjoint problem, thus we have all ingredients to propose a explicit wavenumber convergence analysis for h-FEM with Lagrange element. In the third chapter, we consider a non conforming hp-finite element approximation for domains with a smooth boundary. To perform a wavenumber explicit error analysis, we split the solution of the original problem (or its adjoint) into a regular but oscillating part and a rough component that behaves nicely for large frequencies. This result allows to prove convergence analysis for our FEM, again explicit in the wavenumber. The last chapter is dedicated to the Helmholtz equation with PML. The Helmholtz equation in full space is often used to model time harmonic acoustic scattering problems, with Sommerfeld radiation condition at infinity. Adding a PML is a way to reduce the infinite domain to a finite one. It corresponds to add an artificial absorbing layer surrounding a computational domain, in which scattered wave will decrease very quickly. We first propose a wavenumber explicit stability result for such problem. Then, we propose two numerical discretizations: an hp-FEM and a multiscale method based on local subspace correction. The stability result is used to relate the choice of the parameters in the numerical methods to the wavenumber. A priori error estimates are shown. At the end of each chapter, we perform numerical tests to confirm our theoritical results
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Alberti, Giovanni S. "On local constraints and regularity of PDE in electromagnetics : applications to hybrid imaging inverse problems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1b30b3b7-29b1-410d-ae30-bd0a87c9720b.
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The first contribution of this thesis is a new regularity theorem for time harmonic Maxwell's equations with less than Lipschitz complex anisotropic coefficients. By using the Lp theory for elliptic equations, it is possible to prove H1 and Hölder regularity results, provided that the coefficients are W1,p for some p = 3. This improves previous regularity results, where the assumption W1,∞ for the coefficients was believed to be optimal. The method can be easily extended to the case of bi-anisotropic materials, for which a separate approach turns out to be unnecessary. The second focus of this work is the boundary control of the Helmholtz and Maxwell equations to enforce local constraints inside the domain. More precisely, we look for suitable boundary conditions such that the corresponding solutions and their derivatives satisfy certain local non-zero constraints. Complex geometric optics solutions can be used to construct such illuminations, but are impractical for several reasons. We propose a constructive approach to this problem based on the use of multiple frequencies. The suitable boundary conditions are explicitly constructed and give the desired constraints, provided that a finite number of frequencies, given a priori, are chosen in a fixed range. This method is based on the holomorphicity of the solutions with respect to the frequency and on the regularity theory for the PDE under consideration. This theory finds applications to several hybrid imaging inverse problems, where the unknown coefficients have to be imaged from internal measurements. In order to perform the reconstruction, we often need to find suitable boundary conditions such that the corresponding solutions satisfy certain non-zero constraints, depending on the particular problem under consideration. The multiple frequency approach introduced in this thesis represents a valid alternative to the use of complex geometric optics solutions to construct such boundary conditions. Several examples are discussed.
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Charih, Fouad. "Comparaisons théorique et expérimentale de machines à aimants permanents pour la traction de véhicules électriques." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2023/document.
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Le travail de thèse s’inscrit dans le cadre du projet TRAX. Il s’agit là du développement de moteurs électriques destinés à la traction des petits véhicules électriques urbains. Les caractéristiques clés d’une machine électrique pour une application de traction sont le couple, le rendement, la fiabilité, l’encombrement et la plage de vitesse à puissance maximale (dé-fluxage). Les machines électriques à aimants permanents répondent à ces exigences. C’est pourquoi ce travail de thèse s’est intéressé à l’étude des performances de machines à aimants permanents en proposant une étude comparative. Un état de l’art basé sur l’étude des brevets des machines électriques dans les applications automobiles est réalisé. Une description des dernières avancées des moteurs électriques principalement des structures à aimants permanents est fournit. Nous avons modélisé une première machine avec une méthode ana-lytique simplifiée basée sur la résolution des équations de Maxwell en 2D. Cette méthode est confrontée à une méthode numérique. Trois nouvelles machines sont définies à partir de la première en modifiant la configuration du rotor. La comparaison de quatre structures à aimants permanents est réalisée par des modèles numériques. Les performances à vide et en charge ainsi que le calcul des inductances dans l’axe direct et en quadrature sont évaluées. Les résultats théoriques sont comparés aux essais expérimentauxThe thesis is part of the TRAX project. It deals with development of electric motors used for traction of small urban electric vehicles. The key characteristics of an electric machine for traction application are the torque, efficiency, reliability, size and flux-weakening. The permanents magnets electric machines meet these requirements. That’s why this thesis takes interest in the performances of permanents magnets machines by proposing a comparative study. A study of patents for electrical machines in automotive applications is realized. A description of the latest advances in electrical motors, mainly in permanent magnet structures, is provided. We started to model a first machine with a simplified analytical method based on the resolution of Maxwell's equations in 2D. This method is compared with a numerical method. Three new machines are defined from the first one by changing the configuration of the rotor. The comparison of four structures with permanent magnets is realized by numerical models. No load and load performances, as well as the calculation of inductances in the direct and quadrature axis, are evaluated. The theoretical results are compared with experimental tests
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Pham, Duc Nghia. "Investigation of quality changes during intermittent microwave convective drying of fruits." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/128338/1/Duc%20Nghia_Pham_Thesis.pdf.
Full textAbstract:
This research experimentally and theoretically investigated the complex changes of fruit quality during intermittent microwave assisted convective drying. Mathematical correlations between this advanced drying method and quality attributes were established. It will be of value both for academics and industries by providing a comprehensive understanding of the mechanism of quality change during drying and suggesting optimal regime for quality and process improvement.