Relevant bibliographies by topics / Perfectly Matched Layers (PML)

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Academic literature on the topic 'Perfectly Matched Layers (PML)'

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Published: 26 January 2024

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Journal articles on the topic "Perfectly Matched Layers (PML)"

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Zhang, Jianfeng, and Hongwei Gao. "Irregular perfectly matched layers for 3D elastic wave modeling." GEOPHYSICS 76, no. 2 (March 2011): T27—T36. http://dx.doi.org/10.1190/1.3533999.

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We have developed a perfectly matched layer (PML) absorbing boundary condition that can be imposed along an arbitrary geometric boundary in 3D elastic wave modeling. The scheme is developed by using the local coordinate system-based PML splitting equations and integral approach of the PML equations under a discretization of tetrahedral grids. However, no explicit coordinate transformations arise. The local coordinate system-based PML splitting equations make it possible to decay incident waves around the direction normal to the irregular geometric boundaries, instead of a coordinate axis direction. Based on the resulting 3D irregular PML model, we can flexibly construct the computational domain with smaller nodes by cutting uninterested zones. This results in significant reductions in computational cost and memory requirements for 3D simulations. By building a smooth artificial boundary, the irregular PML model can avoid the respective treatments to the edges and corners of the artificial boundaries. Also, the irregular PML model may reduce the grazing incidence that makes the PML model less efficient by changing the shapes of the artificial boundaries. Numerical testing was used to demonstrate the performance of the irregular PML model.
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Ge, Ju, Liping Gao, and Rengang Shi. "Well-Designed Termination Wall of Perfectly Matched Layers for ATS-FDTD Method." International Journal of Antennas and Propagation 2019 (June 2, 2019): 1–6. http://dx.doi.org/10.1155/2019/6343641.

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This paper presents a well-designed termination wall for the perfectly matched layers (PML). This termination wall is derived from Mur’s absorbing boundary condition (ABC) with special difference schemes. Numerical experiments illustrate that PML and the termination wall works well with ATS-FDTD(Shi et al. 2015). With the help of termination wall, perfectly matched layers can be decreased to two layers only; meanwhile, the reflection error still reaches -60[dB] when complex waveguide is simulated by ATS-FDTD.
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Bunting, Gregory, Arun Prakash, Timothy Walsh, and Clark Dohrmann. "Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains." Journal of Theoretical and Computational Acoustics 26, no. 02 (June 2018): 1850015. http://dx.doi.org/10.1142/s2591728518500159.

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Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this paper, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. This provides an additional advantage of PML over the infinite element approach.
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Chen, Yong H., Weng Cho Chew, and Michael L. Oristaglio. "Application of perfectly matched layers to the transient modeling of subsurface EM problems." GEOPHYSICS 62, no. 6 (November 1997): 1730–36. http://dx.doi.org/10.1190/1.1444273.

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Berenger's perfectly matched layers (PML) have been found to be very efficient as a material absorbing boundary condition (ABC) for finite‐difference time‐domain (FDTD) modeling of lossless media. In this paper, we apply the PML technique to truncate the simulation region of conductive media. Examples are given to show some possible applications of the PML technique to subsurface problems with lossy media. To apply the PML ABC for lossy media, we first modify the original 3-D Maxwell's equations to achieve PML at the boundaries of the simulation region. The modified equations are then solved by using a staggered grid with a central‐differencing scheme. A 3-D FDTD code has been written on the basis of our PML formulation to simulate the electromagnetic field responses of a dipole source in both lossless and lossy media. The code is first tested against analytical solutions for homogeneous media of different losses and then applied to some subsurface problems, such as a geological fault and a buried gas tank. Very interesting propagation and scattering phenomena are observed from the simulation results. Some analyses are also given to explain the physical phenomena of the calculated waveforms.
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He, Yanbin, Tianning Chen, Jinghuai Gao, and Zhaoqi Gao. "Superior performance of optimal perfectly matched layers for modeling wave propagation in elastic and poroelastic media." Journal of Geophysics and Engineering 19, no. 1 (February 2022): 106–19. http://dx.doi.org/10.1093/jge/gxac002.

