Browsing by Author "Perez-Arancibia, Carlos"

Now showing 1 - 7 of 7
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    Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
    (2019) Labarca, Ignacio; Faria, Luiz M.; Perez-Arancibia, Carlos
    This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two spatial dimensions. The proposed methodology relies on convolution quadrature (CQ) schemes and the recently introduced windowed Green function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is used to transform the problem into a finite number of (complex) frequency-domain problems posed, in our case, on the domains containing unbounded penetrable interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method-which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Nystrom or boundary element Helmholtz integral equation solvers capable of handling complex wavenumbers with large imaginary part. A high-order Nystrom method based on Alpert's quadrature rules is used here. A variety of CQ schemes and numerical examples, including wave propagation in open waveguides as well as scattering from multiple layered media, demonstrate the capabilities of the proposed approach.
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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.
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    General-purpose kernel regularization of boundary integral equations via density interpolation
    (2021) Faria, Luiz M.; Perez-Arancibia, Carlos; Bonnet, Marc
    This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderon calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed technique relies on interpolating the density function around the kernel singularity in terms of solutions of the underlying homogeneous PDE, so as to recast singular and nearly singular integrals in terms of bounded (or more regular) integrands. We present here a simple interpolation strategy which, unlike previous approaches, does not entail explicit computation of high-order derivatives of the density function along the surface. Furthermore, the proposed approach is kernel-and dimension-independent in the sense that the sought density interpolant is constructed as a linear combination of point-source fields, given by the same Green's function used in the integral equation formulation, thus making the procedure applicable, in principle, to any PDE with known Green's function. For the sake of definiteness, we focus here on Nystr'om methods for the (scalar) Laplace and Helmholtz equations and the (vector) elastostatic and time-harmonic elastodynamic equations. The method's accuracy, flexibility, efficiency, and compatibility with fast solvers are demonstrated by means of a variety of large-scale three-dimensional numerical examples. (C) 2021 Elsevier B.V. All rights reserved.
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    On the regularization of Cauchy-type integral operators via the density interpolation method and applications
    (2021) Gomez, Vicente; Perez-Arancibia, Carlos
    This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on the Cauchy formula, the Cauchy-Goursat theorem, and on-curve Taylor interpolations of the input density, the proposed methodology allows to recast the Cauchy and associated integral operators as smooth contour integrals. As such, they can be accurately evaluated everywhere in the complex plane-including at problematic points near and on the contour-by means of elementary quadrature rules. Applications of the technique to the evaluation of the Laplace layer potentials and related integral operators, as well as to the computation conformal mappings, are examined in detail. The former application, in particular, amounts to a significant improvement over the recently introduced harmonic density interpolation method. Spectrally accurate discretization approaches for smooth and piecewise smooth contours are presented. A variety of numerical examples, including the solution of weakly singular and hypersingular Laplace boundary integral equations, and the evaluation of challenging conformal mappings, demonstrate the effectiveness and accuracy of the density interpolation method in this context.
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    Sideways adiabaticity: beyond ray optics for slowly varying metasurfaces
    (2018) Perez-Arancibia, Carlos; Pestourie, Raphael; Johnson, Steven G.
    Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are typically modeled by an approximation akin to ray optics: the reflection or transmission of an incident wave at each point of the surface is computed as if the surface were "locally uniform," and then the total field is obtained by summing all of these local scattered fields via a Huygens principle. (Similar approximations are found in scalar diffraction theory and in ray optics for curved surfaces.) In this paper, we develop a precise theory of such approximations for variable-impedance surfaces. Not only do we obtain a type of adiabatic theorem showing that the "zeroth-order" locally uniform approximation converges in the limit as the surface varies more and more slowly, including a way to quantify the rate of convergence, but we also obtain an infinite series of higher-order corrections. These corrections, which can be computed to any desired order by performing integral operations on the surface fields, allow rapidly varying surfaces to be modeled with arbitrary accuracy, and also allow one to validate designs based on the zeroth-order approximation (which is often surprisingly accurate) without resorting to expensive brute-force Maxwell solvers. We show that our formulation works arbitrarily close to the surface, and can even compute coupling to guided modes, whereas in the far-field limit our zeroth-order result simplifies to an expression similar to what has been used by other authors. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
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    Windowed Green function method for wave scattering by periodic arrays of 2D obstacles
    (2023) Strauszer-Caussade, Thomas; Faria, Luiz M.; Fernandez-Lado, Agustin; Perez-Arancibia, Carlos
    This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction-used to properly impose the Rayleigh radiation condition-yield a robust second-kind BIE that produces superalgebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh-Wood anomalies. The corrected windowed BIE can be discretized by means of off-the-shelf Nystrom and boundary element methods, and it leads to linear systems suitable for iterative linear algebra solvers as well as standard fast matrix-vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.
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    Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems
    (2022) Arrieta, Rodrigo; Perez-Arancibia, Carlos
    This article presents a second-kind surface integral equation (SIE) method for the numerical solution of frequency-domain electromagnetic (EM) scattering problems by locally perturbed layered media in three spatial dimensions. Unlike standard approaches, the proposed methodology does not involve the use of layer Green functions (LGFs). It instead leverages an indirect Muller formulation in terms of free-space Green functions that entails integration over the entire unbounded penetrable boundary. The integral equation domain is effectively reduced to a small-area surface by means of the windowed Green function (WGF) method, which exhibits high-order convergence as the size of the truncated surface increases. The resulting (second-kind) windowed integral equation is then numerically solved by means of the standard Galerkin method of moments (MoM) using the Rao-Wilton-Glisson (RWG) basis functions. The methodology is validated by comparison with the Mie series and Sommerfeld integral exact solutions as well as against an LGF-based MoM. Challenging examples including realistic structures relevant to the design of plasmonic solar cells and all-dielectric metasurfaces demonstrate the applicability, efficiency, and accuracy of the proposed methodology.