Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach

This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the problem of engine noise emanating from the Falcon aircraft is presented. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(NlogN) for high frequency problems.