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Bao, Wentao. "A Simulation and Optimization Study of Spherical Perfectly Matched Layers". The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1494166698903702.
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Erlandsson, Simon. "Evaluation, adaption and implementations of Perfectly Matched Layers in COMSOL Multiphysics". Thesis, KTH, Numerisk analys, NA, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-280757.
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Perfectly matched layer (PML) is a commonly used method of absorbing waves at a computational boundary for partial differential equation (PDE) problems. In this thesis, methods for improving the usability of implementations in Comsol Multiphysics is addressed. The study looks at complex coordinate stretching PMLs in the context of Helmholtz equation using the finite element method (FEM). For a PML to work it has to be set up properly with parameters that takes into account the properties of the problem. It is not always straight forward. Some theory behind PMLs is presented and experimentation on PML properties performed. Methods for PML optimization and adaption is presented. Currently, the way PMLs is applied in COMSOL Multiphysics requires the user to perform many tasks; setting up a geometry, meshing and choosing a suitable complex coordinate stretching. Using a so-called extra-dimension implementation it is possible to attach PMLs as boundary conditions in COMSOL Multiphysics. This simplifies for the user since the geometry and mesh is handled by the software.Perfectly matched layer (PML) är en metod som ofta används för vågabsorbering vid randen för problem med partiella differentialekvationer (PDE). I det här examensarbetet presenteras metoder som förenklar användingen av PMLer i COMSOL Multiphysics. Studien kollar på PMLer baserade på komplex-koordinatsträckning med fokus på Helmholtz ekvation och finita elementmetoden (FEM). För att en PML ska fungera måste den sättas upp på rätt sätt med parametrar anpassade efter det givna problemet. Att göra detta är inte alltid enkelt. Teori presenteras och experiment på PMLer görs. Flera metoder för optimisering och adaption av PMLer presenteras. I nuläget kräver appliceringen av PMLer i COMSOL Multiphysics att användaren sätter upp en geometri, ett beräkningsnät och väljer den komplexa koordinatsträckningen. Genom att använda COMSOLs implementation av extra dimensioner är det möjligt att applicera PMLer som randvilkor. I en sådan implementation kan geometri och beräkningsnät skötas av mjukvaran vilket underlättar för användaren.
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Appelö, Daniel. "Absorbing Layers and Non-Reflecting Boundary Conditions for Wave Propagation Problems". Doctoral thesis, KTH, Numerisk Analys och Datalogi, NADA, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-448.
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The presence of wave motion is the defining feature in many fields of application,such as electro-magnetics, seismics, acoustics, aerodynamics,oceanography and optics. In these fields, accurate numerical simulation of wave phenomena is important for the enhanced understanding of basic phenomenon, but also in design and development of various engineering applications. In general, numerical simulations must be confined to truncated domains, much smaller than the physical space were the wave phenomena takes place. To truncate the physical space, artificial boundaries, and corresponding boundary conditions, are introduced. There are four main classes of methods that can be used to truncate problems on unbounded or large domains: boundary integral methods, infinite element methods, non-reflecting boundary condition methods and absorbing layer methods. In this thesis, we consider different aspects of non-reflecting boundary conditions and absorbing layers. In paper I, we construct discretely non-reflecting boundary conditions for a high order centered finite difference scheme. This is done by separating the numerical solution into spurious and physical waves, using the discrete dispersion relation. In paper II-IV, we focus on the perfectly matched layer method, which is a particular absorbing layer method. An open issue is whether stable perfectly matched layers can be constructed for a general hyperbolic system. In paper II, we present a stable perfectly matched layer formulation for 2 x 2 symmetric hyperbolic systems in (2 + 1) dimensions. We also show how to choose the layer parameters as functions of the coefficient matrices to guarantee stability. In paper III, we construct a new perfectly matched layer for the simulation of elastic waves in an anisotropic media. We present theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers. In paper IV, we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters which is applicable to all hyperbolic systems, and which we prove is well-posed and perfectly matched. We also use an automatic method, derived in paper V, for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell s equations, the linearized Euler equations, as well as arbitrary 2 x 2 systems in (2 + 1) dimensions. In paper V, we use the method of Sturm sequences for bounding the real parts of roots of polynomials, to construct an automatic method for checking Petrowsky well-posedness of a general Cauchy problem. We prove that this method can be adapted to automatically symmetrize any well-posed problem, producing an energy estimate involving only local quantities.QC 20100830
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Srinivasan, Harish. "FINITE ELEMENT ANALYSIS AND EXPERIMENTAL VERIFICATION OF SOI WAVEGUIDE LOSSES". UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_theses/485.
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Bending loss in silicon-on-insulator rib waveguides was calculated using conformal mapping of the curved waveguide to an equivalent straight waveguide. Finite-element analysis with perfectly matched layer boundaries was used to solve the vector wave equation. Transmission loss was experimentally measured as a function of bend radius for several SOI waveguides. Good agreement was found between simulated and measured losses, and this technique was confirmed as a good predictor for loss and for minimum bend radius for efficient design.
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Long, Zeyu. "Introduction of the Debye media to the filtered finite-difference time-domain method with complex-frequency-shifted perfectly matched layer absorbing boundary conditions". Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/introduction-of-the-debye-media-to-the-filtered-finitedifference-timedomain-method-with-complexfrequencyshifted-perfectly-matched-layer-absorbing-boundary-conditions(441271dc-d4ea-4664-82e6-90bf93f5c2b7).html.
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The finite-difference time-domain (FDTD) method is one of most widely used computational electromagnetics (CEM) methods to solve the Maxwell's equations for modern engineering problems. In biomedical applications, like the microwave imaging for early disease detection and treatment, the human tissues are considered as lossy and dispersive materials. The most popular model to describe the material properties of human body is the Debye model. In order to simulate the computational domain as an open region for biomedical applications, the complex-frequency-shifted perfectly matched layers (CFS-PML) are applied to absorb the outgoing waves. The CFS-PML is highly efficient at absorbing the evanescent or very low frequency waves. This thesis investigates the stability of the CFS-PML and presents some conditions to determine the parameters for the one dimensional and two dimensional CFS-PML.The advantages of the FDTD method are the simplicity of implementation and the capability for various applications. However the Courant-Friedrichs-Lewy (CFL) condition limits the temporal size for stable FDTD computations. Due to the CFL condition, the computational efficiency of the FDTD method is constrained by the fine spatial-temporal sampling, especially in the simulations with the electrically small objects or dispersive materials. Instead of modifying the explicit time updating equations and the leapfrog integration of the conventional FDTD method, the spatial filtered FDTD method extends the CFL limit by filtering out the unstable components in the spatial frequency domain. This thesis implements filtered FDTD method with CFS-PML and one-pole Debye medium, then introduces a guidance to optimize the spatial filter for improving the computational speed with desired accuracy.
