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31
Recent Developments in Finite Element Methods for Structural Acoustics
, 1996
"... This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics ..."
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This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics
Coupling of a nonoverlapping domain decomposition method for a nodal finite element method with a boundary element method
, 2002
"... Nonoverlapping domain decomposition techniques are used both to solve the finite element equations and to couple them with a boundary element method. A suitable approach dealing with finite element nodes common to more than two subdomains, the socalled crosspoints, endows the method with the foll ..."
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Cited by 9 (2 self)
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Nonoverlapping domain decomposition techniques are used both to solve the finite element equations and to couple them with a boundary element method. A suitable approach dealing with finite element nodes common to more than two subdomains, the socalled crosspoints, endows the method with the following advantages. It yields a robust and efficient procedure to solve the equations resulting from the discretization process. Only small size finite element linear systems and a dense linear system related to a simple boundary integral equation are solved at each iteration and each of them can be solved in a stable way. We also show how to choose the parameter definining the augmented local matrices in order to improve the convergence. Several numerical simulations in 2D and 3D validating the treatment of the crosspoints and illustrating the strategy to accelerate the iterative procedure are presented.
Fast Numerical Solution Of Exterior Helmholtz Problems With Radiation Boundary Condition By Imbedding
, 1994
"... The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix metho ..."
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Cited by 8 (2 self)
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The development of efficient solution algorithms for Poisson's equation on domains allowing for separation of variables prompted research towards extending these algorithms to domains of general shape. The resulting numerical techniques are known as imbedding methods or capacitance matrix methods. In this dissertation, we develop capacitance matrix methods for exterior boundary value problems for the Helmholtz equation, a secondorder elliptic PDE which governs timeharmonic wave propagation. Solutions of exterior Helmholtz problems must satisfy an asymptotic boundary condition at infinity in order to be uniquely determined. We incorporate this boundary condition into the discretization by posing the DirichlettoNeumann (DtN) condition, an exact nonlocal boundary condition, on a circular artificial boundary. A fast Helmholtz solver of complexity O(nm log n) can then be obtained for the resulting discrete problem on an m \Theta n grid when the underlying computational domain is an an...
A FETIlike domain decomposition method for coupling finite elements and boundary elements in largesize scattering problems of acoustic scattering
 COMPUT. & STRUCTURES
, 2005
"... Numerical simulations of acoustic scattering in the frequency domain based on hybrid methods coupling finite elements and boundary elements are the most suited for dealing with problems involving wave propagation in inhomogeneous media. Furthermore, it is necessary to resort to high performance comp ..."
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Cited by 6 (3 self)
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Numerical simulations of acoustic scattering in the frequency domain based on hybrid methods coupling finite elements and boundary elements are the most suited for dealing with problems involving wave propagation in inhomogeneous media. Furthermore, it is necessary to resort to high performance computing to effectively solve the large size problems. However, the direct coupling yields a linear system with a matrix which is partly dense and partly sparse and thus not adapted to high performance computing. To avoid this difficulty, we present a new iterative method constructed from a non overlapping domain decomposition technique.
A multistep procedure for enriching limited twodimensional acoustic farfield pattern measurements
 in "Journal of Inverse and IllPosed Problems
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An analysis of the BEMFEM nonoverlapping domain decomposition method for a scattering problem
, 2005
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The limiting absorption principle for elastic wave propagation problems in perturbed stratified media R3
, 1996
"... ABSTRACT. We consider the selfadjoint operator governing the propagation of elastic waves in perturbed stratified media $\mathrm{R}^{3} $ with free boundaryinterface conditions. In this paper we establish the limiting absorption principle for this selfadjoint operator in appropriate Hilbert spac ..."
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ABSTRACT. We consider the selfadjoint operator governing the propagation of elastic waves in perturbed stratified media $\mathrm{R}^{3} $ with free boundaryinterface conditions. In this paper we establish the limiting absorption principle for this selfadjoint operator in appropriate Hilbert space. The proof of the limiting absorption principle is based on the division theorem which is proved by means of eigenfunction expansions for the selfadjoint operator governing the propagation of elastic waves in unperturbed stratified media $\mathrm{R}^{3} $. 1.
Continuous Fr ' Echet Differentiability With Respect To Lipschitz Domain And A Stability Estimate For Direct Acoustic Scattering Problems
"... . We consider direct acoustic scattering problems with either a soundsoft or soundhard obstacle, or lossy boundary conditions, and establish continuous Fr'echet differentiability with respect to the shape of the scatterer of the scattered field and its corresponding farfield pattern. Our proo ..."
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. We consider direct acoustic scattering problems with either a soundsoft or soundhard obstacle, or lossy boundary conditions, and establish continuous Fr'echet differentiability with respect to the shape of the scatterer of the scattered field and its corresponding farfield pattern. Our proof is based on the Implicit Function Theorem, and assumes that the boundary of the scatterer as well as the deformation are only Lipschitz continuous. From continuous Fr'echet differentiability, we deduce a stability estimate governing the variation of the farfield pattern with respect to the shape of the scatterer. We illustrate this estimate with numerical results obtained for a twodimensional highfrequency acoustic scattering problem. Key words. Scattering, acoustics, Fr'echet differentiability, stability, domain derivative, Lipschitz boundary, Lipschitz continuous transformation, Implicit Function Theorem, unbounded domain 1. Introduction. The determination of the shape of an obstacle from...
FIELD BEHAVIOR NEAR THE EDGE OF A MICROSTRIP ANTENNA BY THE METHOD OF MATCHED ASYMPTOTIC EXPANSIONS
, 2010
"... Abstract. The cavity model is a widespread powerful empirical approach for the numerical simulation of microstrip antennas. It is based on several hypotheses assumed a priori: a dimension reduction in the cavity, that is, the zone limited by a metallic patch and the ground plane in which is fed the ..."
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Abstract. The cavity model is a widespread powerful empirical approach for the numerical simulation of microstrip antennas. It is based on several hypotheses assumed a priori: a dimension reduction in the cavity, that is, the zone limited by a metallic patch and the ground plane in which is fed the antenna, supplied by the additional condition that the open sides of the cavity act as magnetic walls. An additional important assumption of this model consists in an adequate description of the singular field behavior in the proximity of the edge of the patch. A simplified twodimensional problem incorporating the main features of the field behavior near the edge of the patch and inside the cavity is addressed. The method of matched asymptotic expansions is used to carry out a twoscale asymptotic analysis of the field relatively to the thickness of the cavity. All the empirical hypotheses at the basis of the derivation of the cavity model can thus be recovered. Proved error estimates are given in a simplified framework where the dielectric constants of the substrate are assumed to be 1 in order to avoid some unimportant technical difficulties. 1.
Approximation by multipoles of the multiple acoustic scattering by small obstacles and application to the Foldy theory of isotropic scattering
 ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
, 2014
"... The asymptotic analysis, carried out in this paper, for the problem of a multiple scattering of a timeharmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by ..."
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The asymptotic analysis, carried out in this paper, for the problem of a multiple scattering of a timeharmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by point sources. Among other issues, this asymptotic expansion of the wave furnishes a mathe