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Optimizing Perfectly Matched Layers in Discrete Contexts Modave, Axel ; Delhez, Eric ; Geuzaine, Christophe in International Journal for Numerical Methods in Engineering (2014), 99(6), 410437 Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic ... [more ▼] Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyse how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one- and two-dimensional representative time-dependent cases. This study highlights the advantages of the so-called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions. [less ▲] Detailed reference viewed: 105 (23 ULg)Analysis of transient scattering problems using a discontinuous Galerkin method: application to the shielding effectiveness of enclosures with heterogeneous walls ; ; et al in International Journal of Numerical Modelling: Electronic Networks, Devices and Fields (2014), 27(3), 626-635 In this paper, different formulations of Maxwell equations are combined for computing the shielding effectiveness of enclosures made from heterogeneous periodic materials. The validity of the homogenized ... [more ▼] In this paper, different formulations of Maxwell equations are combined for computing the shielding effectiveness of enclosures made from heterogeneous periodic materials. The validity of the homogenized parameters given by Maxwell-Garnett rules in the frequency domain are tested in the time domain using a nodal discontinuous Galerkin method, which uses an interface condition based on analytical solution in the frequency domain to replace a conductive sheet. This interface condition allows to avoid meshing the thin sheet, thus reducing the computational cost. Results of scattering by composite enclosures are presented in the frequency domain thanks to a Fast Fourier Transform. [less ▲] Detailed reference viewed: 65 (13 ULg)3-D Modeling of Thin Sheets in the Discontinuous Galerkin Method for Transient Scattering Analysis ; ; et al in IEEE Transactions on Magnetics (2014), 50(2), 493-496 This paper presents a modeling of thin sheets. An interface condition based on analytical solution is used to avoid a fine mesh. This condition is integrated in a time domain Discontinuous Galerkin method ... [more ▼] This paper presents a modeling of thin sheets. An interface condition based on analytical solution is used to avoid a fine mesh. This condition is integrated in a time domain Discontinuous Galerkin method in order to evaluate the shielding effectiveness. This approach is validated by a comparison with analytical solution. 2D and 3D cavities are simulated to illustrate the efficiency of the condition. [less ▲] Detailed reference viewed: 42 (7 ULg)Evaluation of shielding effectiveness of composite wall with a time domain discontinuous Galerkin method ; Modave, Axel ; et al in European Physical Journal : Applied physics (2013), 64(2), 24508 This article presents a Time Domain Discontinuous Galerkin method applied for solving the conservative form of Maxwell equations and computing the radiated fields in electromagnetic compatibility problems ... [more ▼] This article presents a Time Domain Discontinuous Galerkin method applied for solving the conservative form of Maxwell equations and computing the radiated fields in electromagnetic compatibility problems. The results obtained in homogenous media for the transverse magnetic waves are validated in two cases. We compare our solution to an analytical solution of Maxwell’s equations based on characteristic method. Our results on shielding effectiveness of a conducting wall are same as those obtained from analytical expression in frequency domain. The propagation in heterogeneous medium is explored. The shielding effectiveness of a composite wall partially filled by circular conductives inclusions is computed. The proposed results are in conformity with the classical predictive homogenizations rules. [less ▲] Detailed reference viewed: 85 (10 ULg)An optimum PML for scattering problems in the time domain Modave, Axel ; ; et al in European Physical Journal : Applied physics (2013), 64(2), 24502 In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded ... [more ▼] In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded. The perfectly matched layer (PML) is widely used to simulate the truncation of the computational domain. However, its performance depends critically on an absorption function. This function is generally tuned by using case-dependent optimization procedures. In this paper, we will present some efficient functions that overcome any tuning. They will be compared using a realistic scattering benchmark solved with the Discontinuous Galerkin method. [less ▲] Detailed reference viewed: 106 (32 ULg)Absorbing