| Abstract | High frequency simulations of acoustics are among the most expensive problems to simulate. Inpractice 6 to 10 points per wavelength are required. Since the wavenumber k is inversely proportional
to wavelength, if a numerical method is a surface based method (such as the BEM), then problem
size scales as O(k2D2), where D is the size of the domain. Dense matrices appear and typical iter-
ative solution can be achieved for O(k4D4) memory and O(k4D4) per iteration cost. We employ an
algorithm based on the fast multipole method (FMM) using coaxial and diagonal translation operators
based on the frequency of simulation to reduce the memory requirements and per iteration cost to
O(k2D2 log kD) for larger kD (kD ~250). The number of iterations needed depend upon the condition
of the matrix, and preconditioning chosen. Preconditioned Krylov methods such as the flexible gen-
eralized minimum residual method (FGMRES), with preconditioning based upon a lower accuracy
FMM, usually ensure a convergent iteration. Example calculations are presented.
|
