Browsing by Author "Nedelec, JC"

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    Numerical stability in the calculation of eigenfrequencies using integral equations
    (ELSEVIER SCIENCE BV, 2001) Duran, M; Miguez, M; Nedelec, JC
    We comment on a phenomenon of instability that appears while computing eigenfrequencies using the integral equation framework. More precisely, it is currently known that the real symmetric matrices are well, and sometimes the best, adapted to numerical treatment. However, we show that this is not the case, if we wish to determine with high accuracy the spectrum of elliptic, and other related operators, using integral representations. (C) 2001 Elsevier Science B.V. All rights reserved.
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    The Helmholtz equation with impedance in a half-plane
    (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2005) Duran, M; Muga, I; Nedelec, JC
    This Note gives answers to the uniqueness and existence questions for solutions of the Helmholtz equation in an half-plane with an impedance or mixed boundary condition. We deal with unbounded domains which boundaries are unbounded too. The radiation conditions are different from the ones that we found in an usual exterior problem due to the appearance of surface waves. We first compute and study the half-plane Green's function to see how the solutions behave at infinity, and second obtain integral representation for these solutions. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.
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    The Helmholtz equation with impedance in a half-space
    (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2005) Duran, M; Muga, I; Nedelec, JC
    In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space R-+(3) with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data.