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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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Silberstein, Éric. "Généralisation de la méthode modale de Fourier aux problèmes de diffraction en optique intégrée : application aux convertisseurs modaux par ingénierie des modes de Bloch". Paris 6, 2002. https://pastel.archives-ouvertes.fr/tel-00003101.
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Métral, Jérôme. "Modélisation et simulation numérique de l'écoulement d'un plasma atmosphérique pour l'étude de l'activité électrique des plasmas sur avion". Châtenay-Malabry, Ecole centrale de Paris, 2002. http://www.theses.fr/2002ECAP0868.
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Un gaz ionisé (ou plasma) présente la propriété d'absorber ou de réfléchir les ondes électromagnétiques radar, si son taux d'ionisation est suffisant. Cette propriété suscite un intérêt particulier pour des applications dans le domaine de l'aéronautique. L'objectif de cette thèse est de pouvoir prédire les caractéristiques (électriques et énergétique) d'un plasma d'air faiblement ionisé dans un écoulement à pression atmosphérique. La description du plasma repose sur un modèle à deux températures, inspiré des modèles hors- équilibre thermique. L'écoulement du plasma est alors décrit par un système d'équations de l'hydrodynamique à deux températures couplé à un modèle collisionnel (description des échanges énergétiques) et à la cinétique chimique (réactions chimiques). Nous avons mis en œuvre un algorithme pour simuler le plasma en écoulement axisymétrique. Il s'agit d'un schéma numérique bidimensionnel de type Lagrange + Projection dont la phase de projection est un schéma d'ordre 2, adapté au transport multi- espèces. Cet algorithme nous permet de simuler des expérimentations sur l'écoulement d'un plasma atmosphérique pour valider les paramètres du modèle. Dans une deuxième partie, nous étudions la méthode des couches absorbantes parfaitement adaptées (PML) qui constitue une condition de bord pour la simulation en milieu ouvert. Son efficacité étant reconnue pour les problèmes de propagation d'onde électromagnétique, nous nous penchons sur un moyen d'adapter cette méthode de l'aéroacoustique (équations d'Euler linéarisées). Pour cela nous présentons deux approches : une méthode simple visant à éviter les oscillations numériques, et une approche plus générale où nous définissons une nouvelle formulation de couches absorbantes qui mène à des problèmes bien posésA ionized gas (or plasma) has the ability of absorbing or reflecting electromagnetic (radar) waves if its ionization rate is high enough. This is particularly interesting for aeronautics. This study aims at predicting the electric and energetic characteristics of a weakly ionized air plasma in an atmospheric pressure flow. The plasma is described by a two-temperature model, coming from the non-equilibrium description of plasmas. Plasma flow is then described by a two-temperature hydrodynamic system coupled with a collisional model (energy exchanges rates) and a kinetic model (chemical reactions). An algorithm was built to simulate plasma flow in axisymetric geometry. The algorithm is a 2D Lagrange + Projection scheme. The projection step was adapted to multi-components advection, using a second order, non oscillating, and bidimensionnal scheme. This algorithm allows the simulation of experiments concerning atmospheric pressure plasma and then the validation of the model parameters. In a second part, we study the Perfectly Matched Layer (PML) which is a boundary condition to simulate wave propagation in open domains. This method is particularly efficient for electromagnetic problems, and we want to enlarge this approach to aeroacoutics problems (linearized Euler equations). We propose two solutions: a practical approach to avoid numerical oscillations of the solution and a more general approach which consists in a new absorbing layer formulation which leads to well-posed problems
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Duru, Kenneth. "Perfectly matched layers for second order wave equations". Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-124538.
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Numerical simulation of propagating waves in unbounded spatial domains is a challenge common to many branches of engineering and applied mathematics. Perfectly matched layers (PML) are a novel technique for simulating the absorption of waves in open domains. The equations modeling the dynamics of phenomena of interest are usually posed as differential equations (or integral equations) which must be solved at every time instant. In many application areas like general relativity, seismology and acoustics, the underlying equations are systems of second order hyperbolic partial differential equations. In numerical treatment of such problems, the equations are often rewritten as first order systems and are solved in this form. For this reason, many existing PML models have been developed for first order systems. In several studies, it has been reported that there are drawbacks with rewriting second order systems into first order systems before numerical solutions are obtained. While the theory and numerical methods for first order systems are well developed, numerical techniques to solve second order hyperbolic systems is an on-going research. In the first part of this thesis, we construct PML equations for systems of second order hyperbolic partial differential equations in two space dimensions, focusing on the equations of linear elasto-dynamics. One advantage of this approach is that we can choose auxiliary variables such that the PML is strongly hyperbolic, thus strongly well-posed. The second is that it requires less auxiliary variables as compared to existing first order formulations. However, in continuum the stability of both first order and second order formulations are linearly equivalent. A turning point is in numerical approximations. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability for any given resolution. The second order discretization behaves much more stably. In the second order setting instability occurs only if unstable modes are well resolved. The second part of this thesis discusses the construction of PML equations for the time-dependent Schrödinger equation. From mathematical perspective, the Schrödinger equation is unique, in the sense that it is only first order in time but second order in space. However, with slight modifications, we carry over our ideas from the hyperbolic systems to the Schrödinger equations and derive a set of asymptotically stable PML equations. The new model can be viewed as a modified complex absorbing potential (CAP). The PML model can easily be adapted to existing codes developed for CAP by accurately discretizing the auxiliary variables and appending them accordingly. Numerical experiments are presented illustrating the accuracy and absorption properties of the new PML model. We are hopeful that the results obtained in this thesis will find useful applications in time-dependent wave scattering calculations.
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Ramli, Khairun N. "Modelling and analysis of complex electromagnetic problems using FDTD subgridding in hybrid computational methods. Development of hybridised Method of Moments, Finite-Difference Time-Domain method and subgridded Finite-Difference Time-Domain method for precise computation of electromagnetic interaction with arbitrarily complex geometries". Thesis, University of Bradford, 2011. http://hdl.handle.net/10454/5443.
