Browsing by Author "Jerez Hanckes, Carlos"

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    Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides
    (GLOBAL SCIENCE PRESS, 2012) Jerez Hanckes, Carlos; Nedelec, Jean Claude
    We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If x = (x(1), x(2), x(3)) is an element of R-3, with x(3) denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x(3) | > parallel to x parallel to(gamma), for gamma is an element of (1/4, 1/2) and x large. For |x(3)| < parallel to x parallel to(gamma). and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.
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    EXPLICIT VARIATIONAL FORMS FOR THE INVERSES OF INTEGRAL LOGARITHMIC OPERATORS OVER AN INTERVAL
    (SIAM PUBLICATIONS, 2012) Jerez Hanckes, Carlos; Nedelec, Jean Claude
    We introduce explicit and exact variational formulations for the weakly singular and hypersingular operators over an open interval as well as for their corresponding inverses. Contrary to the case of a closed curve, these operators no longer map fractional Sobolev spaces in a dual fashion but degenerate into different subspaces depending on their extensibility by zero. We show that an average and jump decomposition leads to precise coercivity results and characterize the mismatch occurring between associated functional spaces. Through this setting, we naturally define Calderon-type identities with their potential use as preconditioners. Moreover, we provide an interesting relation between the logarithmic operators and one-dimensional Laplace Dirichlet and Neumann problems. This work is a detailed and extended version of the article "Variational Forms for the Inverses of Integral Logarithmic Operators over an Interval" by Jerez-Hanckes and Nedelec [C. R. Acad. Sci. Paris Ser. I, 349 (2011), pp. 547-552].
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    Variational forms for the inverses of integral logarithmic operators over an interval
    (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2011) Jerez Hanckes, Carlos; Nedelec, Jean Claude
    We present explicit and exact variational formulations for the weakly singular and hypersingular operators over an interval as well as for their corresponding inverses. By decomposing the solutions in symmetric and antisymmetric parts, we precisely characterize the associated Sobolev spaces. Moreover, we are able to define novel Calderon-type identities in each case. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.