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.
High-order kernel regularization of singular and hypersingular Helmholtz boundary integral operators
POEMS, CNRS, Inria, ENSTA Paris, Institut Polytechnique de Paris（POEMS，CNRS，Inria，ENSTA巴黎，巴黎理工学院）；Department of Applied Mathematics, University of Twente（特温特大学应用数学系）；Department of Mathematics, Farmingdale State College, SUNY（萨福克大学法明代尔州立学院数学系）