Layers for Wave-Like Time-Dependent Problems - Design, Discretization and Optimization Modave, Axel Doctoral thesis (2013) The numerical simulation of wave-like phenomena occurring in large or infinite domains is a great challenge for a wide range of technological and scientifical problems. A classical way consists in ... [more ▼] The numerical simulation of wave-like phenomena occurring in large or infinite domains is a great challenge for a wide range of technological and scientifical problems. A classical way consists in considering only a limited computational domain with an artificial boundary that requires a specific treatment. In this thesis, \textit{absorbing layers} are developed and studied for time-dependent problems in order to deal with such artificial boundary. A large part of this thesis is dedicated to the \textit{perfectly matched layers} (PMLs), which exhibit appealing properties. They are first studied in a fundamental case with non-dispersive linear scalar waves. A procedure for building PMLs is proposed for convex domains with regular boundary. It permits a great flexibility when choosing the shape of the computational domain. After, the issue of choosing PML parameters is addressed with the aim of optimizing the PML effectiveness in discrete contexts. The role of each parameter, including the so-called \textit{absorption function}, is highlighted by means of analytical and numerical results. A systematic comparison of different kinds of absorption functions is performed for several classical numerical schemes (based on finite differences, finite volumes or finite elements). Then, while the PMLs do not a priori account for incoming signals generated outside the computational domain, different problem formulations that account for such forcing are detailed and compared. The interest of the whole approach is finally illustrated with two- and three-dimensional numerical examples in electromagnetism and acoustics, using a discontinuous finite element scheme. In regional oceanic models, modeling open-sea boundaries brings new difficulties. Indeed, additional linear/nonlinear dynamics are involved and the external forcing is generally poorly known. In this context, different absorbing layers and the widely used Flather boundary condition are compared by means of classical benchmarks. The choice of the absorption function and the way of prescribing the external forcing are discussed in specific marine cases. [less ▲] Detailed reference viewed: 414 (69 ULg)Modeling of Weakly Conducting Thin Sheets in the Discontinuous Galerkin Method for Shielding Effectiveness Evaluation ; ; Modave, Axel et al in ACES Journal (2013), 28(10), 931 This paper presents a modeling of weakly conducting thin sheets in the time domain discontinuous Galerkin method. This interface condition is used to avoid the mesh of resistive sheets in order to ... [more ▼] This paper presents a modeling of weakly conducting thin sheets in the time domain discontinuous Galerkin method. This interface condition is used to avoid the mesh of resistive sheets in order to evaluate the shielding effectiveness in high frequency electromagnetic compatibility problems. This condition is valid when the thickness of the sheet is smaller than the skin depth. This approach is validated by a comparison with an analytical solution. A 1D two sheets example, 2D and 3D cavities are treated to illustrate the efficiency of the condition. [less ▲] Detailed reference viewed: 44 (7 ULg)3D Modeling of Thin Resistive Sheets in the Discontinuous Galerkin Method for Transient Scattering Analysis ; ; et al in Proceedings of the 19th Conference on the Computation of Electromagnetic Fields (COMPUMAG 2013) (2013, July 03) This papers presents a modeling of thin resistive sheets. An interface condition is used to avoid the fine mesh. The electromagnetic fields are computed with a time domain Discontinuous Galerkin method in ... [more ▼] This papers presents a modeling of thin resistive sheets. An interface condition is used to avoid the fine mesh. The electromagnetic fields are computed with a time domain Discontinuous Galerkin method in order to evaluate the shielding effectiveness. A 3D cavity is treated to illustrate the efficiency of the condition. [less ▲] Detailed reference viewed: 44 (5 ULg)A PML for convex truncated domains in time-dependent acoustics with a DG-FE discretization Modave, Axel ; ; Delhez, Eric et al in Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013) (2013, June 03) A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when ... [more ▼] A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when classical shapes of truncated domains are less appropriate. A numerical discretization based on the discontinuous Galerkin