A novel fast direct solver for 3D elastic inclusion problems with the isogeometric boundary element method

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.