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The main objective of this research is to model and analyse complex electromagnetic problems
by means of a new hybridised computational technique combining the frequency domain
Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded
Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the
ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric
materials irradiated by geometrically intricate sources. The Method of Moments modelling
employed a two-dimensional electric surface patch integral formulation solved by independent
linear basis function methods in the circumferential and axial directions of the antenna wires. A
similar orthogonal basis function is used on the end surface and appropriate attachments with
the wire surface are employed to satisfy the requirements of current continuity. The surface
current distributions on structures which may include closely spaced parallel wires, such as
dipoles, loops and helical antennas are computed. The results are found to be stable and showed
good agreement with less comprehensive earlier work by others.
The work also investigated the interaction between overhead high voltage transmission lines and
underground utility pipelines using the FDTD technique for the whole structure, combined with
a subgridding method at points of interest, particularly the pipeline. The induced fields above
the pipeline are investigated and analysed.
FDTD is based on the solution of Maxwell¿s equations in differential form. It is very useful for
modelling complex, inhomogeneous structures. Problems arise when open-region geometries
are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to
circumvent this difficulty. The establishment of edge elements has greatly improved the
performance of this method and the computational burden due to huge numbers of time steps, in
the order of tens of millions, has been eased to tens of thousands by employing quasi-static
methods.
This thesis also illustrates the principle of the equivalent surface boundary employed close to
the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid
techniques due to their ability to analyse a system of multiple discrete regions by employing the
principle of equivalent sources to excite the coupling surfaces. The method has been applied for
modelling human body interaction with a short range RFID antenna to investigate and analyse
the near field and far field radiation pattern for which the cumulative distribution function of
antenna radiation efficiency is presented. The field distributions of the simulated structures
show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of
the phenomena in the interaction between electromagnetic fields and human tissues.Ministry of Higher Education Malaysia and Universiti Tun Hussein Onn Malaysia (UTHM)
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Ramli, Khairun Nidzam. "Modelling and analysis of complex electromagnetic problems using FDTD subgridding in hybrid computational methods : development of hybridised Method of Moments, Finite-Difference Time-Domain method and subgridded Finite-Difference Time-Domain method for precise computation of electromagnetic interaction with arbitrarily complex geometries". Thesis, University of Bradford, 2011. http://hdl.handle.net/10454/5443.
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The main objective of this research is to model and analyse complex electromagnetic problems by means of a new hybridised computational technique combining the frequency domain Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric materials irradiated by geometrically intricate sources. The Method of Moments modelling employed a two-dimensional electric surface patch integral formulation solved by independent linear basis function methods in the circumferential and axial directions of the antenna wires. A similar orthogonal basis function is used on the end surface and appropriate attachments with the wire surface are employed to satisfy the requirements of current continuity. The surface current distributions on structures which may include closely spaced parallel wires, such as dipoles, loops and helical antennas are computed. The results are found to be stable and showed good agreement with less comprehensive earlier work by others. The work also investigated the interaction between overhead high voltage transmission lines and underground utility pipelines using the FDTD technique for the whole structure, combined with a subgridding method at points of interest, particularly the pipeline. The induced fields above the pipeline are investigated and analysed. FDTD is based on the solution of Maxwell's equations in differential form. It is very useful for modelling complex, inhomogeneous structures. Problems arise when open-region geometries are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to circumvent this difficulty. The establishment of edge elements has greatly improved the performance of this method and the computational burden due to huge numbers of time steps, in the order of tens of millions, has been eased to tens of thousands by employing quasi-static methods. This thesis also illustrates the principle of the equivalent surface boundary employed close to the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid techniques due to their ability to analyse a system of multiple discrete regions by employing the principle of equivalent sources to excite the coupling surfaces. The method has been applied for modelling human body interaction with a short range RFID antenna to investigate and analyse the near field and far field radiation pattern for which the cumulative distribution function of antenna radiation efficiency is presented. The field distributions of the simulated structures show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of the phenomena in the interaction between electromagnetic fields and human tissues.
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Cigánek, Jan. "Hranové konečné prvky v časové oblasti". Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-218744.
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Diplomová práce se zabývá metodou hybridních (hranových a uzlových) konečných prvků ve frekvenční i časové oblasti. Tato metoda je použita pro analýzu vlnovodu parallel-plate, v kterém jsou umístěny dvě dielektrické vrstvy. Jako ukončení vlnovodu je implementována dokonale přizpůsobená vrstva označována PML. Projekt řeší možný výběr PML vrstvy v časové oblasti. Metoda je programována v programu MATLAB a výsledky jsou porovnány s programem COMSOL Multiphysics.
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Duru, Kenneth. "Perfectly Matched Layers and High Order Difference Methods for Wave Equations". Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173009.
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The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete. We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials. We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML. Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.
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Dorostkar, Ali. "Applications of the perfectly matched layers in a discontinuous fluid media". Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-176541.
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In this thesis we study the applications of the PML in a multi-layered media. The PML is constructed for the scalar wave equation and the convergence and stability of the continuous problem is studied using the normal mode analysis. A high order accurate semi-discrete problem is constructed by approximating the spatial derivatives with high order finite difference operators satisfying the summation-by-parts properties. To have a stable semi-discrete approximation of the problem, we impose boundary conditions as well as interface conditions using the simultaneous approximation term technique. In order to gain accuracy, a transformed interface condition is constructed for the PML. The semi-discrete problem is approximated using second order accurate central difference scheme. To achieve higher order accuracy we modify the time marching scheme to eliminate truncation errors. Numerical experiments are presented showing that using the proposed transformed interface conditions, higher order of accuracy and convergence are achieved.
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MORVARIDI, MARYAM. "Flexural Wave Propagation in Microstructured Media. Perfectly Matched Layers and Elastic Metamaterials". Doctoral thesis, Università degli Studi di Cagliari, 2018. http://hdl.handle.net/11584/255943.
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The work is divided into two main topics. In the first part a formulation for Perfectly Matched Layers is given. Surprisingly, such formulation was absent in the scientific literature. In the second part a new type of periodic plate is proposed.
In particular, an analytical model of Perfectly Matched Layers (PMLs) for flexural waves within elongated beam structures is given. The model is based on transformation optics techniques and it is efficient both in time harmonic and transient regimes. A comparison between flexural and longitudinal waves is detailed and it is shown that the bending problem requires special interface conditions. A connection with transformation of eigenfrequencies and eigenmodes is given and the effect of the additional boundary conditions introduced at the border of the Perfectly Matched Layer domain is discussed in detail.
Such a model is particularly useful for Finite Element analyses pertaining propagating flexural waves in infinite domain.
