| Abstract | The development of a fast multipole method accelerated iterativesolution of the boundary element equations for large problems involving
hundreds of thousands elements for the Helmholtz equations in 3D is
described. The BEM requires several approximate computations (numerical
quadrature, approximations of the boundary shapes using elements) and
the convergence criterion for iterative computation. When accelerated
using the FMM, 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 used, choices of representations, and boundary
element integration consistent with these approximations are described.
A novel preconditioner for accelerating convergence, using a low
accuracy FMM accelerated solver as a right preconditioner is also
described. Results of the developed and tested solvers for boundary
value problems for the Helmholtz equations using the solver are
presented for the number of unknowns N <= 106 and product of wavenumber
k times domain size D, kD <= 200 and show good performance close to
theoretical expectations.
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