TY - JOUR
T1 - A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation
JF - The Journal of the Acoustical Society of America
Y1 - 2009
A1 - Gumerov, Nail A.
A1 - Duraiswami, Ramani
KW - acoustic wave scattering
KW - boundary-elements methods
KW - boundary-value problems
KW - Helmholtz equations
KW - iterative methods
AB - The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001≲kD≲500 are presented and shown to perform close to theoretical expectations.
VL - 125
UR - http://link.aip.org/link/?JAS/125/191/1
CP - 1
M3 - 10.1121/1.3021297
ER -