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Abstract The perfectly matched layer (PML) technique is a popular truncation method to model wave propagation in unbounded elastic media. Both numerical efficiency and high stability are important improvement areas in the field. In this study, we extend the optimal PML, previously proposed for acoustic media, to elastic and poroelastic media, which turns out to be more efficient and flexible than the classical PML. We investigate the accuracy and stability of the optimal PML by comparing it with the classical PML in several scenarios. First, the effectiveness of the optimal PML is studied using frequency-domain and time-domain simulations for isotropic and homogeneous elastic solids. The efficiency and accuracy of the optimal PML and classical PML are then compared across a wide range of Poisson's ratios of elastic media. The stability of the optimal PML and the classical PML is also compared taking into account the effect of the outer boundary conditions of the PML as well as the heterogeneity of the geological model. Moreover, the optimal PML is applied to poroelastic media to address the instability problem of the classical PML. Comprehensive analyses of numerical results show that the optimal PML can absorb the outgoing waves. This can be done using thinner layers and with higher accuracy than for classical PMLs. In addition, the long-time stability of optimal PML increases.
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Lei, Da, Liangyong Yang, Changmin Fu, Ruo Wang, and Zhongxing Wang. "The application of a novel perfectly matched layer in magnetotelluric simulations." GEOPHYSICS 87, no. 3 (March 29, 2022): E163—E175. http://dx.doi.org/10.1190/geo2020-0393.1.

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Truncation boundaries are needed when simulating a region in magnetotelluric (MT) modeling. As an efficient alternative truncation boundary, perfectly matched layers (PMLs) have been widely applied in many high-frequency wavefield simulations. However, the governing equation of most electromagnetic exploration methods is for the diffusion field, in which the conduction current is significantly greater than the displacement current. Because the wave and diffusion fields have completely different relations for the frequency and constitutive parameters, conventional PMLs, which are mainly designed for the wavefield, are not a good choice for the diffusion field. For this reason, we propose a formula for a PML that covers the entire frequency band, including the wave and the diffusion fields. It is based on a uniaxial PML. Moreover, we derive a simplified form for the diffusion field. To check the feasibility and application potential of the proposed formula for a PML in MT simulations, we have implemented PMLs using a finite-element method and compared our results with those for a conventional long-distance extended grid. The results of the 1D simulation demonstrate that PMLs can achieve high accuracy and stable performance and have a broad application range. In 2D and 3D models, the air layer is an obstacle in the application of a PML. By selecting appropriate parameters for the PML, 2D and 3D models can achieve satisfactory performance. Therefore, the proposed PML is useful for MT simulations and can achieve satisfactory truncation performance.
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CHEW, W. C., and Q. H. LIU. "PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION." Journal of Computational Acoustics 04, no. 04 (December 1996): 341–59. http://dx.doi.org/10.1142/s0218396x96000118.

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The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two- and three-dimensional computer simulations of the PML for the linearized equations of elastodynamics. Comparison with Liao’s ABC will be given.
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Bérenger, Jean-Pierre. "Perfectly Matched Layer (PML) for Computational Electromagnetics." Synthesis Lectures on Computational Electromagnetics 2, no. 1 (January 2007): 1–117. http://dx.doi.org/10.2200/s00030ed1v01y200605cem008.

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Hervella-Nieto, Luis M., Andrés Prieto, and Sara Recondo. "Computation of Resonance Modes in Open Cavities with Perfectly Matched Layers." Proceedings 54, no. 1 (August 18, 2020): 2. http://dx.doi.org/10.3390/proceedings2020054002.

