Nyström discretizations of boundary integral equations for the solution of 2D elastic scattering problems
Consultable a partir de
2025-10-01
Fecha
2024Versión
Acceso embargado / Sarbidea bahitua dago
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
//PID2022-136441NB-I00
Impacto
|
10.1016/j.cam.2023.115622
Resumen
We present three high-order Nyström discretization strategies of various boundary
integral equation formulations of the impenetrable time-harmonic Navier equations
in two dimensions. One class of such formulations is based on the four classical
Boundary Integral Operators (BIOs) associated with the Green’s function of the Navier
operator. We consider two types of Nyström discretizations of th ...
[++]
We present three high-order Nyström discretization strategies of various boundary
integral equation formulations of the impenetrable time-harmonic Navier equations
in two dimensions. One class of such formulations is based on the four classical
Boundary Integral Operators (BIOs) associated with the Green’s function of the Navier
operator. We consider two types of Nyström discretizations of these operators, one that
relies on Kussmaul–Martensen logarithmic splittings (Chapko et al., 2000; Domínguez
and Turc, 2000), and the other on Alpert quadratures (Alpert, 1999). In addition, we
consider an alternative formulation of Navier scattering problems based on Helmholtz
decompositions of the elastic fields (Dong et al., 2021), which can be solved via a
system of boundary integral equations that feature integral operators associated with
the Helmholtz equation. Owing to the fact that some of the BIOs that are featured in
those formulations are non-standard, we use Quadrature by Expansion (QBX) methods
for their high order Nyström discretization. Alternatively, we use Maue integration by
parts techniques to recast those non-standard operators in terms of single and double
layer Helmholtz BIOs whose Nyström discretizations is amenable to the Kussmaul–
Martensen methodology. We present a variety of numerical results concerning the high
order accuracy that our Nyström discretization elastic scattering solvers achieve for both
smooth and Lipschitz boundaries. We also present extensive comparisons regarding the
iterative behavior of solvers based on different integral equations in the high frequency
regime. Finally, we illustrate how some of the Nyström discretizations we considered
can be incorporated seamlessly into the Convolution Quadrature (CQ) methodology to
deliver high-order solutions of the time domain elastic scattering problems. [--]
Materias
Time-domain and time-harmonic Navier scattering problems,
Boundary integral equations,
Nyström discretizations,
Preconditioners
Editor
Elsevier
Publicado en
Journal of Computational and Applied Mathematics 440 (2024) 115622
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
Catalin Turc gratefully acknowledges support from NSF through contract DMS-1908602. Víctor Domínguez is partially supported by projects “Adquisición de conocimiento
minería de datos, funciones especiales
métodos numéricos avanzados” from Universidad Pública de Navarra, Spain and “Técnicas innovadoras para la resolución de problemas evolutivos”, ref. PID2022-136441NB-I00 from Ministerio de Ciencia e Innovación, Gobierno de España, Spain .