The Experts below are selected from a list of 43428 Experts worldwide ranked by ideXlab platform
Xavier Antoine - One of the best experts on this subject based on the ideXlab platform.
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A Coupling between Integral Equations and On-Surface Radiation Conditions for Diffraction Problems by Non Convex Scatterers
'MDPI AG', 2021Co-Authors: Saleh Mousa Alzahrani, Xavier Antoine, Chokri ChnitiAbstract:The aim of this paper is to introduce an orignal coupling procedure between surface integral equation formulations and on-surface Radiation Condition (OSRC) methods for solving two-dimensional scattering problems for non convex structures. The key point is that the use of the OSRC introduces a sparse block in the surface operator representation of the wave field while the integral part leads to an improved accuracy of the OSRC method in the non convex part of the scattering structure. The procedure is given for both the Dirichlet and Neumann scattering problems. Some numerical simulations show the improvement induced by the coupling method
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an improved surface Radiation Condition for high frequency acoustic scattering problems
Computer Methods in Applied Mechanics and Engineering, 2006Co-Authors: Xavier Antoine, Marion Darbas, Ya Yan LuAbstract:A new artificial boundary Condition for two-dimensional acoustic scattering problems is constructed in this paper. It is designed from the principal symbol of the Dirichlet-to-Neumann map so that both the propagating and evanescent fields are properly modeled. In the high-frequency regime, the new artificial boundary Condition can be used as an on-surface Radiation Condition for efficient approximation of the wave field. The accuracy and efficiency of our method are demonstrated in numerical examples.
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alternative integral equations for the iterative solution of acoustic scattering problems
Quarterly Journal of Mechanics and Applied Mathematics, 2005Co-Authors: Xavier Antoine, Marion DarbasAbstract:This paper addresses the first step of the derivation of well-Conditioned integral formulations for the iterative solution of exterior acoustic boundary-value problems. These new formulations are designed to be implemented in a fast multipole method coupled to a Krylov subspace iterative algorithm. Their construction is based on the on-surface Radiation Condition formalism. Both theoretical developments and numerical aspects are examined in detail. This approach can be viewed as a generalization of the usual Burton-Miller integral equations.
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fast approximate computation of a time harmonic scattered field using the on surface Radiation Condition method
Ima Journal of Applied Mathematics, 2001Co-Authors: Xavier AntoineAbstract:The numerical study of the on-surface Radiation Condition method applied to two- and three-dimensional time-harmonic scattering problems is examined. This approach allows us to quickly compute an approximate solution to the initial exact boundary-value problem. A general background for the numerical treatment of arbitrary convex-shaped objects is stated. New efficient on-surface Radiation Conditions leading in a natural way to a symmetrical boundary variational formulation are introduced. The approximation is based upon boundary finite-element methods. Moreover, this study requires a specific numerical treatment of the curvature operator. To this end, a numerical procedure using some results about the theory of local approximation of surfaces is described. Finally, the effectiveness and generality of the approach is numerically tested for several scatterers.
Francois Castella - One of the best experts on this subject based on the ideXlab platform.
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Radiation Condition at infinity for the high frequency helmholtz equation optimality of a non refocusing criterion
arXiv: Analysis of PDEs, 2012Co-Authors: Aurelien Klak, Francois CastellaAbstract:We consider the high frequency Helmholtz equation with a variable refraction index $n^2(x)$ ($x \in \R^d$), supplemented with a given high frequency source term supported near the origin $x=0$. A small absorption parameter $\alpha_{\varepsilon}>0$ is added, which somehow prescribes a Radiation Condition at infinity for the considered Helmholtz equation. The semi-classical parameter is $\varepsilon>0$. We let $\eps$ and $\a_\eps$ go to zero {\em simultaneaously}. We study the question whether the indirectly prescribed Radiation Condition at infinity is satisfied {\em uniformly} along the asymptotic process $\eps \to 0$, or, in other words, whether the conveniently rescaled solution to the considered equation goes to the {\em outgoing} solution to the natural limiting Helmholtz equation. This question has been previously studied by the first autor. It is proved that the Radiation Condition is indeed satisfied uniformly in $\eps$, provided the refraction index satisfies a specific {\em non-refocusing Condition}, a Condition that is first pointed out in this reference. The non-refocusing Condition requires, in essence, that the rays of geometric optics naturally associated with the high-frequency Helmholtz operator, and that are sent from the origin $x=0$ at time $t=0$, should not refocus at some later time $t>0$ near the origin again. In the present text we show the {\em optimality} of the above mentionned non-refocusing Condition, in the following sense. We exhibit a refraction index which {\em does} refocus the rays of geometric optics sent from the origin near the origin again, and, on the other hand, we completely compute the asymptotic behaviour of the solution to the associated Helmholtz equation: we show that the limiting solution {\em does not} satisfy the natural Radiation Condition at infinity. More precisely, we show that the limiting solution is a {\em perturbation} of the outgoing solution to the natural limiting Helmholtz equation, and that the perturbing term explicitly involves the contribution of the rays radiated from the origin which go back to the origin. This term is also conveniently modulated by a phase factor, which turns out to be the action along the above rays of the hamiltonian associated with the semiclassical Helmholtz equation.