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During the last decade, several authors have addressed that the Perfectly Matched Layers (PML) technique can be used not only for the computation of the near-field in time-dependent and time-harmonic scattering problems, but also to compute numerically the resonances in open cavities. Despite such complex resonances are not natural eigen-frequencies of the physical system, the numerical determination of this kind of eigenvalues provides information about the model, what can be used in further applications. The present work will be focused on two main specific goals—firstly, the mathematical analysis of the frequency-dependent highly non-linear eigenvalue problem associated to the computation of resonances with the standard PML technique. Second, the implementation of a robust numerical method to approximate resonances in open cavities.
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Cao, Da, Naohisa Inoue, and Tetsuya Sakuma. "Finite element analysis of bending waves in Mindlin plates with Perfectly Matched Layers." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2527–34. http://dx.doi.org/10.3397/in_2022_0355.

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It is important to determine the boundary conditions of walls and floors precisely when simulating the building acoustics. For a certain room, the extension of the spans can be considered as infinite edges. The Perfect Matched Layer(PML) is an artificial absorbing domain for the wave propagations and is widely used in finite element analysis to simulate the acoustical free field conditions right now. In this paper, an effective PML technique for the plate structure will be presented. The PML formulation will be derived based on the Mindlin plate theory and the implementation method will be introduced. This technique will be validated through the numerical experiments. The accuracy and limits of the presented technique will be discussed based on the numerical results compared with the analytical results. The results show that the presented PML technique is effective and accurate to simulate the plate as an infinite large plate. It is expected to implement the technique in the further research of the structure borne sound, such as floor impact sounds.
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Dissertations / Theses on the topic "Perfectly Matched Layers (PML)"

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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 théoriques
In 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 posés
A 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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Books on the topic "Perfectly Matched Layers (PML)"

1

Bérenger, Jean-Pierre. Perfectly Matched Layer (PML) for Computational Electromagnetics. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7.

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Bérenger, Jean-Pierre. Perfectly matched layer (PML) for computational electromagnetics. [San Rafael, Calif.]: Morgan & Claypool Publishers, 2007.

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Center, Langley Research, ed. The analysis and construction of perfectly matched layers for linearized Euler equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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L, Auriault, Cambuli F, and United States. National Aeronautics and Space Administration., eds. Perfectly matched layer for linearized Euler equations in open and ducted domains. Reston, Va: American Institute of Aeronautics and Astronautics, 1998.

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Bérenger, Jean-Pierre. Perfectly Matched Layer (PML) for Computational Electromagnetics. Springer International Publishing AG, 2007.

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Bérenger, Jean-Pierre. Perfectly Matched Layer (PML) for Computational Electromagnetics. Morgan & Claypool Publishers, 2007.

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Berenger, Jean-Pierre. Perfect Matched Layer (PML) for Computational Electromagnetics (Synthesis Lectures on Computational Electromagnetics). Morgan and Claypool Publishers, 2007.

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Book chapters on the topic "Perfectly Matched Layers (PML)"

1

Bérenger, Jean-Pierre. "The Two-Dimensional Perfectly Matched Layer." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 13–27. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_3.

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Bérenger, Jean-Pierre. "Some Extensions of the PML ABC." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 107–9. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_8.

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Gedney, Stephen D. "The Perfectly Matched Layer (PML) Absorbing Medium." In Introduction to the Finite-DifferenceTime-Domain (FDTD) Method for Electromagnetics, 113–35. Cham: Springer International Publishing, 2011. http://dx.doi.org/10.1007/978-3-031-01712-4_6.

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Bérenger, Jean-Pierre. "The PML ABC for the FDTD Method." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 63–88. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_6.

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Bérenger, Jean-Pierre. "Time Domain Equations for the PML Medium." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 49–61. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_5.

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Bérenger, Jean-Pierre. "Generalizations and Interpretations of the Perfectly Matched Layer." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 29–47. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_4.

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Bérenger, Jean-Pierre. "Optmization of the PML ABC in Wave-Structure Interaction and Waveguide Problems." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 89–106. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_7.

