The non-overlapping domain decomposition method is an efficient approach for solving time harmonic scattering wave problems. It is used here to reduce large size systems solution to that of several systems of small size and to construct... more
The non-overlapping domain decomposition method is an efficient approach for solving time harmonic scattering wave problems. It is used here to reduce large size systems solution to that of several systems of small size and to construct efficient procedures to couple finite element and boundary element methods. The lack of a satisfactory treatment of the so-called cross-points, nodes being shared by more than two domains, prevents one from taking advantage of the simplicity of the standard finite element method and the effectiveness of a domain decomposition procedure at the same time. A new approach overcoming this difficulty is introduced. It mainly consists in keeping a strong coupling at cross-points by enforcing a strong continuity requirement at these points for both trial and the test functions. 1. Introduction. Several methods have been devised in the last couple of years to solve the large size linear systems arising from the discretization of time harmonic scattering probl...
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When coupling a finite element and a domain decomposition method, a cross-point corresponds to a degree of freedom shared by more than two domains. The problem of dealing with such cross-points is addressed for the case of an usual nodal... more
When coupling a finite element and a domain decomposition method, a cross-point corresponds to a degree of freedom shared by more than two domains. The problem of dealing with such cross-points is addressed for the case of an usual nodal finite element solution of the Helmholtz equation. An important feature of the approach relies upon its interpretation as an iterative method for solving the discrete problem in the whole domain. The convergence of the iterative procedure is established in the general case and proved to be scalable, that is, to converge at a rate independent of the mesh when the domain decomposition method involves no cross-points.
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This paper describes an investigation of the acoustic properties of a rigid plate with a periodic pattern of holes, in a compressible, ideal, inviscid fluid in the absence of mean flow. Leppington & Levine (J. Fluid Mech., vol. 61, 1973,... more
This paper describes an investigation of the acoustic properties of a rigid plate with a periodic pattern of holes, in a compressible, ideal, inviscid fluid in the absence of mean flow. Leppington & Levine (J. Fluid Mech., vol. 61, 1973, pp. 109–127) obtained an approximation of the reflection and transmission coefficients of a plane wave incident on an infinitely thin plate with a rectangular array of perforations, assuming that a characteristic size of the perforations is negligible relative to that of the unit cell of the grating, itself assumed to be negligible relative to the wavelength. One part of the present study is of methodological interest. It establishes that it is possible to extend their approach to thick plates with a skew grating of perforations, thus confirming recent results of Bendali et al. (SIAM J. Appl. Math., vol. 73 (1), 2013, pp. 438–459), but in a much simpler way without using complex matched asymptotic expansions of the full wave or to a grating of multi...
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ABSTRACT A general finite-element method is applied to compute the skin current of a perfectly conducting surface illuminated by an incident electromagnetic wave. Surface charges over any element and currents flowing through any edge are... more
ABSTRACT A general finite-element method is applied to compute the skin current of a perfectly conducting surface illuminated by an incident electromagnetic wave. Surface charges over any element and currents flowing through any edge are approximated by polynomials of degree m. Some radiation patterns of two horns are calculated and compared with those obtained from experiment.
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ABSTRACT In this paper, we construct an asymptotic expansion of a time-harmonic wave scattered by N small spheres. This construction is based on the method of matched asymptotic expansions. Error estimates give a theoretical background to... more
ABSTRACT In this paper, we construct an asymptotic expansion of a time-harmonic wave scattered by N small spheres. This construction is based on the method of matched asymptotic expansions. Error estimates give a theoretical background to the approach.
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ABSTRACT We derive the second-order asymptotic expansion of an eigenvalue problem for the Laplace eigenfunction with Dirichlet boundary conditions set in a domain corresponding to two cavities linked by a small iris. Several convergence... more
ABSTRACT We derive the second-order asymptotic expansion of an eigenvalue problem for the Laplace eigenfunction with Dirichlet boundary conditions set in a domain corresponding to two cavities linked by a small iris. Several convergence rates are obtained and illustrated by numerical experiments.
The cavity model is a widespread empirical approach for the numerical simulation of patch antennas. An attempt to give a rigorous mathematical background for this way to proceed is presented. The justification is carried out in the... more
The cavity model is a widespread empirical approach for the numerical simulation of patch antennas. An attempt to give a rigorous mathematical background for this way to proceed is presented. The justification is carried out in the framework of a two-dimensional ...
