We present a novel fast direct solver to simulate 3D large scale elastic inclusion problems. The method combines the isogeometric analysis boundary element method (IGABEM) and the hierarchical off-diagonal low-rank (HODLR) matrix based on non-uniform rational B-splines (NURBS). Hence the 3D geometric surface can be accurately described by the bivariate NURBS basis functions. In order to solve the large scale problems, a stable accelerated algorithm is used to approximate the off-diagonal submatrices by low-rank matrices. Based on the accelerated algorithm, a hybrid approximation algorithm consisting of singular value decomposition (SVD) and adaptive cross approximation (ACA) is proposed to solve the 3D elastic inclusion problems. The validity and accuracy of the method are verified by testing the four methods. Among the numerical results obtained from the four methods, the method proposed in this paper uses less CPU time and storage space to obtain accurate results.

我们提出了一种新颖的快速直接求解器来模拟3D大规模弹性夹杂问题。该方法结合了等几何分析边界元方法（IGABEM）和基于非均匀有理B样条（NURBS）的分层非对角低秩（HODLR）矩阵。因此，可以通过二元NURBS基函数准确地描述3D几何表面。为了解决大规模问题，使用稳定的加速算法通过低秩矩阵近似非对角子矩阵。在加速算法的基础上，提出了一种由奇异值分解（SVD）和自适应交叉逼近（ACA）组成的混合逼近算法，以解决3D弹性夹杂问题。通过测试这四种方法，验证了该方法的有效性和准确性。