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) methods in conjunction with 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 utilized to transform the problem into a finite number of (complex) frequency-domain problems posed on the domains involving penetrable unbounded 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 Helmholtz boundary integral equation solver capable of handling complex wavenumbers with a large imaginary part. A high-order Nyström method based on Alpert quadrature rules is utilized here. A variety of numerical examples including wave propagation in open waveguides as well as scattering from multiply layered media, demonstrate the capabilities of the proposed approach.(CQ) methods [25,26], in particular, have effectively enabled the use of (complex) frequencydomain boundary integral equation (BIE) solvers to tackle a variety of wave propagation problems, by providing a stable procedure to discretize the associated convolution equations for the unknown time evolution of the relevant surface densities; see [33] for the mathematical foundations of the method, and [5,19] for details on the algorithmic implementation. In the case of the scalar wave equation with piecewise constant wavespeed, to which this paper is devoted to, approximate traces at discrete times are produced all at once from a finite sequence of independent Helmholtz problems that can be solved in parallel by means of BIE methods. Although this CQ-BIE approach has proven to be competitive to volume discretization methods in the context of obstacle scattering problems [3,4,34], its extension to problems involving unbounded material interfaces is severely hindered by the fact that standard BIE formulations require the knowledge of problem-specific Green functions to deal with the unboundedness of the material interfaces. These Green functions, however, are often unavailable (in terms of tractable mathematical expressions) or are given in terms of computationally expensive Sommerfeld integrals 1 [27,29,30].Recent advances on BIE methods for time-harmonic problems of scattering from unbounded material interfaces have led to the development of highly efficient solvers that completely bypass the use of problem-specific Green functions [10,12,13,24,30,37]. The windowed Green function (WGF) method, in particular, has successfully...

RESUMEN: La formación del paladar ocurre entre la quinta y undécima semana de vida intrauterina producto de la unión del paladar primario y secundario. Por otra parte, la formación del labio superior ocurre entre la quinta y sexta semana del desarrollo, y se configura en su parte media por la fusión de los procesos nasales mediales y lateralmente, a expensas de los procesos maxilares. La prevalencia de las fisuras labiales y/o fisura palatina varía según las distintas etnias, con cifras entre 0,7 hasta 1,1 casos por 1000 nacidos vivos. El objetivo de este trabajo fue realizar una revisión bibliográfica sobre aspectos epidemiológicos, mecanismos genéticos moleculares y ambientales que influyen en la ocurrencia de la fisura labial, fisura palatina y fisura labio palatina. La búsqueda bibliográfica se realizó en las bases de datos PUBMED, SCOPUS, SPRINGER, SCIENCEDIRECT utilizando los términos en inglés "cleft lip and palate", "cleft lip", "cleft palate" y "embriology". Entre los criterios de inclusión se consideraron estudios realizados en humanos y animales, publicados entre los años 2015 y 2021. La búsqueda arrojó un total de 407 trabajos, de los cuales tras un filtro por título y resumen quedaron un total de 38 artículos, en los cuales se realizó un análisis de texto completo para finalmente seleccionar 26 artículos que abarcan temas genéticos-moleculares, ambientales, epidemiológicos y sindrómicos. Además se incorporaron por búsqueda manual, 6 documentos asociados a libros de texto, y artículos científicos, sin considerar el criterio inclusión de tiempo. Dentro de esta revisión se describe la fuerte asociación entre las fisuras orales y las mutaciones de genes Msx1, sonic hedgehog, proteínas morfogenéticas óseas y factor de crecimiento fibroblástico durante la migración de las células de la cresta neural y la modelación y formación del paladar. La ausencia de ácido fólico durante el desarrollo del paladar y la presencia de hipoxia por exposición a humo, son los factores ambientales observados con mayor frecuencia en malformaciones orofaciales.

We study frequency domain acoustic scattering at a bounded, penetrable, and inhomogeneous obstacle Ω − ⊂ R d \Omega^{-}\subset\mathbb{R}^{d} , d = 2 , 3 d=2,3 . By defining constant reference coefficients, a representation formula for the pressure field is derived. It contains a volume integral operator, related to the one in the Lippmann–Schwinger equation. Besides, it features integral operators defined on ∂ Ω − \partial\Omega^{-} and closely related to boundary integral equations of single-trace formulations (STF) for transmission problems with piecewise constant coefficients. We show well-posedness of the continuous variational formulation and asymptotic convergence of Galerkin discretizations. Numerical experiments in 2D validate our expected convergence rates.

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain boundary integral formulation valid in two and three dimensions. Numerically, our two-dimensional non-conforming spatial discretization uses spectral elements based on second kind Chebyshev polynomials while a convolution quadrature scheme is performed in the complex frequency domain. Computational experiments reveal multistep and multistage convolution quadrature expected convergence results for a variety of complex domains.