Then, Perfectly Matched Layers for flexural waves are extended to plate structures. Again, the analytical model is based on transformation optics techniques applied on the biharmonic fourth-order partial differential equation describing flexural vibrations in Kirchhoff-Love plates. It is shown that perfect boundary conditions are not an optimal solution, since they depend on the incident waves. The full analytical form of PMLs and zero reflection conditions at the boundary between homogeneous and PML domains are given. The implementation in a Finite Element (FEM) code is described and an eigenfrequency analysis is given as a possible methodology to check the implementation. A measure of the performance of the PMLs is introduced and the effects of element discretization, boundary conditions, frequency, dimension of the PML, amount of transformation and dissipation are detailed.
The model gives excellent results also when the applied load approaches the PML domain.
In the last part of the work we propose a new type of platonic crystal. The microstructured plate includes snail resonators with low-frequency resonant vibrations. The special dynamic effect of the resonators are highlighted by a comparative analysis of dispersion properties of homogeneous and perforated plates. Analytical and numerical estimates of classes of standing waves are given and the analysis on a macrocell shows the possibility to obtain localization, wave trapping and edge waves. Applications include transmission amplification within two plates separated by a small ligament.
Finally we proposed a design procedure to suppress low-frequency flexural vibrations in an elongated plate implementing a by-pass system re-routing waves within the mechanical system.
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Lee, Patrick. "Modélisation d'un injecteur laser-plasma pour l'accélération multi-étages". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS180/document.
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L’accélération par sillage laser (ASL) repose sur l’interaction entre un faisceau laser intense et un plasma sous-dense. Au travers de cette interaction, une onde de plasma est générée avec un fort champ accélérateur, de trois ordres de grandeur plus élevé que celui d’un accélérateur conventionnel, rendant envisageable la réalisation d’accélérateurs futurs plus compacts. Pour la conception d’un futur accélérateur, un faisceau d’électrons de forte charge, faible dispersion en énergie et faible émittance doit être accéléré à des grandes énergies. Pour ce faire, la solution consiste à accélérer ces électrons dans un schéma multi-étages, qui est composé de trois étages: un injecteur, une ligne de transport et un accélérateur. Ce travail de thèse porte sur la modélisation de l’injecteur avec le code PIC Warp et sur les méthodes numériques telles que la technique de Lorentz-boosted frame pour diminuer le temps de calcul et la couche absorbante parfaite de Bérenger (PML) pour assurer la précision des calculs numériques. Ce travail de thèse a démontré l’efficacité de la PML dans les schémas FDTD à des ordres élevés et pseudo-spectral. Il a aussi démontré la convergence des résultats des simulations réalisées avec la technique de Lorentz-boosted frame dans un régime fortement non-linéaire de l’injecteur, permettant d’accélérer les calculs d’un facteur important (36) tout en assurant leur précision. La modélisation effectuée dans cette thèse a permis d’analyser et de comprendre les résultats expérimentaux, ainsi que de prédire les résultats des futures expériences. Plusieurs méthodes d’optimisation de l’injecteur ont également été proposées pour la génération d’un faisceau d’électrons conforme aux spécifications d’un futur accélérateurLaser Wakefield Acceleration (LWFA) relies on the interaction between an intense laser pulse and an under-dense plasma. This interaction generates a plasma wave with a strong accelerating field, which is three orders of magnitude higher than the one of the conventional accelerator; more compact accelerator is therefore theoretically possible. In the design of a future accelerator, a high quality electron bunch with a high charge, low energy spread and low emittance has to be accelerated to high energies. A solution for this is a multi-stage accelerator, which consists of an injector, a transport line and accelerator stages. This research work focuses on the modelling of the injector using the PIC code Warp and on the numerical methods such as the Lorentz-boosted frameto speedup calculations and the Perfectly Matched Layer (PML) to ensure the precision in numerical calculations. The outcome of this thesis has demonstrated the efficiency of the PML in the high-order FDTD and the pseudo-spectral solvers. Besides, it has also demonstrated the convergence of the results performed in simulations using the Lorentz-boosted frame technique. This technique speeds up simulations by a large factor (36) while preserving their accuracy. The modelling work in this thesis has allowed analysis and understanding of experimental results, as well as prediction of results for future experiments. This thesis has also shown ways to optimize the injector to deliver an electron bunch that conforms with the specifications of future accelerators
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Pelteku, Altin E. "Development of an electromagnetic glottal waveform sensor for applications in high acoustic noise environments". Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0114104-142855/.
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Thesis (M.S.)--Worcester Polytechnic Institute.Keywords: basis functions; perfectly matched layers; PML; neck model; parallel plate resonator; finite element; circulator; glottal waveform; multi-transmission line; dielectric properties of human tissues; radiation currents; weighted residuals; non-acoustic sensor. Includes bibliographical references (p. 104-107).
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Xu, Boqing y 許博卿. "Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/208043.
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A general convolutional version of perfectly matched layer (PML) formulation for second-order wave equations with displacement as the only unknown based on the coordinate stretching is proposed in this study, which overcomes the limitation of classical PML in splitting the displacement field and requires only minor modifications to existing finite element programs.
The first contribution concerns the development of a robust and efficient finite element program QUAD-CPML based on QUAD4M capable of simulating wave propagation in an unbounded domain. The more efficient hybrid-stress finite element was incorporated into the program to reduce the number of iterations for the equivalent linear dynamic analysis and the total time for the direct time integration. The incorporation of new element types was verified with the QUAD4M solutions to problems of dynamic soil response and the efficiency of hybrid-stress finite element was demonstrated compared to the classical finite elements.
The second development involves the implementation of a general convolutional perfectly matched layer (CPML) as an absorbing boundary condition for the modeling of the radiation of wave energy in an unbounded domain. The proposed non-split CPML formulation is displacement-based, which shows great compatibility with the direct time integration. This CPML formulation treats the convolutional terms as external forces and includes an updating scheme to calculate the temporal convolution terms arising from the Fourier transform. In addition, the performance of the CPML has been examined by various problems including a parametric study on a number of key coefficients that control the absorbing ability of the CPML boundary.