method is then described and validated. An example of realistic three-dimensional application is finally proposed. [less ▲] Detailed reference viewed: 93 (13 ULg)Evaluation of Shielding Effectiveness in the Time Domain using a DG Method with an Efficient PML Modave, Axel ; Geuzaine, Christophe ; et al Poster (2013, April 24) Development of new electric and electronic devices leads to an increasing importance for solving electromagnetic compatibility problems. In particular, the optimization of radiated emissions is ... [more ▼] Development of new electric and electronic devices leads to an increasing importance for solving electromagnetic compatibility problems. In particular, the optimization of radiated emissions is increasingly done through numerical modeling. In this context, numerical methods allow to evaluate the effectiveness of more and more elaborate shielding enclosures. We propose an application of the nodal Discontinuous Galerkin method to evaluate the effectiveness of composite shieldings in the time domain. This numerical method provides convenient advantages to deal with shielding problems. Firstly, heterogeneous media are naturally included in the discrete formulation. After, the method is famous to allow a massive parallelization for the numerical resolution. Finally, a resolution in the time domain allows to consider transient signals. The numerical scheme is firstly validated using an academic benchmark. In the same way, the PML used to truncate the computational domain is optimized and validated. Applications are then presented for homogeneous and composite shieldings. The preliminary results are in conformity with classical predictive rules. [less ▲] Detailed reference viewed: 78 (10 ULg)An optimum PML for scattering problems in the time domain Modave, Axel ; Delhez, Eric ; et al in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC 2012) (2012, July 05) The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on an absorption coefficient. This coefficient is generally tuned by using case ... [more ▼] The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on an absorption coefficient. This coefficient is generally tuned by using case-dependent optimization procedures. In this paper we will present some efficient profiles of the coefficient that overcome every tuning. These profiles and others will be compared by using a scattering benchmark solved with the Discontinuous Galerkin method. [less ▲] Detailed reference viewed: 95 (16 ULg)Evaluation de l'efficacité de blindage de parois hétérogènes par une méthode de Galerkin discontinue en domaine temporel ; Modave, Axel ; et al in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC 2012) (2012, July 03) Detailed reference viewed: 52 (10 ULg)Optimisation des PML dans des contextes discrets Modave, Axel ; Delhez, Eric ; Geuzaine, Christophe Conference (2012, May 21) Detailed reference viewed: 59 (8 ULg)Optimizing the PML in the discrete context Modave, Axel Scientific conference (2012, March 30) Perfectly Matched Layers (PML) are widely used for the simulation of unbounded wave-like problems. However their performance depends critically on both an absorption coefficient and the spatial ... [more ▼] Perfectly Matched Layers (PML) are widely used for the simulation of unbounded wave-like problems. However their performance depends critically on both an absorption coefficient and the spatial discretization. Tuning the coefficient requires a costly (and case-dependent) optimization procedures... so that in most applications it is set empirically. In this talk we discuss the influence of the absorption coefficient on the PML performance for time-domain simulations, in both continuous and discrete contexts. We present efficient coefficients that allow to avoid any tuning in discrete contexts, and compare those with other frequent choices by means of benchmarks solved with both finite differences and finite elements (continuous and discontinuous). A realistic 3D discontinuous Galerkin benchmark for Maxwell's equations will highlight the advantages of our approach. [less ▲] Detailed reference viewed: 53 (10 ULg)On the Parameters of the Perfectly Matched Layer in Discrete Contexts Modave, Axel ; Delhez, Eric ; Geuzaine, Christophe in Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2011) (2011, July 26) Perfectly Matched Layer (PML) techniques are widely used for dealing with unbounded problems. However their performance depends critically on both an absorption coefficient and the numerical method. The ... [more ▼] Perfectly Matched Layer (PML) techniques are widely used for dealing with unbounded problems. However their performance depends critically on both an absorption coefficient and the numerical method. The