Dublin Core
Title
Convolution quadrature methods for time domain acoustic wave propagation in layered media and composite materials
Subject
Convolution quadrature
Time domain acoustic scattering
Wave propagation
Boundary integral equations
Multiple traces formulation
Layered media scattering
Waveguides
620
Ingeniería
Description
Tesis (Master of Science in Engineering)--Pontificia Universidad Católica, 2022
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.
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.
Creator
Labarca Figueroa, Ignacio Javier
Date
2022-10-05T17:01:35Z
2022-10-05T17:01:35Z
2019
Contributor
Jerez Hanckes, Carlos F.
Pontificia Universidad Católica de Chile. Escuela de Ingeniería
Rights
acceso abierto
Format
xiii, 88 páginas
application/pdf
Language
en
Type
tesis de maestría
Identifier
10.7764/tesisUC/ING/64977
https://doi.org/10.7764/tesisUC/ING/64977
https://repositorio.uc.cl/handle/11534/64977