二维动力孔隙弹性问题的高精度超奇异边界积分方程方法
An accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions
摘要：
本文用边界积分方程法求解二维动力多孔弹性外Neumann边值问题。本文的主要贡献包括两个方面：提出了一种新的正则化边界积分方程，以及强奇异和超奇异边界积分算子的新的正则化形式。首先，利用双层算子的谱性质和相应的多孔弹性Calderón关系，提出了一种新的低GMRES迭代积分方程，其特征值远离零和无穷大。其次，借助Günter导数，将强奇异和超奇异积分算子转化为弱奇异算子和切向导数的组合.所提出的方法的精度和效率通过几个数值例子证明。
英文摘要：
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.
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