Convolution quadrature methods for time domain acoustic wave propagation in layered media and composite materials
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Date
2019
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Abstract
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.
Description
Tesis (Master of Science in Engineering)--Pontificia Universidad Católica, 2022
Keywords
Convolution quadrature, Time domain acoustic scattering, Wave propagation, Boundary integral equations, Multiple traces formulation, Layered media scattering, Waveguides