coefficient is generally tuned by using costly and case-dependent optimization procedures or set empirically. In this paper we present some efficient profiles of the coefficient that allow to avoid any tuning in discrete contexts. These profiles are compared by means of two benchmarks with different numerical methods. [less ▲] Detailed reference viewed: 105 (25 ULg)Optimization of the PML in the Discrete Context for Wave-Like Problems Modave, Axel ; Delhez, Eric ; Geuzaine, Christophe Conference (2011, July 18) The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on both an absorption coefficient and the numerical method. The coefficient is generally ... [more ▼] The Perfectly Matched Layer (PML) is widely used for unbounded problems. However its performances depend critically on both an absorption coefficient and the numerical method. The coefficient is generally tuned by using optimization procedures. In this talk we will present some efficient profiles of the coefficient that overcome every tuning in discrete contexts. These profiles and others will be compared by using benchmarks with different numerical methods. [less ▲] Detailed reference viewed: 99 (20 ULg)Absorbing layers for shallow water models Modave, Axel ; ; Delhez, Eric Conference (2010, May 11) Detailed reference viewed: 148 (40 ULg)On the parameters of absorbing layers for shallow water models Modave, Axel ; ; Delhez, Eric in Ocean Dynamics (2010), 60(1), 65-79 Absorbing/sponge layers used as boundary conditions for ocean/marine models are examined in the context of the shallow water equations with the aim to minimize the reflection of outgoing waves at the ... [more ▼] Absorbing/sponge layers used as boundary conditions for ocean/marine models are examined in the context of the shallow water equations with the aim to minimize the reflection of outgoing waves at the boundary of the computationaldomain. The ptimization of the absorption coefficient is not an issue in continuous models, for the reflection coefficient of outgoing waves can then be made as small as we please by increasing the absorption coefficient. The optimization of the parameters of absorbing layers is therefore a purely discrete problem. A balance must be found between the efficient damping of outgoing waves and the limited spatial resolution with which the resulting spatial gradients must be described. Using a one-dimensional model as a test case, the performances of various spatial distributions of the absorption coefficient are compared. Two shifted hyperbolic distributions of the absorption coefficient are derived from theoretical considerations for a pure propagative and a pure advective problems. These distribution show good performances. Their free parameter has a well-defined interpretation and can therefore be determined on a physical basis. The properties of the two shifted hyperbolas are illustrated using the classical two-dimensional problems of the collapse of a Gaussianshaped mound of water and of its advection by a mean current. The good behavior of the resulting boundary scheme remains when a full non-linear dynamics is taken into account. [less ▲] Detailed reference viewed: 213 (92 ULg)Étude de modèles de frontière ouverte pour des problèmes de propagation d'ondes Modave, Axel Master's dissertation (2008) Ce travail est consacré à l'étude expérimentale de conditions aux limites et de couches absorbantes qui modélisent des frontières ouvertes dans des problèmes de propagation d'ondes. Nous considérons ici ... [more ▼] Ce travail est consacré à l'étude expérimentale de conditions aux limites et de couches absorbantes qui modélisent des frontières ouvertes dans des problèmes de propagation d'ondes. Nous considérons ici la condition de Flather et les versions de la condition de radiation proposées par Orlanski et Raymond & Kuo. Du côté des couches absorbantes, nous étudions la zone FRS de Martinsen & Engedahl, la "Pretty good sponge" de Lavelle et une version complète de PML. L'étude commence par une analyse caractéristique de l'équation d'onde et une présentation détaillée des différents modèles de frontière ouverte. Après, deux problèmes de base sont proposés pour permettre de quantifier la qualité de ces modèles. L'influence des différents paramètres des couches absorbantes est étudiée afin de déterminer les valeurs optimales. Ensuite, le comportement des différents champs est analysé au sein des couches optimales. Enfin, les différents modèles de frontière ouverte sont comparés sur base des deux problèmes. Les couches absorbantes le sont également sur un cas d'ajustement géostrophique, déjà traité par Lavelle dans un article récent. [less ▲] Detailed reference viewed: 156 (42 ULg) |
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