The final task of this thesis is to apply the developed CPML models to the dynamic analyses of soil-structure interaction (SSI) problems. Typical loading conditions including external load on the structure and underground wave excitation on the medium has been considered. Practical applications of CPML models include the numerical study on the effectiveness of the rubber-soil mixture (RSM) as an earthquake protection material and the report of vibrations induced by the passage of a high-speed train. The former investigates the effectiveness of the CPML models for the evaluation of the performance of RSM subject to seismic excitation and the latter tests the boundary effects on the accuracy of the results for train induced vibrations. Both studies show that CPML as an absorbing boundary condition is theoretically sound and effective for the analysis of soil-structure dynamic response.published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
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Peynaud, Emilie. "Rayonnement sonore dans un écoulement subsonique complexe en régime harmonique : analyse et simulation numérique du couplage entre les phénomènes acoustiques et hydrodynamiques". Thesis, Toulouse, INSA, 2013. http://www.theses.fr/2013ISAT0019/document.
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La thèse porte sur la simulation, en régime fréquentiel, du rayonnement acoustique en écoulement subsonique quelconque et dans un domaine infini. L'approche choisie s'appuie sur la résolution d'un système équivalent aux équations d'Euler linéarisées : le modèle de Galbrun. Ce modèle repose sur une représentation mixte Lagrange-Euler et aboutit à une équation dont l'unique inconnue est la perturbation du déplacement Lagrangien. Une des difficultés de l'approche de Galbrun est qu'une discrétisation directe de cette équation par une méthode d'éléments finis standard n'est pas stable. Un moyen de contourner cet obstacle est d'écrire une équation augmentée en ajoutant une nouvelle inconnue, le rotationnel du déplacement, appelée par abus vorticité. Cette approche conduit à un système qui couple une équation de type équation des ondes avec une équation de transport en régime fréquentiel. Et elle permet l'utilisation de couches parfaitement adaptées (PML) pour borner le domaine de calcul. La première partie du manuscrit est dédiée à l’étude de l’équation de transport harmonique et de sa résolution numérique, en particulier par un schéma de type Galerkin discontinu. Un des points délicats est lié au caractère oscillant des solutions de l'équation. Une fois cette étape franchie, la résolution du problème de propagation acoustique a été abordée. Une approximation basée sur l'utilisation d'éléments finis mixtes continus-discontinus avec couches parfaitement adaptées (PML) a été étudiée. En particulier, les caractères bien posés des problèmes continu et discret ainsi que la convergence du schéma numérique ont été démontrés sous certaines conditions sur l'écoulement porteur. Enfin, une mise en œuvre a été effectuée. Les résultats montrent la validité de cette approche mais aussi sa pertinence dans le cas d'écoulements complexes, voire d'écoulements dits instablesThis thesis deals with the numerical simulation of time harmonic acoustic propagation in an arbitrary mean flow in an unbounded domain. Our approach is based on an equation equivalent to the linearized Euler equations called the Galbrun equation. It is derived from a mixed Eulerian-Lagrangian formulation and results in a single equation whose only unknown is the perturbation of the Lagrangian displacement. A direct solution using finite elements is unstable but this difficulty can be overcome by using an augmented equation which is constructed by adding a new unknown, the vorticity, defined as the curl of the displacement. This leads to a set of equations coupling a wave like equation with a time harmonic transport equation which allows the use of perfectly matched layers (PML) at artificial boundaries to bound the computational domain. The first part of the thesis is a study of the time harmonic transport equation and its approximation by means of a discontinuous Galerkin scheme, the difficulties coming from the oscillating behaviour of its solutions. Once these difficulties have been overcome, it is possible to deal with the resolution of the acoustic propagation problem. The approximation method is based on a mixed continuous-Galerkin and discontinuous-Galerkin finite element scheme. The well-posedness of both the continuous and discrete problems is established and the convergence of the approximation under some mean flow conditions is proved. Finally a numerical implementation is achieved and numerical results are given which confirm the validity of the method and also show that it is relevant in complex cases, even for unstable flows
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Vinoles, Valentin. "Problèmes d'interface en présence de métamatériaux : modélisation, analyse et simulations". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY009/document.
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Nous nous intéressons à des problèmes de transmission entre diélectriques et métamatériaux, milieux présentant des propriétés électromagnétiques inhabituelles comme des caractéristiques effectives négatives à certaines fréquences. Par exemple, ces milieux peuvent être construits comme des assemblages périodiques de microstructures résonantes et dans ce cas la théorie de l'homogénéisation permet de justifier mathématiquement ces propriétés effectives. En régime harmonique et dans des géométries à variables séparables, des calculs analytiques peuvent être menés. Ils révèlent dans des cas dits critiques des difficultés mathématiques: les solutions n'ont pas la régularité standard, voire le problème peut être mal posé.La première partie étudie ces problèmes de transmission en régime temporel pour lequel les métamatériaux sont modélisés par des modèles dispersifs (modèle de Drude ou de Lorentz). Les difficultés résident dans le choix d'un schéma de discrétisation mais surtout dans la construction de conditions absorbantes. La méthode retenue ici est celle des Perfectly Matched Layers (PMLs). Comme les PMLs classiques sont instables pour ces modèles du fait de la présence d'ondes inverses, nous proposons une nouvelle classe de PMLs pour lesquelles nous menons une analyse de stabilité. Cette dernière permet de construire des PMLs stables. Elles sont ensuite utilisées pour simuler le comportement en temps long d'un problème de transmission; nous illustrons alors le fait que le principe d'amplitude limite peut être mis en défaut en raison de résonances d'interface.La deuxième partie vise à pallier ces phénomènes d'interface en régime harmonique en revenant sur le processus d'homogénéisation classique, pour un milieu dissipatif. Pour des problèmes de transmission, il est connu que les modèles issus de cette méthode perdent en précision du fait de la présence de couches limites à l'interface. Nous proposons un modèle enrichi au niveau de l'interface. En combinant la méthode d'homogénéisation double-échelle et celle des développements asymptotiques raccordés, nous construisons des conditions de transmission non standards faisant intervenir des opérateurs différentiels le long de l'interface. Le calcul de ces conditions nécessite la résolution de problèmes de cellule et de problèmes non standards posés dans des bandes périodiques infinies. Une analyse d'erreur confirme l'amélioration de la précision du modèle. Des simulations numériques illustrent l'efficacité de ces nouvelles conditions. Enfin, cette démarche est reproduite formellement dans le cas des matériaux à fort contraste se comportant comme des métamatériaux. Nous montrons alors que ces nouvelles conditions permettent de régulariser le problème de transmission dans les cas critiquesWe are interested in transmission problems between dielectrics and metamaterials, that is to say media with unusual electromagnetic properties such as negative constants at some frequencies. These media are often made of periodic assemblies of resonant micro-structures and in this case the homogenization theory can justify mathematically these effective properties. A preliminary part deals with these problems in the harmonic domain and in geometry with separation of variables.Analytical computations are done and reveal in the so-called critical cases some mathematical diffculties: the solutions do not have the standard regularity and the problem can even be ill-posed.The first part examines these transmission problems in the time domain for which metamaterials are modelled by dispersive models (Drude model or Lorentz model for instance). The diffculties reside in the choice of a discretization scheme but especially in the construction of absorbing conditions. The method used here is the use of Perfectly Matched Layers (PMLs). Since classical PMLs are unstable for these models due to the presence of backward waves, we propose a new class of PMLs for which we conduct a stability analysis. The latter allows us to build stable PMLs. They are then used to simulate the long-time behaviour of a transmission problem; we illustrate the fact that the limit amplitude principle can be faulted because of interface resonances.The second part aims to overcome these phenomena by coming back to the classical homogenization in the harmonic domain, for dissipative media. For transmission problems, it is known that models resulting from this method lose accuracy due to the presence of boundary layers at the interface. We propose an enriched model at the interface: by combining the method of two-scale homogenization and that of matched asymptotic expansions, we build non-standard transmission conditions involving tangential derivatives along the interface (Laplace-Beltrami operators). This requires to solve cell problems and non-standardproblems in infinite periodic bands. An error analysis confirms the improvement of the accuracy of the model and numerical simulations show the effectiveness of these new conditions. Finally, this approach is formally reproduced in the case of high contrast materials which behave like metamaterials. We show that these new conditions regularise the transmission problem in the critical cases
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Rejiba, Fayçal. "Modélisation de la propagation des ondes électromagnétiques en milieux hétérogènes : application au radar sol". Paris 6, 2002. http://www.theses.fr/2002PA066313.
