Browsing by Author "Labarca Figueroa, Ignacio Javier"

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    Convolution quadrature methods for time domain acoustic wave propagation in layered media and composite materials
    (2019) Labarca Figueroa, Ignacio Javier; Jerez Hanckes, Carlos F.; Pontificia Universidad Católica de Chile. Escuela de Ingeniería
    We present a novel computational scheme to solve time domain acoustic scattering in two particular situations, using multistep and multistage Convolution Quadrature (CQ) methods for a time domain discretization. First, we study two dimensional layered media problems, i.e. scattering from unbounded penetrable interfaces. The proposed methodology relies on the Windowed Green Function method, which reduces a second-kind boundary integral equation to a bounded interface, introducing errors that decay superalgebraically as the window size increases. The boundary integral equation is then solved by a high-order Nystr¨om method based on Alpert’s quadrature rule. A variety of numerical examples, including wave propagation on open waveguides, demonstrate the capabilities of the proposed methodology. The second problem that we study is the one of scattering over composite materials in two dimensions, i.e. penetrable obstacles displaying triple points are found. We rely on a Multiple Traces Formulation (MTF), discretized using a spectral Galerkin method based on second kind Chebyshev polynomials. Although spectral convergence in space is not expected due to the presence of Lipschitz domains, the method remains as a high-order choice to solve the MTF, resulting in an efficient combination with a CQ scheme. Numerical examples are shown, with different configurations of geometries and parameters.