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

Víctor Domínguez; Tonatiuh Sánchez-Vizuet; Francisco Javier Sayas

doi:10.1016/j.camwa.2015.01.016

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

Víctor Domínguez, Tonatiuh Sánchez-Vizuet, Francisco Javier Sayas

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	620-635
Number of pages	16
Journal	Computers and Mathematics with Applications
Volume	69
Issue number	7
DOIs	https://doi.org/10.1016/j.camwa.2015.01.016
State	Published - Apr 1 2015
Externally published	Yes

Keywords

Calderón calculus
Elastic wave scattering
Time domain boundary integral equations

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2015.01.016

Cite this

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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.",

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T1 - A fully discrete Calderón calculus for the two-dimensional elastic wave equation

AU - Domínguez, Víctor

AU - Sánchez-Vizuet, Tonatiuh

AU - Sayas, Francisco Javier

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

AB - 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.

KW - Calderón calculus

KW - Elastic wave scattering

KW - Time domain boundary integral equations

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

Abstract

Keywords

ASJC Scopus subject areas

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