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the Radiation Condition at infinity for the high frequency helmholtz equation with source term a wave packet approach
Journal of Functional Analysis, 2005Co-Authors: Francois CastellaAbstract:Abstract We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter α > 0 . The high-frequency (or: semi-classical) parameter is ɛ > 0 . We let ɛ and α go to zero simultaneously. We assume that the zero energy is non-trapping for the underlying classical flow. We also assume that the classical trajectories starting from the origin satisfy a transversality Condition, a generic assumption. Under these assumptions, we prove that the solution u ɛ radiates in the outgoing direction, uniformly in ɛ . In particular, the function u ɛ , when conveniently rescaled at the scale ɛ close to the origin, is shown to converge towards the outgoing solution of the Helmholtz equation, with coefficients frozen at the origin. This provides a uniform version (in ɛ ) of the limiting absorption principle. Writing the resolvent of the Helmholtz equation as the integral in time of the associated semi-classical Schrodinger propagator, our analysis relies on the following tools: (i) for very large times, we prove and use a uniform version of the Egorov Theorem to estimate the time integral; (ii) for moderate times, we prove a uniform dispersive estimate that relies on a wave-packet approach, together with the above-mentioned transversality Condition; (iii) for small times, we prove that the semi-classical Schrodinger operator with variable coefficients has the same dispersive properties as in the constant coefficients case, uniformly in ɛ .
F. Dias - One of the best experts on this subject based on the ideXlab platform.
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On satisfying the Radiation Condition in free surface flows
Journal of Fluid Mechanics, 2009Co-Authors: F. DiasAbstract:Binder & Vanden-Broeck (2005) showed there are no subcritical or critical solutions satisfying the Radiation Condition for steady flows past a flat plate. By using a weakly nonlinear analysis, it is shown that such flows exist for a curved plate. Fully nonlinear solutions are computed by a boundary integral equation method, and new nonlinear solutions for supercritical and generalized critical flows past a curved plate are presented.
Sina Bahrami - One of the best experts on this subject based on the ideXlab platform.
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asymptotics with a positive cosmological constant iv the no incoming Radiation Condition
Physical Review D, 2019Co-Authors: Abhay Ashtekar, Sina BahramiAbstract:Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity. In the case with zero cosmological constant $\Lambda$, the gravitational Radiation emitted by such systems is described by the well established, 50+ year old framework due to Bondi, Sachs, Penrose and others. However, so far we do not have a satisfactory extension of this framework to include a \emph{positive} cosmological constant --or, more generally, the dark energy responsible for the accelerated expansion of the universe. In particular, we do not yet have an adequate gauge invariant characterization of gravitational waves in this context. As the next step in extending the Bondi et al framework to the $\Lambda >0$ case, in this paper we address the following questions: How do we impose the `no incoming Radiation' Condition for such isolated systems in a gauge invariant manner? What is the relevant past boundary where these Conditions should be imposed, i.e., what is the \emph{physically relevant} analog of past null infinity $\mathcal{I}^{-}_{0}$ used in the $\Lambda=0$ case? What is the symmetry group at this boundary? How is it related to the Bondi-Metzner-Sachs (BMS) group? What are the associated conserved charges? What happens in the $\Lambda \to 0$ limit? Do we systematically recover the Bondi-Sachs-Penrose structure at $\mathcal{I}^{-}_{0}$ of the $\Lambda=0$ theory, or do some differences persist even in the limit? We will find that while there are many close similarities, there are also some subtle but important differences from the asymptotically flat case. Interestingly, to analyze these issues one has to combine conceptual structures and mathematical techniques introduced by Bondi et al with those associated with \emph{quasi-local horizons}.
Ya Yan Lu - One of the best experts on this subject based on the ideXlab platform.
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an improved surface Radiation Condition for high frequency acoustic scattering problems
Computer Methods in Applied Mechanics and Engineering, 2006Co-Authors: Xavier Antoine, Marion Darbas, Ya Yan LuAbstract:A new artificial boundary Condition for two-dimensional acoustic scattering problems is constructed in this paper. It is designed from the principal symbol of the Dirichlet-to-Neumann map so that both the propagating and evanescent fields are properly modeled. In the high-frequency regime, the new artificial boundary Condition can be used as an on-surface Radiation Condition for efficient approximation of the wave field. The accuracy and efficiency of our method are demonstrated in numerical examples.