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Laurens, Sophie. "Approximation de haute précision des problèmes de diffraction". Phd thesis, Université Paul Sabatier - Toulouse III, 2010. http://tel.archives-ouvertes.fr/tel-00475286.
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Cette thèse examine deux façons de diminuer la complexité des problèmes de propagation d'ondes diffractées par un obstacle borné : la diminution des domaines de calcul à l'aide de milieux fictifs absorbants permettant l'adjonction de conditions aux limites exactes et la recherche d'une nouvelle approximation spatiale sous forme polynomiale donnant lieu à des schémas explicites où la stabilité est indépendante de l'ordre choisi. Dans un premier temps, on réduit le domaine de calcul autour de domaines non nécessairement convexes, mais propres aux problèmes de scattering (non trapping), à l'aide de la méthode des Perfectly Matched Layers (PML). Il faut alors considérer des domaines d'exhaustion difféomorphes à des convexes avec des hypothèses "presque" nécessaires. Pour les Equations de type Maxwell et Ondes, l'existence et l'unicité sont montrées dans tout l'espace et en domaine artificiellement borné, tant en fréquentiel qu'en temporel. La décroissance est analysée localement et asymptotiquement et des simulations numériques sont proposées. La deuxième partie de ce travail est une alternative à l'approximation de type Galerkin Discontinu, inspirée des résultats de régularité de J. Rauch, présentant l'avantage de conserver une condition CFL de type Volumes Finis indépendante de l'ordre d'approximation, aussi bien pour des maillages structurés que déstructurés. La convergence de cette méthode est démontrée via la consistance et la stabilité, grâce au théorème d'équivalence de Lax-Richtmyer pour des domaines structurés. En déstructuré, la consistance ne pouvant plus s'établir au moyen de la formulation de Taylor, la convergence n'est plus assurée, mais les premiers tests numériques bidimensionnels donnent d'excellents résultats.
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Ljung, Jonathan. "Parametric Studies of Soil-Steel Composite Bridges for Dynamic Loads, a Frequency Domain Approach using 3D Finite Element Modelling". Thesis, KTH, Bro- och stålbyggnad, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-254343.
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In this thesis, parametric studies have been performed for a soil-steel compositebridge to determine and investigate the most influential parameters on the dynamicresponse.High-speed railways are currently being planned in Sweden by the Swedish TransportAdministration with train speeds up to 320 km/h. According to the European designcodes, bridges must be verified with respect to dynamic resonance behaviour for trainspeeds exceeding 200 km/h. However, there are no guidelines or design criterion forperforming dynamic verifications of soil-steel composite bridges. The aim of thisthesis has therefore been to investigate the influence of the geometry and materialproperties of soil-steel composite bridges on their dynamic response.This thesis is based upon the frequency domain approach for dynamic analysis ofa soil-steel composite bridge using finite element software. In 2018, field measurementswere performed on a soil-steel composite bridge in Hårestorp, Sweden. Areference finite element model was developed based on previous research and wasverified against these field measurements. Parametric studies where performed byextrapolating the geometry of the reference model, focusing primarily on the crownheight, culvert span width and the location of the bedrock. Sensitivity analyses ofthe density- and stiffness of the soil was also performed.The parametric studies showed that the crown height was the most influential parameterwith respect to the amplitude of the resonance peak. Increasing it from 1 mto 3 m reduced the amplitude by approximately 70 %. An increased span width ofthe culvert was found to reduce the frequency and amplitude of the resonance peak,however increasing the stiffness of the culvert increased the resonance frequency.The position of the rock layer also reduced the amplitude of the resonance peak iflowered, likely because of lessened wave reflection. The lowest rock level investigatedshowed a significant decrease of more than 70 % in amplitude. However, the modelused to calculate this response was heavily extrapolated and thus difficult to verify.The sensitivity analyses showed that the soil density- and stiffness was negativelyand positively correlated with the resonance frequency, respectively. Additionally,the soil density lowered the amplitude of the resonance peak if increased.
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Ma, Congcong. "The research of acoustic resonance in the waveguide associated with Galbrun equation". Electronic Thesis or Diss., Compiègne, 2020. http://www.theses.fr/2020COMP2560.
