Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver

Rapid calculation of large-scale acoustic scattering from complex targets is the basis of many acoustic technologies. The key issue is to efficiently solve the dense and ill-conditioned linear equations caused by semi -analytical boundary collocation method. This article aims to establish a dual-level fast direct solver to replace the GMRES for solving such a large-scale dense linear system. The core idea of the dual-level fast direct solver is to construct a sparse approximate inverse matrix to indirectly approximate the solution of linear equations. The solution process consists of the smoothing process and the correction process. Therefore, the dual-level fast direct solver only needs to solve a small-scale coarse-mesh matrix and a series of small-scale least squares problems defined on fine mesh. The drawback that the GMRES cannot efficiently solve large-scale dense linear system is overcome. Several practical engineering problems are analyzed by the dual-level fast direct solver, such as the acoustic scattering from an A320 aircraft and acoustic scattering from a human head.