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Bérenger, Jean-Pierre. "The Requirements for the Simulation of Free Space and a Review of Existing Absorbing Boundary Conditions." In Perfectly Matched Layer (PML) for Computational Electromagnetics, 5–12. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01696-7_2.

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Li, Jichun, and Yunqing Huang. "Perfectly Matched Layers." In Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials, 215–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33789-5_8.

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Hebermehl, G., F. K. Hübner, R. Schlundt, T. Tischler, H. Zscheile, and B. Heinrich. "Perfectly matched layers in transmission lines." In Numerical Mathematics and Advanced Applications, 281–90. Milano: Springer Milan, 2003. http://dx.doi.org/10.1007/978-88-470-2089-4_26.

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Conference papers on the topic "Perfectly Matched Layers (PML)"

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Jones, Simon. "Harmonic Response of a Layered Halfspace Using Reduced Finite Element Model With Perfectly-Matched Layer Boundaries." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65438.

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The current paper investigates the use of perfectly-matched layers (PML) as absorbing elements for a finite element (FE) model simulating a semi-infinite medium. This formulation is convenient for application of Craig-Bampton reduction (CBR), which significantly reduce the number active degrees-of-freedom in the model in an attempt to improve the computational efficiency. The results from this investigation suggest the PML elements worked seamlessly with the FE elements to approximate the elastodynamic response of a 2D layered halfspace subjected to a surface load; the wave energy appears to be fully absorbed by the PMLs regardless of incident angle or wavelength. The size of the model is reduced by approximately 77% using the CBR, which transforms the system into a mixed set of coordinates, including both modal and spatial coordinates. The model reduction is accomplished by neglecting modal frequencies for the system above one and a half times the maximum forcing frequency of interest. By only transforming the frequency-independent FE section into modal coordinates, and leaving the frequency-dependent PML elements as spatial degrees-of-freedom, the mode-shapes must only be solved once and can then be reused for different forcing frequencies. The results from this investigation suggest this could provide computational benefits if a number of cases are being computed for different frequencies.
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Smithe, David, and Lars Ludeking. "PML (Perfectly Matched Layer) Implementation in the Magic Software." In IEEE Conference Record - Abstracts. 2005 IEEE International Conference on Plasma Science. IEEE, 2005. http://dx.doi.org/10.1109/plasma.2005.359396.

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Rao Changwei, Tian Yu, Gao Bo, Chen Yan, and Tong Ling. "A new modified perfectly matched layer( PML) without split-field." In 2008 International Conference on Microwave and Millimeter Wave Technology (ICMMT). IEEE, 2008. http://dx.doi.org/10.1109/icmmt.2008.4540507.

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Ji, Jinzu, Peilin Huang, and Yunpeng Ma. "Auxiliary differential equation (ADE) implementation of complex-frequency shifted perfectly matched layer (CFS-PML)." In First International Conference on Information Sciences, Machinery, Materials and Energy. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/icismme-15.2015.42.

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Madsen, S., S. Krenk, and O. Hededal. "PERFECTLY MATCHED LAYER (PML) FOR TRANSIENT WAVE PROPAGATION IN A MOVING FRAME OF REFERENCE." In 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2014. http://dx.doi.org/10.7712/120113.4819.c1228.

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Huang, W. P., C. L. Xu, W. W. Lui, and K. Yokoyama. "The Perfectly Matched Layer (PML) Boundary Condition for the Simulation of Guided-Wave Optical Devices." In Integrated Photonics Research. Washington, D.C.: OSA, 1996. http://dx.doi.org/10.1364/ipr.1996.imb5.

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Li, YiFeng, Olivier Bou Matar, Vladimir Preobrazhensky, and Philippe Pernod. "Convolution-Perfectly Matched Layer (C-PML) absorbing boundary condition for wave propagation in piezoelectric solid." In 2008 IEEE Ultrasonics Symposium (IUS). IEEE, 2008. http://dx.doi.org/10.1109/ultsym.2008.0382.

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Cipolla, Jeffrey L. "Design for a Hybrid Absorbing Element in the Time Domain Using PML and Infinite Element Concepts." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37159.

