Browsing by Author "Ramaciotti, Pedro"

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    ABOUT SOME BOUNDARY INTEGRAL OPERATORS ON THE UNIT DISK RELATED TO THE LAPLACE EQUATION
    (2017) Ramaciotti, Pedro; Nedelec, Jean-Claude
    We introduce four integral operators related to the Laplace equation in three dimensions on the circular unit disk. Two of them are related to the weakly singular operator and the other two are related to the hypersingular operator. We provide series expressions for their kernels using proposed bases for the Sobolev trace spaces involved in the symmetric Dirichlet and antisymmetric Neumann Laplace screen problems on the disk. We then provide explicit and closed variational forms suitable for boundary element computations. We develop numerical computation schemes for the associated Galerkin matrices and test their use as preconditioners for the matrices arising from the integral equations associated with the solution of the mentioned screen problems.
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    Fast multipole boundary element method for the Laplace equation in a locally perturbed half-plane with a Robin boundary condition
    (2012) Perez-Arancibia, Carlos; Ramaciotti, Pedro; Hein, Ricardo; Duran, Mario
    A fast multipole boundary element method (FM-BEM) for solving large-scale potential problems ruled by the Laplace equation in a locally-perturbed 2-D half-plane with a Robin boundary condition is developed in this paper. These problems arise in a wide gamut of applications, being the most relevant one the scattering of water-waves by floating and submerged bodies in water of infinite depth. The method is based on a multipole expansion of an explicit representation of the associated Green's function, which depends on a combination of complex-valued exponential integrals and elementary functions. The resulting method exhibits a computational performance and memory requirements similar to the classic FM-BEM for full-plane potential problems. Numerical examples demonstrate the accuracy and efficiency of the method. (C) 2012 Elsevier B.V. All rights reserved.