A fully discrete Calderón calculus for the two-dimensional elastic wave equation
A fully discrete Calderón calculus for the two-dimensional elastic wave equation
复制标题
二维弹性波方程的完全离散卡尔德隆微积分
DOI：
10.1016/j.camwa.2015.01.016
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
F. Sayas
中科院分区：
文献类型：
--
作者：
V. Domínguez;Tonatiuh Sánchez;F. Sayas
本文给出了平面可参数化光滑闭曲线上弹性波动方程的层势和边界积分算子的全离散化。该方法可以被理解为一个非协调的Petrov-Galerkin离散化，通过对称地组合两个交错网格上的元素，并使用环视求积公式，测试功能的一个非常精确的选择。与这项工作的声学对应物不同，弹性双层算子的内核包括周期性希尔伯特变换，需要特别选择混合参数。我们给出了这一事实的数学证明。最后，我们在一些频域和时域问题上测试了该方法，并证明了其对光滑开放弧的适用性。
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.