论文标题
在二维中的动态孔隙弹性的准确的超细胞边界积分方程方法
An accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions
论文作者
论文摘要
本文与边界积分方程方法有关，用于解决二维中动态弹性性的外部Neumann边界值问题。这项工作的主要贡献包括两个ASPESCTS：新型的正规边界积分方程的建议，以及强烈和超细性边界积分算子的新正规配方的呈现。首先，转向双层操作员的光谱特性以及孔弹性的相应calderón关系，我们提出了新型的低敏化积分方程，其特征值远离零和无限。其次，在Günter衍生物的帮助下，我们将强烈的和超单明的积分算子重新制定为弱小操作员和切向衍生物的组合。提出方法的准确性和效率通过几个数值示例证明。
This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the proposal of a novel regularized boundary integral equation, and the presentation of new regularized formulations of the strongly-singular and hyper-singular boundary integral operators. Firstly, turning to the spectral properties of the double-layer operator and the corresponding Calderón relation of the poroelasticity, we propose the novel low-GMRES-iteration integral equation whose eigenvalues are bounded away from zero and infinity. Secondly, with the help of the Günter derivatives, we reformulate the strongly-singular and hyper-singular integral operators into combinations of the weakly-singular operators and the tangential derivatives. The accuracy and efficiency of the proposed methodology are demonstrated through several numerical examples.
