TY - JOUR

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

AU - Domínguez, Víctor

AU - Sánchez-Vizuet, Tonatiuh

AU - Sayas, Francisco Javier

N1 - Funding Information:
The second and third authors were partially supported by NSF grant DMS 1216356 .
Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.

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

UR - http://www.scopus.com/inward/record.url?scp=84924785877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84924785877&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2015.01.016

DO - 10.1016/j.camwa.2015.01.016

M3 - Article

AN - SCOPUS:84924785877

SN - 0898-1221

VL - 69

SP - 620

EP - 635

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 7

ER -