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We introduce an approach blending the Perfectly Matched Layer (PML) and infinite element paradigms, to achieve better performance and wider applicability than either approach alone. In this paper, we address the specific challenges of unbounded problems when using time-domain explicit finite elements: 1. The algorithm must be spatially local, to minimize storage and communication cost, 2. It must contain second-order time derivatives for compatibility with the explicit central-difference time integration scheme, 3. Its coefficient for the second-order derivatives must be diagonal (“lumped mass”), 4. It must be time-stable when used with central-differences, 5. It must converge to the correct low-frequency (Laplacian) limit, 6. It should exhibit high accuracy across typically encountered dynamic frequencies, i.e. at short to long wavelengths, 7. Its user interface should be as simple as possible. Here, we will describe the derivation of a time-domain implementation of the hybrid PML/infinite element, and discuss its advantages for implementation.
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Liu, J., S. J. Zhang, and Y. S. Chen. "Predictions of Radiative Properties of Patterned Silicon Wafers by Solving Maxwell’s Equations in the Time Domain." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47424.

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A rigorous electromagnetic model is developed to predict the radiative properties of patterned silicon wafers. For nonplanar structures with characteristic length close to the wavelength of incident radiation, Maxwell’s equations must be used to describe the associated radiative interaction and they are solved by the finite difference time-domain (FDTD) method. In the die area, only one period of the structure is modeled due to its periodicity in geometry. To truncate a computational domain, both the Mur condition and perfectly matched layer (PML) technique are available to absorb outgoing waves. With the steady state time-harmonic electromagnetic field known, the Poynting vector is used to calculate the radiative properties. Due to its importance, the reflection error is checked at first for two absorbing boundary conditions. As expected, the PML technique yields much lower errors than the Mur condition and it is thus used in this study. To validate the present model, radiative interactions with a planar structure and a nonplanar structure are investigated, and predicted reflectivities are found to match available other solutions very well. To demonstrate the importance of the present study, a patterned wafer consisting of periphery and die area is also investigated. While the thin film theory is accurate for the wafer periphery, the rigorously electromagnetic model described in this study is found to be necessary to accurately predict the radiative properties in the die area.
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Dey, Saikat, and Joseph J. Shirron. "Computation of Acoustic Transmission Loss Through Doubly-Periodic 3D Elastic Panels." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13713.

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We address acoustic transmission loss through doubly-periodic elastic panels separating two semi-infinite fluid half-spaces. This involves the computation of the transmitted and reflected sound fields due to an incident plane wave. The elastic panel may have complex internal structures, for example, a sandwiched honeycomb core. Our computations are based on using high order (p-version) finite element discretization. The semi-infinite fluid half-spaces on either side of the elastic panel are truncated using perfectly matched layer (PML) approximations. We verify our model using data for transmission loss for thin and thick homogeneous elastic plates using analytic solutions based on 3D elasticity as well as thin and thick plate theory. This is followed by a study of transmission loss though sandwiched honeycomb panel for a range of frequencies and incident angles.
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Reports on the topic "Perfectly Matched Layers (PML)"

1

Banks, H. T., and Brian L. Browning. Time Domain Electromagnetic Scattering Using Finite Elements and Perfectly Matched Layers. Fort Belvoir, VA: Defense Technical Information Center, June 2003. http://dx.doi.org/10.21236/ada451435.

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Michler, C., L. Demkowicz, J. Kurtz, and D. Pardo. Improving the Performance of Perfectly Matched Layers by Means of hp-Adaptivity. Fort Belvoir, VA: Defense Technical Information Center, January 2006. http://dx.doi.org/10.21236/ada457406.

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Elson, J. M. Three Dimensional Finite-Difference Time- Domain Solution of Maxwell's Equations With Perfectly Matched Absorbing Layers. Fort Belvoir, VA: Defense Technical Information Center, September 1999. http://dx.doi.org/10.21236/ada369016.

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