Hierarchical Adaptive Cross Approximation GMRES Technique for Solution of Acoustic Problems Using the Boundary Element Method

Abstract

In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. The applications presented include the problem of noise acting on a row of aircraft seats and problem of engine noise emanating from the Falcon aircraft. For the first example, the new RABEM is shown to be faster than the Fast Multipole Methods. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(N logN) for high frequency problems.