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ABSTRACT The initial problem we want to solve is the radiation of an antenna located on a large metallic structure. The proposed approach is based on a domain decomposition method (DDM) with a new adaptive absorbing boundary condition... more
ABSTRACT The initial problem we want to solve is the radiation of an antenna located on a large metallic structure. The proposed approach is based on a domain decomposition method (DDM) with a new adaptive absorbing boundary condition (AABC). In this paper, we have proposed a new DDM approach coupling finite element method (FEM) and boundary integral equation (BIE). This approach is well-adapted for both radiation and scattering problems in which FEM is used in a reduced zone.
ABSTRACT A model problem in the scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell is examined. In previous studies, the contrast coefficients of the thin shell are assumed to tend to infinity in order... more
ABSTRACT A model problem in the scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell is examined. In previous studies, the contrast coefficients of the thin shell are assumed to tend to infinity in order to compensate for the thickness considered. In this paper, these coefficients are assumed to remain finite. Such a treatment leads to a singular perturbation term that creates a typical difficulty for the asymptotic analysis of the problem with respect to the thickness of the coating. As a result, the asymptotic analysis is essentially based on a suitable handling of the stability of the solution relative to the thickness. As a consequence, it is shown how effective boundary conditions which can be substituted to the thin shell can then be obtained and analyzed in a simple way.
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ABSTRACT In this paper, we construct an asymptotic expansion of a time-harmonic wave scattered by N small spheres. This construction is based on the method of matched asymptotic expansions. Error estimates give a theoretical background to... more
ABSTRACT In this paper, we construct an asymptotic expansion of a time-harmonic wave scattered by N small spheres. This construction is based on the method of matched asymptotic expansions. Error estimates give a theoretical background to the approach.
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Research Interests: Algorithms, Biomedical Engineering, Blindness, Endoscopy, Neural Engineering, and 15 moreFinite Element Analysis, Animals, Retina, Clinical Sciences, Microcomputers, Microtechnology, Rats, Finite Element Model, Three Dimensional, Model Analysis, Spatial resolution, prosthesis Design, Experimental Validation, Neurosciences, and Tissue Fixation
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ABSTRACT A boundary-element method is introduced for solving electromagnetic scattering problems in the frequency domain relative to an impedance boundary condition (IBC) on an obstacle of arbitrary shape. The formulation is based on the... more
ABSTRACT A boundary-element method is introduced for solving electromagnetic scattering problems in the frequency domain relative to an impedance boundary condition (IBC) on an obstacle of arbitrary shape. The formulation is based on the field approach; namely, it is obtained by enforcing the total electromagnetic field, expressed by means of the incident field and the equivalent electric and magnetic currents and charges on the scatterer surface, to satisfy the boundary condition. As a result, this formulation is well-posed at any frequency for an absorbing scatterer. Both of the equivalent currents are discretized by a boundary-element method over a triangular mesh of the surface scatterer. The magnetic currents are then eliminated at the element level during the assembly process. The final linear system to be solved keeps all of the desirable properties provided by the application of this method to the usual perfectly conducting scatterer; that is, its unknowns are the fluxes of the electric currents across the edges of the mesh and its coefficient matrix is symmetric
Research Interests: Boundary Element Methods, Electromagnetic Scattering, Frequency-domain analysis, Assembly, Boundary Element Method, and 14 moreElectromagnetic Fields, Boundary Conditions, Magnetic Domains, Shape, Electromagnetic Field, Linear System, Electric Current, Linear Systems, Current, Boolean Satisfiability, Boundary Condition, Electrical And Electronic Engineering, Frequency Domain, and Backscattering
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Research Interests: Engineering, Distributed Computing, High Performance Computing, Acoustics, Modeling, and 16 moreFinite element method, Boundary Element Methods, Finite Element, Structural Analysis, Numerical Simulation, Boundary Element Method, Wave propagation, Linear System, Acoustic Scattering, High performance computer, Domain Decomposition, Domain decomposition method, Acoustic Waves, Frequency Domain, Inhomogeneous Media, and Hybrid Method
Abstract: The patchs antennas are intensively used in industry (mobile phone, radar, sonar). Due to the presence of boundary layers near the edges of these devices, the classical technique of numerical computation (like finite elements... more
Abstract: The patchs antennas are intensively used in industry (mobile phone, radar, sonar). Due to the presence of boundary layers near the edges of these devices, the classical technique of numerical computation (like finite elements and finite differences) suffers from ...
Summary. Two techniques are coupled to solve a model problem relative to the scattering of a 2D time-harmonic electromagnetic wave by an obstacle including an electrically deep cavity. Both of them are based on a boundary element method.... more
Summary. Two techniques are coupled to solve a model problem relative to the scattering of a 2D time-harmonic electromagnetic wave by an obstacle including an electrically deep cavity. Both of them are based on a boundary element method. The first technique uses a domain decomposition procedure to reduce the contribution of the cavity to a set of equations supported by