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Dans un système ouvert bidimensionnel, lorsque l’onde acoustique se propage dans un conduit avec la présence d’un obstacle, il y aura amplification de la pression acoustique autour de l’obstacle. Les modes piégés existent autour de l’obstacle au-dessous et au-dessus de la fréquence de coupure, et ils causent des dommages considérables au système. Dans les recherches précédentes, ils se sont principalement concentrés sur la résolution de l’équation de Helmholtz, ce qui signifie que l’écoulement non-potentiel n’était pas prise en compte. L’objectif de la thèse portent sur le développement de méthodes numériques pour le calcul des modes piégés (Trapped modes en anglais) dans un guide d’onde associé à l’équation de Galbrun. Dans la plupart des études, des conditions aux limites avec des bords artificiels sont introduites pour d’une part rendre le problème borné en vue d’une discrétisation par éléments finis et d’autre part limiter l’apparition des réflexions non physiques en ces bords. Pour réduire ces réflexions, les couches parfaitement adaptés « Perfect Matched Layers » ou PML en anglais a été utilisé. L’efficacité de cette méthode pour calculer et visualiser les modes piégés dans un conduit rectangulaire avec et sans écoulement uniforme en présence d’obstacles de formes rectangulaires et elliptiques a été montré. Les résultats sont comparés avec ceux de la littérature et semblent en bon accord avec ces derniers. Différentes études ont été menées pour mesurer l’influence des positions, des dimensions et des orientations de l’obstacle sur les modes piégés. Enfin, un modèle simplifié excité par une source acoustique a été mise en œuvre pour confirmer que le mode piégé n’est pas affecté par le type de source d’excitation. Enfin, afin de considérer les effets des écoulements non-potentiels. Les modes piégés sont capturés en balayant la fréquence. Dans le même temps, les effets des paramètres d’obstacles sur le mode piégé sont également étudiésIn a two-dimensional open system, when the acoustic wave spreads in the tube with the presence of an obstacle, there will be the amplification of sound pressure around the obstacle. Trapped mode exists surrounding the obstacle below and above the cut-off frequency, and they bring considerable damage to the system in the form of such as noise, stability and security issues. In the previous research, they mainly concentrated on the solving of Helmholtz equation, which means that the variation of non-potential flow was not taken into consideration. The objective of this paper is to numerically compute the trapped mode with the presence of non-potential flow. Firstly, the theoretical framework of this thesis is stated. The mixed Galbrun equation, as well as boundary conditions and the associated energy properties, is represented. And then the perfectly matched layer associated with Galbrun equation is introduced. Secondly, for the analysis of trapped mode, there are already a lot of literature on numerical and physical aspects, but they have studied the trapped mode all associated with Helmholtz equation, which is primarily suitable for the case of without flow or uniform mean flow. Hence, a numerical calculation model involved with Galbrun equationwith the uniform mean flow is proposed and the obtained results are compared with those given in references. Finally, in order to consider the effects of non-potential flow. A coupling method of sound field and flow field associated with Galbrun equation is developed, and the trapped mode is captured through scanning the frequency. At the same time, the effects of various parameters of obstacles on the trapped mode are also studied
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Spa, Carvajal Carlos. "Time-domain numerical methods in room acoustics simulations". Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7565.
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L'acústica de sales s'encarrega de l'estudi del comportament de les ones sonores en espais tancats.La informació acústica de qualsevol entorn, coneguda com la resposta impulsional, pot ser expressada en termes del camp acústic com una funció de l'espai i el temps. En general, és impossible obtenir solucions analítiques de funcions resposta en habitacions reals. Per tant, en aquests últims anys, l'ús d'ordinadors per resoldre aquest tipus de problemes ha emergit com una solució adecuada per calcular respostes impulsionals.En aquesta Tesi hem centrat el nostre anàlisis en els mètodes basats en el comportament ondulatori dins del domini temporal. Més concretament, estudiem en detall les formulacions més importants del mètode de Diferències Finites, el qual s'utilitza en moltes aplicacions d'acústica de sales, i el recentment proposat mètode PseudoEspectral de Fourier. Ambdós mètodes es basen en la formulació discreta de les equacions analítiques que descriuen els fenòmens acústics en espais tancats.
Aquesta obra contribueix en els aspectes més importants en el càlcul numèric de respostes impulsionals: la propagació del so, la generació de fonts i les condicions de contorn de reactància local.
Room acoustics is the science concerned to study the behavior of sound waves in enclosed rooms. The acoustic information of any room, the so called impulse response, is expressed in terms of the acoustic field as a function of space and time. In general terms, it is nearly impossible to find analytical impulse responses of real rooms. Therefore, in the recent years, the use of computers for solving this type of problems has emerged as a proper alternative to calculate the impulse responses.
In this Thesis we focus on the analysis of the wavebased methods in the timedomain. More concretely, we study in detail the main formulations of FiniteDifference methods, which have been used in many room acoustics applications, and the recently proposed Fourier PseudoSpectral methods. Both methods are based on the discrete formulations of the analytical equations that describe the sound phenomena in enclosed rooms.
This work contributes to the main aspects in the computation of impulse responses: the wave propagation, the source generation and the locallyreacting boundary conditions.
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Kucukcoban, Sezgin. "The inverse medium problem in PML-truncated elastic media". Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2183.
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We introduce a mathematical framework for the inverse medium problem arising commonly in geotechnical site characterization and geophysical probing applications, when stress waves are used to probe the material composition of the interrogated medium. Specifically, we attempt to recover the spatial distribution of Lame's parameters ( and μ) of an elastic semi-infinite arbitrarily heterogeneous medium, using surface measurements of the medium's response to prescribed dynamic excitations. The focus is on characterizing near-surface deposits, and to this end, we develop a method that is implemented directly in the time-domain, is driven by the full waveform response collected at receivers on the surface, while the domain of interest is truncated using Perfectly-Matched-Layers (PMLs) to limit the originally semi-infinite extent of the physical domain.
There are two key issues associated with the problem at hand: (a) the forward problem, namely the numerical simulation of the wave motion in the domain of interest; and (b) the framework and strategies for tackling the
inverse problem.
To address the forward problem, it is necessary that the domain of interest be truncated, and the resulting finite domain be forced to mimic the physics of the original problem: to this end, we introduce unsplit-field PMLs, and develop and implement two new formulations, one fully-mixed and one hybrid (mixed coupled with a non-mixed approach) that model wave motion within the, now PML-truncated, domain. To address the inverse problem, we adopt a partial-differential-equation-constrained optimization framework that results in the usual triplet of an initial-and-boundary-value forward problem, a final-and-boundary-value adjoint problem, and a time-independent boundary-value control problem. This triplet of boundary-value-problems is used to guide the optimizer to the target profile of the spatially distributed Lame parameters. Given the multiplicity of solutions, we assist the optimizer, by deploying regularization schemes, continuation schemes (regularization factor and source-frequency content), as well as a physics-driven simple procedure to bias the search directions.
