论文标题
关于动态弹性性的超细胞边界积分方程方法：三维情况
On the hyper-singular boundary integral equation methods for dynamic poroelasticity: three dimensional case
论文作者
论文摘要
在我们以前的作品中[Siam J. Sci。计算。 43（3）（2021）B784-B810]，已经开发了一种精确的超细胞边界积分方程方法，用于在二维中动态孔隙弹性。这项工作致力于研究Neumann边界条件的更复杂和困难的三维问题，并采用了直接和间接方法来构建联合边界积分方程。强烈的和超细的整体运算符被重新构成弱小的积分运算符和切向衍生操作员的组成，这使我们能够以简单的方式证明与毛弹性层势和边界积分运算符相关的跳跃关系。依靠强度较大的操作员的两个研究的光谱特性，这表明相应的特征值积聚在三个点上，其值仅取决于两个laméstonstants，以及普通弹性的calderón关系的光谱特性，我们提出了低温元素列表列表 - 列表列表 - 列表 - 列表 - 列表 - 列表的正规化方程。提出了数值示例，以证明通过基于Chebyshev的矩形偏置求解器来证明所提出的方法的准确性和效率。
In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has been developed. This work is devoted to studying the more complex and difficult three-dimensional problems with Neumann boundary condition and both the direct and indirect methods are adopted to construct combined boundary integral equations. The strongly-singular and hyper-singular integral operators are reformulated into compositions of weakly-singular integral operators and tangential-derivative operators, which allow us to prove the jump relations associated with the poroelastic layer potentials and boundary integral operators in a simple manner. Relying on both the investigated spectral properties of the strongly-singular operators, which indicate that the corresponding eigenvalues accumulate at three points whose values are only dependent on two Lamé constants, and the spectral properties of the Calderón relations of the poroelasticity, we propose low-GMRES-iteration regularized integral equations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed methodology by means of a Chebyshev-based rectangular-polar solver.
