A fully discrete Calderón calculus for the two-dimensional elastic wave equation

Date

2015

Authors

Sánchez Vizuet, Tonatiuh
Sayas, Francisco Javier

Director

Publisher

Elsevier
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

Impacto
No disponible en Scopus

Abstract

In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov–Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.

Description

Keywords

Time domain boundary integral equations, Elastic wave scattering, Calderón calculus

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

Faculty/School

Degree

Doctorate program

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© 2015 Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0.

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