Browsing by Author "Faria, Luiz M."

Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.
  • Thumbnail Image
    Item
    Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
    (2019) Pérez Arancibia, Carlos Andrés; Faria, Luiz M.; Turc, Catalin
  • No Thumbnail Available
    Item
    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.