We report numerical examples attesting to the quality, stability, and efficiency of the forward wave modeling. We also report moderate success with numerical experiments targeting inversion of both smooth and sharp profiles in two dimensions.text
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Thakur, Tapan. "Wave motion simulation using spectral elements and a hybrid PML formulation". Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-3547.
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We are concerned with forward wave motion simulations in two-dimensional elastic, heterogeneous, semi-infinite media. We use Perfectly Matched Layers (PMLs) to truncate the semi-infinite extent of the physical domain to arrive at a finite computational domain. We use a recently developed hybrid formulation, where the Navier equations for the interior domain are coupled with a mixed formulation for an unsplit-field PML. Here, we implement the hybrid formulation using spectral elements, and report on its performance. The motivation stems from the following considerations: Of concern is the long-time instability that has been reported even in homogeneous and isotropic cases, when the standard complex-stretching function is used in the PML. The onset of the instability is always within the PML zone, and it manifests as error growth in time. It has been suggested that the instability arises when waves impinge at grazing angle on the PML-interior domain interface. Yet, the instability does not always appear. Furthermore, different values of the various PML parameters (mesh density, attenuation strength, order of attenuation function, etc) can either hinder or delay the onset of the instability. It is thus conjectured that the instability is associated with the spectral properties of the discrete operators.
In this thesis, we report numerical results based on both Lagrange interpolants, and results based on spectral elements. Spectral elements are explored since they lead to diagonal mass matrices, have improved dispersion error, and, more importantly, have different spectral properties than Lagrangian-based finite elements. Spectral elements are thus used in an attempt to explore whether the reported instability issues could be alleviated. We design numerical experiments involving explosive sources situated at varying depths from the surface, capable of inducing grazing-angle waves. We use the energy decay as the primary metric for reporting the results of comparisons between various spectral element orders and classical Lagrange interpolants. We also report the results of parametric studies. Overall, it is shown that the spectral elements alone are not capable of removing the instability, though, on occasion, they can. Careful parameterization of the PML could also either remove it or alleviate it. The issue remains open.text
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Fathi, Arash. "Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments". Thesis, 2015. http://hdl.handle.net/2152/30515.
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We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.
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Kang, Jun Won 1975. "A mixed unsplit-field PML-based scheme for full waveform inversion in the time-domain using scalar waves". Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-1263.
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We discuss a full-waveform based material profile reconstruction in two-dimensional heterogeneous semi-infinite domains. In particular, we try to image the spatial variation of shear moduli/wave velocities, directly in the time-domain, from scant surficial measurements of the domain's response to prescribed dynamic excitation. In addition, in one-dimensional media, we try to image the spatial variability of elastic and attenuation properties simultaneously.
To deal with the semi-infinite extent of the physical domains, we introduce truncation boundaries, and adopt perfectly-matched-layers (PMLs) as the boundary wave absorbers. Within this framework we develop a new mixed displacement-stress (or stress memory) finite element formulation based on unsplit-field PMLs for transient scalar wave simulations in heterogeneous semi-infinite domains. We use, as is typically done, complex-coordinate stretching transformations in the frequency-domain, and recover the governing PDEs in the time-domain through the inverse Fourier transform. Upon spatial discretization, the resulting equations lead to a mixed semi-discrete form, where both displacements and stresses (or stress histories/memories) are treated as independent unknowns. We propose approximant pairs, which numerically, are shown to be stable.
The resulting mixed finite element scheme is relatively simple and straightforward to implement, when compared against split-field PML techniques. It also bypasses the need for complicated time integration schemes that arise when recent displacement-based formulations are used. We report numerical results for 1D and 2D scalar wave propagation in semi-infinite domains truncated by PMLs. We also conduct parametric studies and report on the effect the various PML parameter choices have on the simulation error.
To tackle the inversion, we adopt a PDE-constrained optimization approach, that formally leads to a classic KKT (Karush-Kuhn-Tucker) system comprising an initial-value state, a final-value adjoint, and a time-invariant control problem. We iteratively update the velocity profile by solving the KKT system via a reduced space approach. To narrow the feasibility space and alleviate the inherent solution multiplicity of the inverse problem, Tikhonov and Total Variation (TV) regularization schemes are used, endowed with a regularization factor continuation algorithm. We use a source frequency continuation scheme to make successive iterates remain within the basin of attraction of the global minimum. We also limit the total observation time to optimally account for the domain's heterogeneity during inversion iterations.
We report on both one- and two-dimensional examples, including the Marmousi benchmark problem, that lead efficiently to the reconstruction of heterogeneous profiles involving both horizontal and inclined layers, as well as of inclusions within layered systems.text
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Lee, Seung Ha. "Application of the perfectly matched layers for seismic soil-structure interaction analysis in the time domain". Thesis, 2006. http://hdl.handle.net/10125/20488.
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楊崇文. "P-adaptive Hierarchal Finite Element Analysis of Unbounded Electromagnetic Wave Problems Terminated with Perfectly Matched Layers". Thesis, 2004. http://ndltd.ncl.edu.tw/handle/86298526022545601807.
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碩士義守大學
電機工程學系
92
There are many numerical methods for solving electromagnetic wave problems, such as finite element method, finite difference time domain method, and method of moment. For solving unbounded electromagnetic wave problems with finite element method, the computational domain must be truncated by an absorbing boundary. Typically, the error of these problems involves boundary and discretization error. The boundary error is a function of the efficiency of the absorbing boundary condition. Perfectly matched layers were found to provide better accuracy than traditional absorbing boundary condition. The discretization error can be reduced by using h-adaptive finite element method or p-adaptive finite element method. Generally, the p-adaptive finite element method is more efficient than the h-adaptive finite element method, because it does not require a re-meshing at each iteration. Unfortunately, the conventional p-adaptive finite element method requires that the polynomial order of elements in the whole domain must be identical. This makes inefficiency usage of degrees of freedom in the model. Hierarchal finite element method allows that the order of elements in the domain be different so that the degrees of freedom can be efficiently re-distributed. The discretization error and the boundary error can be reduced efficiently by using p-adaptive hierarchal finite element analysis both in the finite element and the perfectly matched layers regions. Up until now, there is no research in combining p-adaptive finite element method with the perfectly matched layers. This thesis proposes an efficient approach to reduce both boundary and discertization error by combining the p-adaptive hierarchal finite element method with the perfectly matched layers.
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Tsuji, Paul Hikaru. "Fast algorithms for frequency domain wave propagation". 2012. http://hdl.handle.net/2152/19533.
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High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of
metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime.
The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.text